Nabble - Gnu - GLPK

tag:old.nabble.com,2006:forum-1652 Nabble - Gnu - GLPK 2009-12-01T10:03:00Z The GLPK (GNU Linear Programming Kit) package is intended for solving large-scale linear programming (LP), mixed integer programming (MIP), and other related problems. It is a set of routines written in ANSI C and organized in the form of a callable library. Gnu - GLPK home is <a href="http://www.gnu.org/software/glpk/glpk.html" target="_top" rel="nofollow">here</a>. tag:old.nabble.com,2006:post-26596429 Re: Linear Programming Relaxation 2009-12-01T10:03:00Z 2009-12-01T10:03:00Z Michael Hennebry On Tue, 1 Dec 2009, RC Loh wrote: <br><br>> Thank you for your suggestion. I am currently reading up on SOS1 and see whether it is applicable to my problem. <br><br>It is. <br><br>> According to Andrew, the SOS1 is implemented by a version of Simplex Method. <br>> <br>> Then what is the difference between using SOS1 with the Simplex Method compared to using Integer Programming? <br>> <br>> Integer Programming is also using the Simplex Method, isn't it? <br><br>Here be much conflation of problem type and solution method. <br><br>Integer programming is the solving of optimization problems <br>all of whose variables are required to be integers. <br>Mixed integer programming allows some variables to be real. <br>In either case, a simplex method might or might not be used. <br><br>SOS1 is a type of constraint. <br>It makes the feasible set non-convex. <br>Simplex methods find local optima. <br>That is global for a minimization problem <br>with a convex (e.g. linear) objective function. <br>It might not be good enough for a problem with an SOS constraint. <br><br>-- <br>Michael   <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26596429&i=0" target="_top" rel="nofollow">hennebry@...</a> <br>"Pessimist: The glass is half empty. <br>Optimist:   The glass is half full. <br>Engineer:   The glass is twice as big as it needs to be."<br />_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26596429&i=1" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26593661 Re: Linear Programming Relaxation 2009-12-01T07:24:30Z 2009-12-01T07:24:30Z Jeffrey Kantor On Tue, Dec 1, 2009 at 5:41 AM, RC Loh <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26593661&i=0" target="_top" rel="nofollow">rc_loh@...</a>> wrote: <div class='shrinkable-quote'><br>> Hi Andrew, Jeffrey, <br>> <br>> Thank you for your suggestion. I am currently reading up on SOS1 and see <br>> whether it is applicable to my problem. <br>> <br>> However, I have another question to clarify. <br>> <br>> According to Andrew, the SOS1 is implemented by a version of Simplex Method. <br>> <br>> Then what is the difference between using SOS1 with the Simplex Method <br>> compared to using Integer Programming? <br>> <br>> Integer Programming is also using the Simplex Method, isn't it? </div><br>Yes and No.  Integer programming typically involves the iterative <br>addition of constraints that eventually force the solution of a linear <br>programming problem to have integer values where desired. You <br>generally need to solve many linear programming problems in the course <br>of finding a solution to an MIP problem. <br><br>The particular method you use to solve the LP's is therefore a choice <br>-- which can be a simplex method.  You could use an interior point <br>method, so you could do integer programming without invoking a simplex <br>routine. <br><div class='shrinkable-quote'><br>> <br>> Rdgs, <br>> Paul <br>> <br>> ________________________________ <br>> From: Andrew Makhorin <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26593661&i=1" target="_top" rel="nofollow">mao@...</a>> <br>> To: <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26593661&i=2" target="_top" rel="nofollow">rc_loh@...</a> <br>> Cc: <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26593661&i=3" target="_top" rel="nofollow">help-glpk@...</a> <br>> Sent: Tuesday, 1 December 2009 5:34:27 <br>> Subject: Re: [Help-glpk] Linear Programming Relaxation <br>> <br>>>> What I am trying to obtain is that though using LPR, the solution <br>>>> is bounded, but the solution does not satisfy what I need which is <br>>>> "x1+x2<=1" which means that "x1" and "x2" cannot co-exist together in <br>>>> a solution. <br>>> <br>>> In mathematics "x1+x2<=1" does not mean "that x1 and x2 cannot co-exist <br>>> together in a solution"; it means that the sum of x1 and x2 is not <br>>> greater than 1. The constraint you need is "NOT x1 OR NOT x2"; this <br>>> constraint is *not* equivalent to "x1+x2<=1" until x1 and x2 are <br>>> restricted to be binary, and being non-convex this constraint cannot be <br>>> modeled within linear program (LP). If you restrict some variables to <br>>> be binary, you get integer program (MIP), not LP. <br>> <br>> I would like to add that there exists a version of the simplex method <br>> (which is not implemented in glpk), where you can declare a set of <br>> variables {x1, x2, ..., xk} to be so called Special Ordered Set of <br>> Type 1 (SOS1 for brevity). SOS1 means that at most one of its variables <br>> can be basic while all its other variables must be non-basic. Assuming <br>> that all variables are non-negative, i.e. xj >= 0, SOS1 then means that <br>> at most one of its variables can take non-zero value while values of its <br>> other variables must be zero. Processing SOS1 constraints can be easily <br>> embedded into the simplex method: if some SOS1 variable is basic, <br>> a non-basic variable from the same SOS1 must not be chosen to enter the <br>> basis. However, in general case such version of the simplex method can <br>> find only a local optimum, because SOS1 constraints are non-convex. <br>> <br>> <br>> ________________________________ <br>> Get your new Email address! <br>> Grab the Email name you've always wanted before someone else does! </div><br><br>_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26593661&i=4" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26592346 Re: Linear Programming Relaxation 2009-12-01T06:04:58Z 2009-12-01T06:04:58Z Jeffrey Kantor You might try this reference: <br><br>Smoothed analysis of algorithms: Why the simplex algorithm usually <br>takes polynomial time - <br>DA Spielman, SH Teng - Journal of the ACM (JACM), 2004 - portal.acm.org <br><br>available here: <a href="http://arxiv.org/pdf/cs/0111050" target="_top" rel="nofollow">http://arxiv.org/pdf/cs/0111050</a>   The introduction to <br>this paper gives an outstanding discussion of the issues of complexity <br>in the simplex method.  The body of the paper is very dense, but the <br>introduction is well worth reading for anyone interested in simplex <br>methods. <br><br>Jeff <br><br><br><br>On Tue, Dec 1, 2009 at 5:32 AM, RC Loh <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26592346&i=0" target="_top" rel="nofollow">rc_loh@...</a>> wrote: <div class='shrinkable-quote'><br>> Hi Ali, <br>> <br>> Thank you for your response. <br>> <br>> I was trying to find in the Internet under which conditions did the Simplex <br>> Method runs in polynomial time but I could not find anything. <br>> <br>> Can you direct me to some papers or web site that indicate under which <br>> conditions will the Simplex Method runs in polynomial time? <br>> <br>> Thank you. <br>> <br>> Rdgs, <br>> Paul <br>> <br>> ________________________________ <br>> From: Ali Baharev <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26592346&i=1" target="_top" rel="nofollow">ali.baharev@...</a>> <br>> To: RC Loh <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26592346&i=2" target="_top" rel="nofollow">rc_loh@...</a>> <br>> Cc: <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26592346&i=3" target="_top" rel="nofollow">help-glpk@...</a> <br>> Sent: Monday, 30 November 2009 7:50:47 <br>> Subject: Re: [Help-glpk] Linear Programming Relaxation <br>> <br>> Hi, <br>> <br>>> However, when I did the LPR, "x1" and "x2" can become "0.5". Though it <br>>> still <br>>> satisfies the constraint "x1+x2<=1", but that is NOT what I want. <br>> <br>> Please re-read Andrew's e-mail: <br>> <br>>> LP relaxation is just an LP problem, where all variables are allowed <br>>> to take any *continuous* values, if only they are satisfied to all LP <br>>> constraints. You require that x1 + x2 <= 1 but do not require that <br>>> x1 and x2 are integer-valued, so why do you surprise that you get <br>>> x1 = x2 = 0.5? Aren't these values satisfy to x1 + x2 <= 1? <br>> <br>> Please answer his questions. <br>> <br>> You have no choice but to declare those variables binary in order to <br>> achieve what you want. <br>> <br>>> And I understand that LP runs in exponential time, however, LPR can run in <br>>> polynomial time. <br>> <br>> Correction: the simplex method shows exponential complexity in the <br>> worst case. In practice, it runs in polynomial time. This is <br>> theoretically proven (under certain conditions). <br>> <br>> Have you actually faced performance problems with your problems? <br>> <br>> Good luck anyhow, <br>> <br>> Ali <br>> <br>> ________________________________ <br>> New Email names for you! <br>> Get the Email name you've always wanted on the new @ymail and @rocketmail. <br>> Hurry before someone else does! <br>> _______________________________________________ <br>> Help-glpk mailing list <br>> <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26592346&i=4" target="_top" rel="nofollow">Help-glpk@...</a> <br>> <a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br>> <br>> </div><br><br>_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26592346&i=5" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26589801 Re: Linear Programming Relaxation 2009-12-01T02:41:32Z 2009-12-01T02:41:32Z Paul Loh <html><head></head><body><div style="font-family:arial, helvetica, sans-serif;font-size:14pt"><DIV>Hi Andrew, Jeffrey,</DIV> <DIV> </DIV> <DIV>Thank you for your suggestion. I am currently reading up on SOS1 and see whether it is applicable to my problem.</DIV> <DIV> </DIV> <DIV>However, I have another question to clarify. </DIV> <DIV> </DIV> <DIV>According to Andrew, the SOS1 is implemented by a version of Simplex Method. </DIV> <DIV> </DIV> <DIV>Then what is the difference between using SOS1 with the Simplex Method compared to using Integer Programming? </DIV> <DIV> </DIV> <DIV>Integer Programming is also using the Simplex Method, isn't it?</DIV> <DIV> </DIV> <DIV>Rdgs,</DIV> <DIV>Paul</DIV> <DIV><BR> </DIV> <DIV style="FONT-FAMILY: arial, helvetica, sans-serif; FONT-SIZE: 14pt"><BR> <DIV style="FONT-FAMILY: arial, helvetica, sans-serif; FONT-SIZE: 13px"><FONT size=2 face=Tahoma> <HR SIZE=1> <B><SPAN style="FONT-WEIGHT: bold">From:</SPAN></B> Andrew Makhorin <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26589801&i=0" target="_top" rel="nofollow">mao@...</a>><BR><B><SPAN style="FONT-WEIGHT: bold">To:</SPAN></B> <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26589801&i=1" target="_top" rel="nofollow">rc_loh@...</a><BR><B><SPAN style="FONT-WEIGHT: bold">Cc:</SPAN></B> <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26589801&i=2" target="_top" rel="nofollow">help-glpk@...</a><BR><B><SPAN style="FONT-WEIGHT: bold">Sent:</SPAN></B> Tuesday, 1 December 2009 5:34:27<BR><B><SPAN style="FONT-WEIGHT: bold">Subject:</SPAN></B> Re: [Help-glpk] Linear Programming Relaxation<BR></FONT><div class='shrinkable-quote'><BR>>> What I am trying to obtain is that though using LPR, the solution<BR>>> is bounded, but the solution does not satisfy what I need which is<BR>>> "x1+x2<=1" which means that "x1" and "x2" cannot co-exist together in<BR>>> a solution.<BR>> <BR>> In mathematics "x1+x2<=1" does not mean "that x1 and x2 cannot co-exist<BR>> together in a solution"; it means that the sum of x1 and x2 is not<BR>> greater than 1. The constraint you need is "NOT x1 OR NOT x2"; this<BR>> constraint is *not* equivalent to "x1+x2<=1" until x1 and x2 are<BR>> restricted to be binary, and being non-convex this constraint cannot be<BR>> modeled within linear program (LP). If you restrict some variables to<BR>> be binary, you get integer program (MIP), not LP.</div><BR>I would like to add that there exists a version of the simplex method<BR>(which is not implemented in glpk), where you can declare a set of<BR>variables {x1, x2, ..., xk} to be so called Special Ordered Set of<BR>Type 1 (SOS1 for brevity). SOS1 means that at most one of its variables<BR>can be basic while all its other variables must be non-basic. Assuming<BR>that all variables are non-negative, i.e. xj >= 0, SOS1 then means that<BR>at most one of its variables can take non-zero value while values of its<BR>other variables must be zero. Processing SOS1 constraints can be easily<BR>embedded into the simplex method: if some SOS1 variable is basic,<BR>a non-basic variable from the same SOS1 must not be chosen to enter the<BR>basis. However, in general case such version of the simplex method can<BR>find only a local optimum, because SOS1 constraints are non-convex.<BR><BR></DIV></DIV></div><br> <hr size=1> <a href="http://sg.rd.yahoo.com/sg/mail/domainchoice/mail/signature/*http://mail.promotions.yahoo.com/newdomains/sg/" target="_top" rel="nofollow"> Get your new Email address! </a> <br> Grab the Email name you've always wanted before someone else does!</body></html><br />_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26589801&i=3" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26589701 Re: Linear Programming Relaxation 2009-12-01T02:32:33Z 2009-12-01T02:32:33Z Paul Loh <html><head></head><body><div style="font-family:arial, helvetica, sans-serif;font-size:14pt"><DIV>Hi Ali,</DIV> <DIV> </DIV> <DIV>Thank you for your response. </DIV> <DIV> </DIV> <DIV>I was trying to find in the Internet under which conditions did the Simplex Method runs in polynomial time but I could not find anything.</DIV> <DIV> </DIV> <DIV>Can you direct me to some papers or web site that indicate under which conditions will the Simplex Method runs in polynomial time?</DIV> <DIV> </DIV> <DIV>Thank you.</DIV> <DIV> </DIV> <DIV>Rdgs,</DIV> <DIV>Paul<BR></DIV> <DIV style="FONT-FAMILY: arial, helvetica, sans-serif; FONT-SIZE: 14pt"><BR> <DIV style="FONT-FAMILY: arial, helvetica, sans-serif; FONT-SIZE: 13px"><FONT size=2 face=Tahoma> <HR SIZE=1> <B><SPAN style="FONT-WEIGHT: bold">From:</SPAN></B> Ali Baharev <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26589701&i=0" target="_top" rel="nofollow">ali.baharev@...</a>><BR><B><SPAN style="FONT-WEIGHT: bold">To:</SPAN></B> RC Loh <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26589701&i=1" target="_top" rel="nofollow">rc_loh@...</a>><BR><B><SPAN style="FONT-WEIGHT: bold">Cc:</SPAN></B> <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26589701&i=2" target="_top" rel="nofollow">help-glpk@...</a><BR><B><SPAN style="FONT-WEIGHT: bold">Sent:</SPAN></B> Monday, 30 November 2009 7:50:47<BR><B><SPAN style="FONT-WEIGHT: bold">Subject:</SPAN></B> Re: [Help-glpk] Linear Programming Relaxation<BR></FONT><BR>Hi,<BR><BR>> However, when I did the LPR, "x1" and "x2" can become "0.5". Though it still<BR>> satisfies the constraint "x1+x2<=1", but that is NOT what I want.<BR><BR>Please re-read Andrew's e-mail:<BR><BR>> LP relaxation is just an LP problem, where all variables are allowed<BR>> to take any *continuous* values, if only they are satisfied to all LP<BR>> constraints. You require that x1 + x2 <= 1 but do not require that<BR>> x1 and x2 are integer-valued, so why do you surprise that you get<BR>> x1 = x2 = 0.5? Aren't these values satisfy to x1 + x2 <= 1?<BR><BR>Please answer his questions.<BR><BR>You have no choice but to declare those variables binary in order to<BR>achieve what you want.<BR><BR>> And I understand that LP runs in exponential time, however, LPR can run in<BR>> polynomial time.<BR><BR>Correction: the simplex method shows exponential complexity in the<BR>worst case. In practice, it runs in polynomial time. This is<BR>theoretically proven (under certain conditions).<BR><BR>Have you actually faced performance problems with your problems?<BR><BR>Good luck anyhow,<BR><BR>Ali<BR></DIV></DIV></div><br> <hr size=1> <a href="http://sg.rd.yahoo.com/sg/mail/domainchoice/mail/signature/*http://mail.promotions.yahoo.com/newdomains/sg/" target="_top" rel="nofollow"> New Email names for you! </a> <br> Get the Email name you've always wanted on the new @ymail and @rocketmail.<br> Hurry before someone else does!</body></html><br />_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26589701&i=3" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26589038 Re: Linear Programming Relaxation 2009-12-01T01:34:27Z 2009-12-01T01:34:27Z Andrew Makhorin <div class='shrinkable-quote'>>> What I am trying to obtain is that though using LPR, the solution <br>>> is bounded, but the solution does not satisfy what I need which is <br>>> "x1+x2<=1" which means that "x1" and "x2" cannot co-exist together in <br>>> a solution. <br>> <br>> In mathematics "x1+x2<=1" does not mean "that x1 and x2 cannot co-exist <br>> together in a solution"; it means that the sum of x1 and x2 is not <br>> greater than 1. The constraint you need is "NOT x1 OR NOT x2"; this <br>> constraint is *not* equivalent to "x1+x2<=1" until x1 and x2 are <br>> restricted to be binary, and being non-convex this constraint cannot be <br>> modeled within linear program (LP). If you restrict some variables to <br>> be binary, you get integer program (MIP), not LP. </div><br>I would like to add that there exists a version of the simplex method <br>(which is not implemented in glpk), where you can declare a set of <br>variables {x1, x2, ..., xk} to be so called Special Ordered Set of <br>Type 1 (SOS1 for brevity). SOS1 means that at most one of its variables <br>can be basic while all its other variables must be non-basic. Assuming <br>that all variables are non-negative, i.e. xj >= 0, SOS1 then means that <br>at most one of its variables can take non-zero value while values of its <br>other variables must be zero. Processing SOS1 constraints can be easily <br>embedded into the simplex method: if some SOS1 variable is basic, <br>a non-basic variable from the same SOS1 must not be chosen to enter the <br>basis. However, in general case such version of the simplex method can <br>find only a local optimum, because SOS1 constraints are non-convex. <br><br><br><br>_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26589038&i=0" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26578372 SV: Python 2009-11-30T08:57:00Z 2009-11-30T08:57:00Z Robert Johansson Ok, but I really want to use Python. The problem is which one to choose (PyMathProg, python-glpk, ctypes-glpk or something else). The math is no problem and the programming bit will be ok if I just can use a language that I know well. In the end I will use it in an educational context so I would rather like to cover several applications than having a cutting edge solution for only one case. <br><br>Thanks! <br><br>/Robert <br><br>-----Ursprungligt meddelande----- <br>Fran: <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26578372&i=0" target="_top" rel="nofollow">help-glpk-bounces+robert=math.umu.se@...</a> [mailto:<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26578372&i=1" target="_top" rel="nofollow">help-glpk-bounces+robert=math.umu.se@...</a>] For Jeffrey Kantor <br>Skickat: den 30 november 2009 15:37 <br>Till: Robert Johansson <br>Kopia: <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26578372&i=2" target="_top" rel="nofollow">help-glpk@...</a> <br>Amne: Re: [Help-glpk] Python <br><br>That's not a lot to go on.  There are a lot of ways to formulate <br>linear programming <br>applications, Python being one.  You may find one of the modeling languages, <br>such as mathprog, may fit your application and require little programming <br>overhead. <br><br>What type of applications to you have in mind? <br><br>On Mon, Nov 30, 2009 at 9:01 AM, Robert Johansson <br><<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26578372&i=3" target="_top" rel="nofollow">rjohansson70@...</a>> wrote: <div class='shrinkable-quote'><br>> Hi! <br>> <br>> I want to use Python to run glpk (under Windows). I looked around for a <br>> while and found PyMathProg, python-glpk and ctypes-glpk. My knowledge in C <br>> is basic but I can write decent Python scripts. I would be much grateful for <br>> any suggestions or advices. <br>> <br>> cheers, Robert <br>> _______________________________________________ <br>> Help-glpk mailing list <br>> <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26578372&i=4" target="_top" rel="nofollow">Help-glpk@...</a> <br>> <a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br>> <br>> </div><br><br>_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26578372&i=5" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><br><br><br><br><br><br>_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26578372&i=6" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26578212 Re: Python 2009-11-30T08:42:49Z 2009-11-30T08:42:49Z Jeffrey Kantor Robert, <br><br>If you're committed to the Python aspect of this, you might also <br>consider CVXOPT (<a href="http://abel.ee.ucla.edu/cvxopt/index.html" target="_top" rel="nofollow">http://abel.ee.ucla.edu/cvxopt/index.html</a>).  CVXOPT <br>is generally for convex optimization, but purportedly allows use of <br>glpk for milp problems. I'm not much of a python programmer, so don't <br>have much direct experience with this. CVXOPT is also integrated into <br>the sage environment which might be nice for the educational context. <br><br>Jeff <br><br><br>On Mon, Nov 30, 2009 at 11:12 AM, Robert Johansson <br><<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26578212&i=0" target="_top" rel="nofollow">robert.johansson@...</a>> wrote: <div class='shrinkable-quote'><br>> Ok, but I really want to use Python. The problem is which one to choose (PyMathProg, python-glpk, ctypes-glpk or something else). The math is no problem and the programming bit will be ok if I just can use a language that I know well. In the end I will use it in an educational context so I would rather like to cover several applications than having a cutting edge solution for only one case. <br>> <br>> Thanks! <br>> <br>> /Robert <br>> <br>> -----Ursprungligt meddelande----- <br>> Från: <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26578212&i=1" target="_top" rel="nofollow">help-glpk-bounces+robert=math.umu.se@...</a> [mailto:<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26578212&i=2" target="_top" rel="nofollow">help-glpk-bounces+robert=math.umu.se@...</a>] För Jeffrey Kantor <br>> Skickat: den 30 november 2009 15:37 <br>> Till: Robert Johansson <br>> Kopia: <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26578212&i=3" target="_top" rel="nofollow">help-glpk@...</a> <br>> Ämne: Re: [Help-glpk] Python <br>> <br>> That's not a lot to go on. There are a lot of ways to formulate <br>> linear programming <br>> applications, Python being one. You may find one of the modeling languages, <br>> such as mathprog, may fit your application and require little programming <br>> overhead. <br>> <br>> What type of applications to you have in mind? <br>> <br>> On Mon, Nov 30, 2009 at 9:01 AM, Robert Johansson <br>> <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26578212&i=4" target="_top" rel="nofollow">rjohansson70@...</a>> wrote: <br>>> Hi! <br>>> <br>>> I want to use Python to run glpk (under Windows). I looked around for a <br>>> while and found PyMathProg, python-glpk and ctypes-glpk. My knowledge in C <br>>> is basic but I can write decent Python scripts. I would be much grateful for <br>>> any suggestions or advices. <br>>> <br>>> cheers, Robert <br>>> _______________________________________________ <br>>> Help-glpk mailing list <br>>> <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26578212&i=5" target="_top" rel="nofollow">Help-glpk@...</a> <br>>> <a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br>>> <br>>> <br>> <br>> <br>> _______________________________________________ <br>> Help-glpk mailing list <br>> <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26578212&i=6" target="_top" rel="nofollow">Help-glpk@...</a> <br>> <a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br>> <br>> </div><br><br>_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26578212&i=7" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26575728 Re: Python 2009-11-30T06:37:00Z 2009-11-30T06:37:00Z Jeffrey Kantor That's not a lot to go on.  There are a lot of ways to formulate <br>linear programming <br>applications, Python being one.  You may find one of the modeling languages, <br>such as mathprog, may fit your application and require little programming <br>overhead. <br><br>What type of applications to you have in mind? <br><br>On Mon, Nov 30, 2009 at 9:01 AM, Robert Johansson <br><<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26575728&i=0" target="_top" rel="nofollow">rjohansson70@...</a>> wrote: <div class='shrinkable-quote'><br>> Hi! <br>> <br>> I want to use Python to run glpk (under Windows). I looked around for a <br>> while and found PyMathProg, python-glpk and ctypes-glpk. My knowledge in C <br>> is basic but I can write decent Python scripts. I would be much grateful for <br>> any suggestions or advices. <br>> <br>> cheers, Robert <br>> _______________________________________________ <br>> Help-glpk mailing list <br>> <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26575728&i=1" target="_top" rel="nofollow">Help-glpk@...</a> <br>> <a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br>> <br>> </div><br><br>_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26575728&i=2" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26575661 Re: Linear Programming Relaxation 2009-11-30T06:29:07Z 2009-11-30T06:29:07Z Jeffrey Kantor On Mon, Nov 30, 2009 at 4:17 AM, RC Loh <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26575661&i=0" target="_top" rel="nofollow">rc_loh@...</a>> wrote: <div class='shrinkable-quote'><br>> Hi Andrew, Jeffrey, Michael, <br>> <br>> Thank you very much for your responses. <br>> <br>> I will read up on Special Ordered Set (SOS) as suggested by Micheal. Because <br>> SOS is new to me. <br>> <br>> <br>> Hi Jeffrey, <br>> <br>> What I am trying to obtain is that though using LPR, the solution <br>> is bounded, but the solution does not satisfy what I need which is <br>> "x1+x2<=1" which means that "x1" and "x2" cannot co-exist together in a <br>> solution. <br>> <br>> Without using LPR, that is, the "x1" and "x2" are binaries, then the <br>> solution obtained by LP is correct. <br>> <br>> However, when I did the LPR, "x1" and "x2" can become "0.5". Though it still <br>> satisfies the constraint "x1+x2<=1", but that is NOT what I want. <br>> <br>> What I want is that "x1" and "x2" CANNOT co-exist together in the solution. </div><br>You are observing correct behavior.  In this instance, relaxation means that the <br>solver is not using the binary constraints on x1 and x2.  This <br>simplifies the problem <br>considerably and provides a lower bound on the objective function you <br>are minimizing. <br><br>This  bound can be very useful.  In your application the lower bound <br>means there is <br>nothing you can do to improve bandwidth or reliability.  If the result <br>you get is not good <br>enough then you need to change the specification in some way. <br>Enforcing the binary <br>constraints will only give a poorer result.  If you don't like <br>bandwidth or reliability <br>you get with the relaxed solution, then you need to re-engineer the <br>specification. This <br>can be very powerful information in many engineering problems. <br><br>Unfortunately, removing the binary constraint on x1 and x2  means that <br>x1 and x2 can take on any value between 0 and 1, which is what you are <br>observing.  If you need for them <br>to be 0 or 1, then you need to enforce the binary constraints. How <br>much the objective increases <br>is problem dependent, but you know it will between the value of the <br>relaxed solution and <br>the value of any feasible solution.  That gap may be wide or narrow, <br>depending on your <br>problem. <br><br>In this case you do have a set of binary variables, x1 and x2, of <br>which only one member <br>can be 1.  This is called a Special Ordered Set (SOS) of Type 1. This <br>situation allows <br>for more efficient solution procedures.  To the best of my knowledge <br>GLPK doesn't use <br>procedures specific to SOS sets. This may or may not be an important <br>consideration for your <br>problem. <br><br>The issue of polynomial time algorithms can be a distraction.  If your <br>problem is relatively <br>small scale and you are getting solutions quickly, then don't worry <br>about it.  More often <br>the bigger issues are whether your model accurately captures the <br>application, the <br>problem is well posed and robust to small modeling error, and if <br>you're getting the accurate <br>answers you need.  Don't worry about computational time unless you're <br>sure its a problem. <br><br><div class='shrinkable-quote'><br>> <br>> And I understand that LP runs in exponential time, however, LPR can run in <br>> polynomial time. <br>> <br>> That is why, I want to use LPR. <br>> <br>> Any suggestion or idea is appreciated. <br>> <br>> Rdgs, <br>> Paul <br>> <br>> <br>> ________________________________ <br>> From: Andrew Makhorin <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26575661&i=1" target="_top" rel="nofollow">mao@...</a>> <br>> To: RC Loh <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26575661&i=2" target="_top" rel="nofollow">rc_loh@...</a>> <br>> Cc: <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26575661&i=3" target="_top" rel="nofollow">help-glpk@...</a> <br>> Sent: Monday, 30 November 2009 2:22:36 <br>> Subject: Re: [Help-glpk] Linear Programming Relaxation <br>> <br>>> However, I was pondering for the last 2 days about your response. It <br>>> seems to me that the global bound is not much use for my problem. <br>>> Because the global will give an *upper bound* for the reliability and <br>>> bandwidth which is of no use. A *lower bound* will be more useful. So <br>> <br>> In case of minimization (like yours) optimal solution to LP relaxation <br>> is just an lower bound to the exact integer optimum while an upper bound <br>> is the one defined by any integer feasible solution. That is, the <br>> following condition always holds: <br>> <br>> lower_bound <= exact_optimum <= upper_bound <br>> <br>>> I was trying to formulate the problem to try to get a *lower bound*, <br>>> but until now I am not successful of doing it. <br>> <br>> Once you have solved LP relaxation, you have got an lower bound. <br>> <br>>> Another question if you do not mind. <br>> <br>> No, I don't. <br>> <br>>> Actually the constraint of "x1+x2<=1" is to prevent x1 and x2 to <br>>> co-exists together in the solution. If x1 and x2 are binary, then GLPK <br>>> can produce a good solution. <br>> <br>>> However, if I will to use LPR, then GLPK gave a solution such that x1 <br>>> and x2 *can* co-exists together in the solution, which is not what I <br>>> want. Is there a way to prevent this? That is, even if LPR is used I <br>>> can prevent x1 and x2 to co-exists together in the solution? <br>> <br>> LP relaxation is just an LP problem, where all variables are allowed <br>> to take any *continuous* values, if only they are satisfied to all LP <br>> constraints. You require that x1 + x2 <= 1 but do not require that <br>> x1 and x2 are integer-valued, so why do you surprise that you get <br>> x1 = x2 = 0.5? Aren't these values satisfy to x1 + x2 <= 1? <br>> <br>> <br>> ________________________________ <br>> New Email names for you! <br>> Get the Email name you've always wanted on the new @ymail and @rocketmail. <br>> Hurry before someone else does! </div><br><br>_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26575661&i=4" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26575228 Python 2009-11-30T06:01:05Z 2009-11-30T06:01:05Z Robert Johansson-2 <div>Hi!</div> <div> </div> <div>I want to use Python to run glpk (under Windows). I looked around for a while and found PyMathProg, python-glpk and ctypes-glpk. My knowledge in C is basic but I can write decent Python scripts. I would be much grateful for any suggestions or advices. </div> <div> </div> <div>cheers, Robert</div> <br />_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26575228&i=0" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26575020 Re: Re: GLPK MingW build files and PyGLPK 2009-11-30T05:50:39Z 2009-11-30T05:50:39Z Luiz Bettoni <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> </head> <body bgcolor="#ffffff" text="#000000"> Hi, Nigel.<br> <br> Thanks. I've missed this point before, but Andrew put some light on it.<br> Really, the difference between the MinGW and MSYS buits are the -O2 CFLAG (missing in default GLPK build with MSYS).<br> <br> So, really thanks.<br> With MSYS I can bypass MinGW makefiles (with no extra dependencies) for my GLPK builds.<br> By the way, in Gusek I'll adopt the Xypron binaries (as discussed before).<br> <br> Hugs,<br> Luiz<br> <br> At 30/11/2009 10:30, Nigel Galloway wrote: <blockquote id="mid_20091130133013_AB0A57BD6E_ws5-10_us4_outblaze_com" cite="mid:20091130133013.AB0A57BD6E@ws5-10.us4.outblaze.com" type="cite"> <div> </div> <div>That sounds like a solution. </div> <div> </div> <div>Note though that whether compiling using your own MingW makefiles or make files compatible with MSYS (and hence Linux) you are using the same MingW compiler (gcc 3.4 as standard or gcc 4.2 if youv'e  gone experimental). The difference must therefore be due to an option you are passing to the compiler, and not the particular make tool.</div> <div> </div> <div>Cygwin is far too complicated and your code will have dependencies. Any timings may depend on how you've built Cygwin.</div> <div> </div> <div>Good Luck,</div> <div> </div> <div>Nigel</div> <div><br> <br> <blockquote id="StationeryCiteGenerated_1" style="border-left: 2px solid rgb(16, 16, 255); padding-left: 5px; margin-left: 5px;">----- Original Message -----<br> From: "Luiz M. M. Bettoni" <BETTONI@CPGEI.CT.UTFPR.EDU.BR><br> To: "Nigel Galloway" <NIGEL_GALLOWAY@OPERAMAIL.COM>, "help-glpk" <HELP-GLPK@GNU.ORG>, "Andrew Makhorin" <MAO@GNU.ORG><br> Subject: Re: Re: [Help-glpk] Re: GLPK MingW build files and PyGLPK<br> Date: Thu, 26 Nov 2009 08:47:00 -0300<br> <br> Hi, Nigel, Andrew.<br> <br> I've build glpsol.exe with MSYS and cygwin.<br> Besides it's useful, the binary file has more than double sized and the solver looks like quite slower.<br> <br> So, for my testing purposes, I'll use my own MingW build files. <br> In Gusek package I'll use Xypron pre-built files.<br> <br> Thanks, guys!<br> Luiz<br> <br> <br> At 16:59, Nigel Galloway wrote: </MAO@GNU.ORG></HELP-GLPK@GNU.ORG></NIGEL_GALLOWAY@OPERAMAIL.COM></BETTONI@CPGEI.CT.UTFPR.EDU.BR> <blockquote id="mid_%3C20091106120803_CBB5B7BD6E_ws5-10_us4_outblaze_com%3E" cite="mid:%3C20091106120803.CBB5B7BD6E@ws5-10.us4.outblaze.com%3E" type="cite"> <pre wrap="">You should probably add the MSYS extensions to MingW, these include a make utility compatible with Linux. This is what I usually use to compile glpk on windows using NetBeans rather than Visual C++ as the IDE. I make no changes. Good Luck, Nigel </pre> <blockquote id="StationeryCiteGenerated_1" type="cite"> <pre wrap="">----- Original Message ----- From: "Andrew Makhorin" <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26575020&i=0" target="_top" rel="nofollow">mao@...</a> To: "Luiz Bettoni" <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26575020&i=1" target="_top" rel="nofollow">bettoni@...</a> Cc: "help-glpk" <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26575020&i=2" target="_top" rel="nofollow">help-glpk@...</a> Subject: [Help-glpk] Re: GLPK MingW build files and PyGLPK Date: Thu, 5 Nov 2009 20:40:50 +0300 </pre> <blockquote id="StationeryCiteGenerated_2" type="cite"> <pre wrap="">You do not intend to include MingW w32 build files in GLPK package anymore? </pre> </blockquote> <blockquote id="StationeryCiteGenerated_3" type="cite"> <pre wrap="">On every GLPK launch i've patched them and sent to the list, but if no-one uses mingw to build GLPK (I'm alone? U), it's wast effort. </pre> </blockquote> <blockquote id="StationeryCiteGenerated_4" type="cite"> <pre wrap="">If MingW build files isn't util anymore, I'm planning replace Gusek glpsol binaries by winglpk pre-build ones. </pre> </blockquote> <pre wrap="">If you build only the glpsol executable, why not to use Cygwin? It allows configuring and building the package in the standard way. Is there anything specific in Gusek that requires Mingw? </pre> </blockquote> <pre wrap=""> </pre> <pre wrap=""> </pre> </blockquote> </blockquote> </div> <br> -- <p>_______________________________________________<br> Surf the Web in a faster, safer and easier way:<br> Download Opera 9 at <a moz-do-not-send="true" href="http://www.opera.com" target="_blank" rel="nofollow">http://www.opera.com</a></p> <br> Powered by Outblaze </blockquote> </body> </html> <br />_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26575020&i=3" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26574827 Re: Linear Programming Relaxation 2009-11-30T05:38:20Z 2009-11-30T05:38:20Z Andrew Makhorin > What I am trying to obtain is that though using LPR, the solution <br>> is bounded, but the solution does not satisfy what I need which is <br>> "x1+x2<=1" which means that "x1" and "x2" cannot co-exist together in <br>> a solution. <br><br>In mathematics "x1+x2<=1" does not mean "that x1 and x2 cannot co-exist <br>together in a solution"; it means that the sum of x1 and x2 is not <br>greater than 1. The constraint you need is "NOT x1 OR NOT x2"; this <br>constraint is *not* equivalent to "x1+x2<=1" until x1 and x2 are <br>restricted to be binary, and being non-convex this constraint cannot be <br>modeled within linear program (LP). If you restrict some variables to <br>be binary, you get integer program (MIP), not LP. <br><br><br><br><br><br>_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26574827&i=0" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26574742 Re: Re: Re: GLPK MingW build files and PyGLPK 2009-11-30T05:30:13Z 2009-11-30T05:30:13Z Nigel Galloway <DIV> </DIV> <DIV>That sounds like a solution. </DIV> <DIV> </DIV> <DIV>Note though that whether compiling using your own MingW makefiles or make files compatible with MSYS (and hence Linux) you are using the same MingW compiler (gcc 3.4 as standard or gcc 4.2 if youv'e  gone experimental). The difference must therefore be due to an option you are passing to the compiler, and not the particular make tool.</DIV> <DIV> </DIV> <DIV>Cygwin is far too complicated and your code will have dependencies. Any timings may depend on how you've built Cygwin.</DIV> <DIV> </DIV> <DIV>Good Luck,</DIV> <DIV> </DIV> <DIV>Nigel</DIV> <DIV><BR><BR> <BLOCKQUOTE style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #1010ff 2px solid">----- Original Message -----<BR>From: "Luiz M. M. Bettoni" <BETTONI@CPGEI.CT.UTFPR.EDU.BR><BR>To: "Nigel Galloway" <NIGEL_GALLOWAY@OPERAMAIL.COM>, "help-glpk" <HELP-GLPK@GNU.ORG>, "Andrew Makhorin" <MAO@GNU.ORG><BR>Subject: Re: Re: [Help-glpk] Re: GLPK MingW build files and PyGLPK<BR>Date: Thu, 26 Nov 2009 08:47:00 -0300<BR><BR>Hi, Nigel, Andrew.<BR><BR>I've build glpsol.exe with MSYS and cygwin.<BR>Besides it's useful, the binary file has more than double sized and the solver looks like quite slower.<BR><BR>So, for my testing purposes, I'll use my own MingW build files. <BR>In Gusek package I'll use Xypron pre-built files.<BR><BR>Thanks, guys!<BR>Luiz<BR><BR><BR>At 16:59, Nigel Galloway wrote: <BLOCKQUOTE id=mid_%3C20091106120803_CBB5B7BD6E_ws5-10_us4_outblaze_com%3E cite=mid:%3C20091106120803.CBB5B7BD6E@ws5-10.us4.outblaze.com%3E type="cite"><PRE wrap="">You should probably add the MSYS extensions to MingW, these include a make utility compatible with Linux. This is what I usually use to compile glpk on windows using NetBeans rather than Visual C++ as the IDE. I make no changes. Good Luck, Nigel </PRE> <BLOCKQUOTE id=StationeryCiteGenerated_1 type="cite"><PRE wrap="">----- Original Message ----- From: "Andrew Makhorin" <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26574742&i=0" target="_top" rel="nofollow">mao@...</a> To: "Luiz Bettoni" <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26574742&i=1" target="_top" rel="nofollow">bettoni@...</a> Cc: "help-glpk" <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26574742&i=2" target="_top" rel="nofollow">help-glpk@...</a> Subject: [Help-glpk] Re: GLPK MingW build files and PyGLPK Date: Thu, 5 Nov 2009 20:40:50 +0300 </PRE> <BLOCKQUOTE id=StationeryCiteGenerated_2 type="cite"><PRE wrap="">You do not intend to include MingW w32 build files in GLPK package anymore? </PRE></BLOCKQUOTE> <BLOCKQUOTE id=StationeryCiteGenerated_3 type="cite"><PRE wrap="">On every GLPK launch i've patched them and sent to the list, but if no-one uses mingw to build GLPK (I'm alone? U), it's wast effort. </PRE></BLOCKQUOTE> <BLOCKQUOTE id=StationeryCiteGenerated_4 type="cite"><PRE wrap="">If MingW build files isn't util anymore, I'm planning replace Gusek glpsol binaries by winglpk pre-build ones. </PRE></BLOCKQUOTE><PRE wrap="">If you build only the glpsol executable, why not to use Cygwin? It allows configuring and building the package in the standard way. Is there anything specific in Gusek that requires Mingw? </PRE></BLOCKQUOTE><PRE wrap=""> </PRE><PRE wrap=""> </PRE></BLOCKQUOTE></BLOCKQUOTE></DIV><BR> -- <p>_______________________________________________<br>Surf the Web in a faster, safer and easier way:<br> Download Opera 9 at <a href="http://www.opera.com" target="_blank" rel="nofollow">http://www.opera.com</a></p> <BR> Powered by Outblaze <br />_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26574742&i=3" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26573559 Re: Linear Programming Relaxation 2009-11-30T03:50:47Z 2009-11-30T03:50:47Z Ali Baharev Hi, <br><br>> However, when I did the LPR, "x1" and "x2" can become "0.5". Though it still <br>> satisfies the constraint "x1+x2<=1", but that is NOT what I want. <br><br>Please re-read Andrew's e-mail: <br><br>> LP relaxation is just an LP problem, where all variables are allowed <br>> to take any *continuous* values, if only they are satisfied to all LP <br>> constraints. You require that x1 + x2 <= 1 but do not require that <br>> x1 and x2 are integer-valued, so why do you surprise that you get <br>> x1 = x2 = 0.5? Aren't these values satisfy to x1 + x2 <= 1? <br><br>Please answer his questions. <br><br>You have no choice but to declare those variables binary in order to <br>achieve what you want. <br><br>> And I understand that LP runs in exponential time, however, LPR can run in <br>> polynomial time. <br><br>Correction: the simplex method shows exponential complexity in the <br>worst case. In practice, it runs in polynomial time. This is <br>theoretically proven (under certain conditions). <br><br>Have you actually faced performance problems with your problems? <br><br>Good luck anyhow, <br><br>Ali <br><br><br>_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26573559&i=0" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26571508 Re: Linear Programming Relaxation 2009-11-30T01:17:58Z 2009-11-30T01:17:58Z Paul Loh <html><head></head><body><div style="font-family:arial, helvetica, sans-serif;font-size:14pt"><DIV>Hi Andrew, Jeffrey, Michael,</DIV> <DIV> </DIV> <DIV>Thank you very much for your responses. </DIV> <DIV> </DIV> <DIV>I will read up on Special Ordered Set (SOS) as suggested by Micheal. Because SOS is new to me. </DIV> <DIV> </DIV> <DIV> </DIV> <DIV>Hi Jeffrey,</DIV> <DIV> </DIV> <DIV>What I am trying to obtain is that though using LPR, the solution is bounded, but the solution does not satisfy what I need which is "x1+x2<=1" which means that "x1" and "x2" cannot co-exist together in a solution.</DIV> <DIV> </DIV> <DIV>Without using LPR, that is, the "x1" and "x2" are binaries, then the solution obtained by LP is correct.</DIV> <DIV> </DIV> <DIV>However, when I did the LPR, "x1" and "x2" can become "0.5". Though it still satisfies the constraint "x1+x2<=1", but that is NOT what I want. </DIV> <DIV> </DIV> <DIV>What I want is that "x1" and "x2" CANNOT co-exist together in the solution. </DIV> <DIV> </DIV> <DIV>And I understand that LP runs in exponential time, however, LPR can run in polynomial time. </DIV> <DIV> </DIV> <DIV>That is why, I want to use LPR.  </DIV> <DIV> <BR>Any suggestion or idea is appreciated.</DIV> <DIV> </DIV> <DIV>Rdgs,</DIV> <DIV>Paul</DIV> <DIV> </DIV> <DIV> </DIV> <DIV style="FONT-FAMILY: arial, helvetica, sans-serif; FONT-SIZE: 14pt"><BR> <DIV style="FONT-FAMILY: arial, helvetica, sans-serif; FONT-SIZE: 13px"><FONT size=2 face=Tahoma> <HR SIZE=1> <B><SPAN style="FONT-WEIGHT: bold">From:</SPAN></B> Andrew Makhorin <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26571508&i=0" target="_top" rel="nofollow">mao@...</a>><BR><B><SPAN style="FONT-WEIGHT: bold">To:</SPAN></B> RC Loh <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26571508&i=1" target="_top" rel="nofollow">rc_loh@...</a>><BR><B><SPAN style="FONT-WEIGHT: bold">Cc:</SPAN></B> <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26571508&i=2" target="_top" rel="nofollow">help-glpk@...</a><BR><B><SPAN style="FONT-WEIGHT: bold">Sent:</SPAN></B> Monday, 30 November 2009 2:22:36<BR><B><SPAN style="FONT-WEIGHT: bold">Subject:</SPAN></B> Re: [Help-glpk] Linear Programming Relaxation<BR></FONT><BR>> However, I was pondering for the last 2 days about your response. It<BR>> seems to me that the global bound is not much use for my problem.<BR>> Because the global will give an *upper bound* for the reliability and<BR>> bandwidth which is of no use. A *lower bound* will be more useful. So<BR><BR>In case of minimization (like yours) optimal solution to LP relaxation<BR>is just an lower bound to the exact integer optimum while an upper bound<BR>is the one defined by any integer feasible solution. That is, the<BR>following condition always holds:<BR><BR>  lower_bound <= exact_optimum <= upper_bound<BR><BR>> I was trying to formulate the problem to try to get a *lower bound*,<BR>> but until now I am not successful of doing it.<BR><BR>Once you have solved LP relaxation, you have got an lower bound.<BR><BR>> Another question if you do not mind.<BR><BR>No, I don't.<BR><BR>> Actually the constraint of "x1+x2<=1" is to prevent x1 and x2 to<BR>> co-exists together in the solution. If x1 and x2 are binary, then GLPK<BR>> can produce a good solution.<BR><BR>> However, if I will to use LPR, then GLPK gave a solution such that x1<BR>> and x2 *can* co-exists together in the solution, which is not what I<BR>> want. Is there a way to prevent this? That is, even if LPR is used I<BR>> can prevent x1 and x2 to co-exists together in the solution?<BR><BR>LP relaxation is just an LP problem, where all variables are allowed<BR>to take any *continuous* values, if only they are satisfied to all LP<BR>constraints. You require that x1 + x2 <= 1 but do not require that<BR>x1 and x2 are integer-valued, so why do you surprise that you get<BR>x1 = x2 = 0.5? Aren't these values satisfy to x1 + x2 <= 1?<BR><BR></DIV></DIV></div><br> <hr size=1> <a href="http://sg.rd.yahoo.com/sg/mail/domainchoice/mail/signature/*http://mail.promotions.yahoo.com/newdomains/sg/" target="_top" rel="nofollow"> New Email names for you! </a> <br> Get the Email name you've always wanted on the new @ymail and @rocketmail.<br> Hurry before someone else does!</body></html><br />_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26571508&i=3" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26565182 Re: Linear Programming Relaxation 2009-11-29T11:34:02Z 2009-11-29T11:34:02Z Jeffrey Kantor Hi Paul, <br><br>As an outside observer to this case, I'm trying to understand <br>precisely what you're after.  As already mentioned by others, an LP <br>relaxation finds a lower bound to your problem, while any feasible <br>integer solution (which may or may not be easy to find) provides an <br>upper bound.  Solving the problem to integer optimality finds an <br>actual solution to your problem. <br><br>Are you trying to solve your integer/binary problem without imposing <br>integer/binary constraints? <br><br>Jeff <br><br>On Sun, Nov 29, 2009 at 8:30 AM, RC Loh <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26565182&i=0" target="_top" rel="nofollow">rc_loh@...</a>> wrote: <div class='shrinkable-quote'><br>> Hi Andrew, <br>> <br>> Thank you very much for your response. <br>> <br>> However, I was pondering for the last 2 days about your response. It seems <br>> to me that the global bound is not much use for my problem. Because the <br>> global will give an *upper bound* for the reliability and bandwidth which is <br>> of no use. A *lower bound* will be more useful. So I was trying to formulate <br>> the problem to try to get a *lower bound*, but until now I am not successful <br>> of doing it. <br>> <br>> Another question if you do not mind. <br>> <br>> Actually the constraint of "x1+x2<=1" is to prevent x1 and x2 to co-exists <br>> together in the solution. If x1 and x2 are binary, then GLPK can produce a <br>> good solution. <br>> <br>> However, if I will to use LPR, then GLPK gave a solution such that x1 and <br>> x2 *can* co-exists together in the solution, which is not what I want. Is <br>> there a way to prevent this? That is, even if LPR is used I can prevent x1 <br>> and x2 to co-exists together in the solution? <br>> <br>> Thanks in advance. <br>> <br>> Rdgs, <br>> Paul <br>> <br>> ________________________________ <br>> From: Andrew Makhorin <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26565182&i=1" target="_top" rel="nofollow">mao@...</a>> <br>> To: RC Loh <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26565182&i=2" target="_top" rel="nofollow">rc_loh@...</a>> <br>> Cc: <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26565182&i=3" target="_top" rel="nofollow">help-glpk@...</a> <br>> Sent: Friday, 27 November 2009 11:11:01 <br>> Subject: Re: [Help-glpk] Linear Programming Relaxation <br>> <br>>> Just to clarify on Linear Programming Relaxation. <br>> <br>>> I am attempting to solve the NP-hard problem of Optimizing Reliability <br>>> Subject to a Bandwidth Constraint using Linear Programming Relaxation <br>>> and I have created 2 LP files for the problem. <br>> <br>>> Test 1: (using Binary structural variables) <br>>> =============================== <br>>> 1) BinaryLinearProgramming_LP_file.txt (see attached file) <br>>> 2) routine lpx_intopt(lp) <br>>> 3) I obtained Output_BinaryLinearProgram.txt (see attached file) <br>> <br>>> Test 2: (using bounds structural variables) <br>>> ================================ <br>>> 1) LinearProgramRelaxed_LP_file.txt (see attached file) <br>>> 2) routine lpx_interior(lp) <br>>> 3) I obtained Output_LinearProgramRelaxed.txt (see attached file) <br>> <br>>> The constraints of "x1+x2<=1" in the LP files is because I do not want <br>>> "x1" and "x2" to be in the solution at the same time because "x1" is <br>>> not edge-disjoint with "x2". Same goes for the rest of the constraints <br>>> in the LP files. <br>> <br>>> I have 3 questions: <br>>> 1) The output from the Test 1 using Binary structural variables is <br>>> correct but why I got all "0.5" for all the structural variables in <br>>> the LP Relaxed? Is my formulation of the LP file using the LP <br>>> Relaxation correct? <br>> <br>> You get fractional solution, because LinearProgramRelaxed_LP_file <br>> does not constraint variables to be integer-valued unlike <br>> BinaryLinearProgramming_LP_file which does. <br>> <br>>> 2) Using the Linear Programming Relaxation (LPR) method to obtain an <br>>> approximate algorithm does not mean that the approximation is for the <br>>> objective function, is that right? Because we cannot guarantee how <br>>> close we are to the optimal result using the LPR, is that right? Using <br>>> the LPR method is more like a heuristics algorithm, is that right? <br>> <br>> LPR does not give you an approximation to the exact solution, because <br>> its solution may be fractional (which it is). It only gives you a global <br>> bound to the exact optimum in the sense that optimal objective value <br>> for the original (non-relaxed) problem *cannot* be better than optimal <br>> objective value for LPR. <br>> <br>>> 3) How do I cite GLPK for a paper conference submission? <br>> <br>> GNU Linear Programming Kit Version X.Y, <a href="http://www.gnu.org/software/glpk/" target="_top" rel="nofollow">http://www.gnu.org/software/glpk/</a> . <br>> <br>> <br>> <br>> ________________________________ <br>> Yahoo! Toolbar is now powered with Search Assist. Download it now! <br>> _______________________________________________ <br>> Help-glpk mailing list <br>> <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26565182&i=4" target="_top" rel="nofollow">Help-glpk@...</a> <br>> <a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br>> <br>> </div><br><br>_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26565182&i=5" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26564528 Re: Linear Programming Relaxation 2009-11-29T10:22:29Z 2009-11-29T10:22:29Z Andrew Makhorin > However, I was pondering for the last 2 days about your response. It <br>> seems to me that the global bound is not much use for my problem. <br>> Because the global will give an *upper bound* for the reliability and <br>> bandwidth which is of no use. A *lower bound* will be more useful. So <br><br>In case of minimization (like yours) optimal solution to LP relaxation <br>is just an lower bound to the exact integer optimum while an upper bound <br>is the one defined by any integer feasible solution. That is, the <br>following condition always holds: <br><br>   lower_bound <= exact_optimum <= upper_bound <br><br>> I was trying to formulate the problem to try to get a *lower bound*, <br>> but until now I am not successful of doing it. <br><br>Once you have solved LP relaxation, you have got an lower bound. <br><br>> Another question if you do not mind. <br><br>No, I don't. <br><br>> Actually the constraint of "x1+x2<=1" is to prevent x1 and x2 to <br>> co-exists together in the solution. If x1 and x2 are binary, then GLPK <br>> can produce a good solution. <br><br>> However, if I will to use LPR, then GLPK gave a solution such that x1 <br>> and x2 *can* co-exists together in the solution, which is not what I <br>> want. Is there a way to prevent this? That is, even if LPR is used I <br>> can prevent x1 and x2 to co-exists together in the solution? <br><br>LP relaxation is just an LP problem, where all variables are allowed <br>to take any *continuous* values, if only they are satisfied to all LP <br>constraints. You require that x1 + x2 <= 1 but do not require that <br>x1 and x2 are integer-valued, so why do you surprise that you get <br>x1 = x2 = 0.5? Aren't these values satisfy to x1 + x2 <= 1? <br><br><br><br>_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26564528&i=0" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26564302 Re: Linear Programming Relaxation 2009-11-29T09:53:53Z 2009-11-29T09:53:53Z Michael Hennebry On Sun, 29 Nov 2009, RC Loh wrote: <br><br>> However, I was pondering for the last 2 days about your response. It seems to me that the global bound is not much use for my problem. Because the global will give an *upper bound* for the reliability and bandwidth which is of no use. A *lower bound* will be more useful. So I was trying to formulate the problem to try to get a *lower bound*, but until now I am not successful of doing it. <br><br>Getting a lower bound pretty much means finding a feasible solution. <br><br>> Another question if you do not mind. <br>> <br>> Actually the constraint of "x1+x2<=1" is to prevent x1 and x2 to co-exists together in the solution. If x1 and x2 are binary, then GLPK can produce a good solution. <br>> <br>> However, if I will to use LPR, then GLPK gave a solution such that x1 and x2 *can* co-exists together in the solution, which is not what I want. Is there a way to prevent this? That is, even if LPR is used I can prevent x1 and x2 to co-exists together in the solution? <br><br>2-item SOS constraint perhaps? <br><br>-- <br>Michael   <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26564302&i=0" target="_top" rel="nofollow">hennebry@...</a> <br>"Pessimist: The glass is half empty. <br>Optimist:   The glass is half full. <br>Engineer:   The glass is twice as big as it needs to be."<br />_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26564302&i=1" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26562084 Re: Linear Programming Relaxation 2009-11-29T05:30:52Z 2009-11-29T05:30:52Z Paul Loh <html><head></head><body><div style="font-family:arial, helvetica, sans-serif;font-size:14pt"><DIV>Hi Andrew,</DIV> <DIV> </DIV> <DIV>Thank you very much for your response. </DIV> <DIV> </DIV> <DIV>However, I was pondering for the last 2 days about your response. It seems to me that the global bound is not much use for my problem. Because the global will give an *upper bound* for the reliability and bandwidth which is of no use. A *lower bound* will be more useful. So I was trying to formulate the problem to try to get a *lower bound*, but until now I am not successful of doing it.</DIV> <DIV> </DIV> <DIV>Another question if you do not mind. </DIV> <DIV> </DIV> <DIV>Actually the constraint of "x1+x2<=1" is to prevent x1 and x2 to co-exists together in the solution. If x1 and x2 are binary, then GLPK can produce a good solution.</DIV> <DIV> </DIV> <DIV>However, if I will to use LPR, then GLPK gave a solution such that  x1 and x2 *can* co-exists together in the solution, which is not what I want. Is there a way to prevent this? That is, even if LPR is used I can prevent x1 and x2 to co-exists together in the solution?</DIV> <DIV> </DIV> <DIV>Thanks in advance.</DIV> <DIV> </DIV> <DIV>Rdgs,</DIV> <DIV>Paul</DIV> <DIV><BR> </DIV> <DIV style="FONT-FAMILY: arial, helvetica, sans-serif; FONT-SIZE: 14pt"><BR> <DIV style="FONT-FAMILY: arial, helvetica, sans-serif; FONT-SIZE: 13px"><FONT size=2 face=Tahoma> <HR SIZE=1> <B><SPAN style="FONT-WEIGHT: bold">From:</SPAN></B> Andrew Makhorin <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26562084&i=0" target="_top" rel="nofollow">mao@...</a>><BR><B><SPAN style="FONT-WEIGHT: bold">To:</SPAN></B> RC Loh <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26562084&i=1" target="_top" rel="nofollow">rc_loh@...</a>><BR><B><SPAN style="FONT-WEIGHT: bold">Cc:</SPAN></B> <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26562084&i=2" target="_top" rel="nofollow">help-glpk@...</a><BR><B><SPAN style="FONT-WEIGHT: bold">Sent:</SPAN></B> Friday, 27 November 2009 11:11:01<BR><B><SPAN style="FONT-WEIGHT: bold">Subject:</SPAN></B> Re: [Help-glpk] Linear Programming Relaxation<BR></FONT><BR>> Just to clarify on Linear Programming Relaxation.<BR><BR>> I am attempting to solve the NP-hard problem of Optimizing Reliability<BR>> Subject to a Bandwidth Constraint using Linear Programming Relaxation<BR>> and I have created 2 LP files for the problem.<BR><BR>> Test 1: (using Binary structural variables)<BR>> ===============================<BR>> 1) BinaryLinearProgramming_LP_file.txt (see attached file)<BR>> 2) routine lpx_intopt(lp)<BR>> 3) I obtained Output_BinaryLinearProgram.txt (see attached file)<BR><BR>> Test 2: (using bounds structural variables)<BR>> ================================<BR>> 1) LinearProgramRelaxed_LP_file.txt (see attached file)<BR>> 2) routine lpx_interior(lp)<BR>> 3) I obtained Output_LinearProgramRelaxed.txt (see attached file)<BR><BR>> The constraints of "x1+x2<=1" in the LP files is because I do not want<BR>> "x1" and "x2" to be in the solution at the same time because "x1" is<BR>> not edge-disjoint with "x2". Same goes for the rest of the constraints<BR>> in the LP files.<BR><BR>> I have 3 questions:<BR>> 1) The output from the Test 1 using Binary structural variables is<BR>> correct but why I got all "0.5" for all the structural variables in<BR>> the LP Relaxed? Is my formulation of the LP file using the LP<BR>> Relaxation correct?<BR><BR>You get fractional solution, because LinearProgramRelaxed_LP_file<BR>does not constraint variables to be integer-valued unlike<BR>BinaryLinearProgramming_LP_file which does.<BR><BR>> 2) Using the Linear Programming Relaxation (LPR) method to obtain an<BR>> approximate algorithm does not mean that the approximation is for the<BR>> objective function, is that right? Because we cannot guarantee how<BR>> close we are to the optimal result using the LPR, is that right? Using<BR>> the LPR method is more like a heuristics algorithm, is that right?<BR><BR>LPR does not give you an approximation to the exact solution, because<BR>its solution may be fractional (which it is). It only gives you a global<BR>bound to the exact optimum in the sense that optimal objective value<BR>for the original (non-relaxed) problem *cannot* be better than optimal<BR>objective value for LPR.<BR><BR>> 3) How do I cite GLPK for a paper conference submission?<BR><BR>GNU Linear Programming Kit Version X.Y, <A href="http://www.gnu.org/software/glpk/" target=_blank rel="nofollow">http://www.gnu.org/software/glpk/</A> .<BR><BR><BR></DIV></DIV></div><br> <hr size=1> Yahoo! Toolbar is now powered with Search Assist. <a href="http://sg.rd.yahoo.com/search/toolbar/mail/signature/*http://sg.toolbar.yahoo.com/" target="_top" rel="nofollow"> Download it now! </a</body></html><br />_______________________________________________ <br>Help-glpk mailing list <br>Help-glpk@... <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26543709 Re: Linear Programming Relaxation 2009-11-27T07:11:01Z 2009-11-27T07:11:01Z Andrew Makhorin > Just to clarify on Linear Programming Relaxation. <br><br>> I am attempting to solve the NP-hard problem of Optimizing Reliability <br>> Subject to a Bandwidth Constraint using Linear Programming Relaxation <br>> and I have created 2 LP files for the problem. <br><br>> Test 1: (using Binary structural variables) <br>> =============================== <br>> 1) BinaryLinearProgramming_LP_file.txt (see attached file) <br>> 2) routine lpx_intopt(lp) <br>> 3) I obtained Output_BinaryLinearProgram.txt (see attached file) <br><br>> Test 2: (using bounds structural variables) <br>> ================================ <br>> 1) LinearProgramRelaxed_LP_file.txt (see attached file) <br>> 2) routine lpx_interior(lp) <br>> 3) I obtained Output_LinearProgramRelaxed.txt (see attached file) <br><br>> The constraints of "x1+x2<=1" in the LP files is because I do not want <br>> "x1" and "x2" to be in the solution at the same time because "x1" is <br>> not edge-disjoint with "x2". Same goes for the rest of the constraints <br>> in the LP files. <br><br>> I have 3 questions: <br>> 1) The output from the Test 1 using Binary structural variables is <br>> correct but why I got all "0.5" for all the structural variables in <br>> the LP Relaxed? Is my formulation of the LP file using the LP <br>> Relaxation correct? <br><br>You get fractional solution, because LinearProgramRelaxed_LP_file <br>does not constraint variables to be integer-valued unlike <br>BinaryLinearProgramming_LP_file which does. <br><br>> 2) Using the Linear Programming Relaxation (LPR) method to obtain an <br>> approximate algorithm does not mean that the approximation is for the <br>> objective function, is that right? Because we cannot guarantee how <br>> close we are to the optimal result using the LPR, is that right? Using <br>> the LPR method is more like a heuristics algorithm, is that right? <br><br>LPR does not give you an approximation to the exact solution, because <br>its solution may be fractional (which it is). It only gives you a global <br>bound to the exact optimum in the sense that optimal objective value <br>for the original (non-relaxed) problem *cannot* be better than optimal <br>objective value for LPR. <br><br>> 3) How do I cite GLPK for a paper conference submission? <br><br>GNU Linear Programming Kit Version X.Y, <a href="http://www.gnu.org/software/glpk/" target="_top" rel="nofollow">http://www.gnu.org/software/glpk/</a> . <br><br><br><br><br>_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26543709&i=0" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26543419 Re: Re: GLPK MingW build files and PyGLPK 2009-11-27T06:50:32Z 2009-11-27T06:50:32Z Andrew Makhorin >> Under cygwin gcc is run with default options '-g' (that includes <br>>> debugging info into the executable) and '-O2'. On my 32-bit windows <br>>> machine I build glpk using 'make CFLAGS=-O3', and the code is about <br>>> 30% faster than the one built with MSVS 2010 'cl -O3'. <br>>>   <br>> I've experienced some issues using O3 cflag in past, but using O2 all <br>> looks great. <br><br>> 30% faster? Good. How you timed this? Testing some models using both <br>> builds (and some others, like MingW), I've seen that there is no build <br>> that runs all models in better time. Maybe in specific operations (like <br>> DB access or problem generation) it can be timed, but not in solve <br>> process (the longest task when reduce time become a problem). <br><br>Sorry, I was wrong. Probably my opinion was based on some inaccurate <br>experiments. <br><br>It is surprising to me, but the code produced with 'gcc -O2' looks to <br>be faster than with 'gcc -O3', though -O3 is claimed as "the third and <br>highest level enables even more optimizations by putting emphasis on <br>speed over size, that includes optimizations enabled at -O2 and <br>rename-register". (However, highly optimized code may overload the <br>instruction cache and thus slow down the CPU performance.) <br><br>Below here are solution times for dfl001.mps from netlib (solved with <br>the lp presolver disabled): <br><br>Cygwin GCC -O2: <br>Time used:   183.3 secs <br>Memory used: 8.1 Mb (8466625 bytes) <br><br>Cygwin GCC -O3: <br>Time used:   204.7 secs <br>Memory used: 8.1 Mb (8466625 bytes) <br><br>MSVC 10.0 -O2: <br>Time used:   197.5 secs <br>Memory used: 8.1 Mb (8466625 bytes) <br><br>> A note about GUSEK: building with cygwin the binary needs cygwin dll, a <br>> little big add to the package. And, if I presume that cygwin dll is as a <br>> system prerequisite, GUSEK will not be self-portable. <br><br>I agree with you. Since Gusek is a Windows application, using a native <br>executable not requiring dll is more convenient for the end-user. <br><br><br><br><br><br>_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26543419&i=0" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26541948 Re: Re: GLPK MingW build files and PyGLPK 2009-11-27T04:44:23Z 2009-11-27T04:44:23Z Luiz Bettoni <br><br>At 26/11/2009 14:35, Andrew Makhorin wrote: <br>> Under cygwin gcc is run with default options '-g' (that includes <br>> debugging info into the executable) and '-O2'. On my 32-bit windows <br>> machine I build glpk using 'make CFLAGS=-O3', and the code is about <br>> 30% faster than the one built with MSVS 2010 'cl -O3'. <br>>   <br>I've experienced some issues using O3 cflag in past, but using O2 all <br>looks great. <br><br>30% faster? Good. How you timed this? Testing some models using both <br>builds (and some others, like MingW), I've seen that there is no build <br>that runs all models in better time. Maybe in specific operations (like <br>DB access or problem generation) it can be timed, but not in solve <br>process (the longest task when reduce time become a problem). <br><br>A note about GUSEK: building with cygwin the binary needs cygwin dll, a <br>little big add to the package. And, if I presume that cygwin dll is as a <br>system prerequisite, GUSEK will not be self-portable. <br><br><br><br><br>_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26541948&i=0" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26537881 Re: Linear Programming Relaxation 2009-11-26T20:36:41Z 2009-11-26T20:36:41Z Paul Loh <html><head></head><body><div style="font-family:arial, helvetica, sans-serif;font-size:14pt"><DIV> <DIV><FONT color=#007f40 size=4>Hi Andrew,</FONT></DIV> <DIV><FONT color=#007f40 size=4></FONT> </DIV> <DIV><FONT color=#007f40 size=4>Just to clarify on Linear Programming Relaxation. </FONT></DIV> <DIV><FONT color=#007f40 size=4></FONT> </DIV> <DIV><FONT color=#007f40 size=4>I am attempting to solve the NP-hard problem of Optimizing Reliability Subject to a Bandwidth Constraint using Linear Programming Relaxation and I have created 2 LP files for the problem.</FONT></DIV> <DIV><FONT color=#007f40 size=4></FONT> </DIV> <DIV><FONT color=#007f40 size=4></FONT> </DIV> <DIV><FONT color=#007f40 size=4>Test 1: (using Binary structural variables)</FONT></DIV> <DIV><FONT color=#007f40 size=4>===============================</FONT></DIV> <DIV><FONT color=#007f40 size=4>1) BinaryLinearProgramming_LP_file.txt (see attached file)</FONT></DIV> <DIV><FONT color=#007f40 size=4>2) routine lpx_intopt(lp)</FONT></DIV> <DIV><FONT color=#007f40 size=4>3) I obtained Output_BinaryLinearProgram.txt (see attached file)</FONT></DIV> <DIV><FONT color=#007f40 size=4></FONT> </DIV> <DIV><FONT color=#007f40 size=4>Test 2: (using bounds structural variables)</FONT></DIV> <DIV><FONT color=#007f40 size=4>================================</FONT></DIV> <DIV><FONT color=#007f40 size=4>1) LinearProgramRelaxed_LP_file.txt (see attached file)</FONT></DIV> <DIV><FONT color=#007f40 size=4>2) routine lpx_interior(lp)</FONT></DIV> <DIV><FONT color=#007f40 size=4>3) I obtained Output_LinearProgramRelaxed.txt (see attached file)</FONT></DIV> <DIV><FONT color=#007f40 size=4></FONT> </DIV> <DIV><FONT color=#007f40 size=4>The constraints of "x1+x2<=1" in the LP files is because I do not want "x1" and "x2" to be in the solution at the same time because "x1" is not edge-disjoint with "x2". Same goes for the rest of the constraints in the LP files.</FONT></DIV> <DIV><FONT color=#007f40 size=4></FONT> </DIV> <DIV><FONT color=#007f40 size=4>I have 3 questions:</FONT></DIV> <DIV><FONT color=#007f40 size=4>1) The output from the Test 1 using Binary structural variables is correct but why I got all "0.5" for all the structural variables in the LP Relaxed? </FONT><FONT color=#007f40 size=4>Is my formulation of the LP file using the LP Relaxation correct?</FONT></DIV> <P><FONT color=#007f40 size=4></FONT> </P> <P><FONT color=#007f40 size=4>2) Using the Linear Programming Relaxation (LPR) method to obtain an approximate algorithm does not mean that the approximation is for the objective function, is that right? Because we cannot guarantee how close we are to the optimal result using the LPR, is that right? Using the LPR method is more like a heuristics algorithm, is that right?</FONT></P> <P><FONT color=#007f40 size=4></FONT> </P> <P><FONT color=#007f40 size=4>3) How do I cite GLPK for a paper conference submission?</FONT></P> <P><FONT color=#007f40 size=4></FONT> </P> <P><FONT color=#007f40 size=4>Thank you.</FONT></P> <P><FONT color=#007f40 size=4></FONT> </P> <P><FONT color=#007f40 size=4>Rdgs,</FONT></P> <P><FONT color=#007f40 size=4>Paul</FONT></P> <P><FONT color=#007f40 size=4> </P></FONT><BR></DIV> <DIV style="FONT-FAMILY: arial, helvetica, sans-serif; FONT-SIZE: 14pt"><BR> <DIV style="FONT-FAMILY: arial, helvetica, sans-serif; FONT-SIZE: 13px"><FONT size=2 face=Tahoma> <HR SIZE=1> <B><SPAN style="FONT-WEIGHT: bold">From:</SPAN></B> Andrew Makhorin <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26537881&i=0" target="_top" rel="nofollow">mao@...</a>><BR><B><SPAN style="FONT-WEIGHT: bold">To:</SPAN></B> RC Loh <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26537881&i=1" target="_top" rel="nofollow">rc_loh@...</a>><BR><B><SPAN style="FONT-WEIGHT: bold">Cc:</SPAN></B> David Bremner <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26537881&i=2" target="_top" rel="nofollow">bremner-dated-1260363255.d81d4d@...</a>>; <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26537881&i=3" target="_top" rel="nofollow">help-glpk@...</a><BR><B><SPAN style="FONT-WEIGHT: bold">Sent:</SPAN></B> Thursday, 26 November 2009 2:48:55<BR><B><SPAN style="FONT-WEIGHT: bold">Subject:</SPAN></B> Re: [Help-glpk] Linear Programming Relaxation<BR></FONT><BR>> What does actually "2-approximation" "3-approximation" or<BR>> "6-approximation" means?<BR><BR>See:<BR><A href="http://en.wikipedia.org/wiki/Approximation_algorithm" target=_blank rel="nofollow">http://en.wikipedia.org/wiki/Approximation_algorithm</A><BR><BR></DIV></DIV></div><br> <hr size=1> <a href="http://us.rd.yahoo.com/SIG=11dvbsnb8/**http%3A%2F%2Fwww.trueswitch.com%2Fyahoo-sg" target="_top" rel="nofollow"> Have a new Yahoo! Mail account?</a><br>Kick start your journey by importing all your contacts!</br></body></html><br />minimize <br>z: -0.067526 x1 -0.443697 x2 -0.245652 x3 -0.039244 x4 -0.170053 x5 -0.107182 x6 -0.164309 x7 -0.079877 x8 -0.083525 x9 -0.042542 x10 -0.149721 x11 -0.073411 x12 -0.062683 x13 -0.041302 x14 -0.090979 x15 -0.046144 x16 -0.025028 x17 <br>subject to <br>bw: 9 x1 + 8 x2 + 8 x3 + 8 x4 + 8 x5 + 8 x6 + 8 x7 + 8 x8 + 8 x9 + 8 x10 + 8 x11 + 8 x12 + 8 x13 + 8 x14 + 8 x15 + 8 x16 + 8 x17  >= 9 <br>r_1: x1 + x2  <= 1 <br>r_2: x1 + x3  <= 1 <br>r_3: x1 + x4  <= 1 <br>r_4: x1 + x5  <= 1 <br>r_5: x1 + x6  <= 1 <br>r_6: x1 + x7  <= 1 <br>r_7: x1 + x9  <= 1 <br>r_8: x1 + x10  <= 1 <br>r_9: x1 + x11  <= 1 <br>r_10: x1 + x12  <= 1 <br>r_11: x1 + x13  <= 1 <br>r_12: x1 + x14  <= 1 <br>r_13: x1 + x15  <= 1 <br>r_14: x1 + x16  <= 1 <br>r_15: x1 + x17  <= 1 <br>r_16: x2 + x3  <= 1 <br>r_17: x2 + x4  <= 1 <br>r_18: x2 + x5  <= 1 <br>r_19: x2 + x8  <= 1 <br>r_20: x2 + x10  <= 1 <br>r_21: x2 + x12  <= 1 <br>r_22: x2 + x13  <= 1 <br>r_23: x2 + x16  <= 1 <br>r_24: x2 + x17  <= 1 <br>r_25: x3 + x4  <= 1 <br>r_26: x3 + x6  <= 1 <br>r_27: x3 + x7  <= 1 <br>r_28: x3 + x8  <= 1 <br>r_29: x3 + x9  <= 1 <br>r_30: x3 + x10  <= 1 <br>r_31: x3 + x11  <= 1 <br>r_32: x3 + x12  <= 1 <br>r_33: x3 + x14  <= 1 <br>r_34: x3 + x15  <= 1 <br>r_35: x3 + x16  <= 1 <br>r_36: x4 + x5  <= 1 <br>r_37: x4 + x6  <= 1 <br>r_38: x4 + x7  <= 1 <br>r_39: x4 + x8  <= 1 <br>r_40: x4 + x9  <= 1 <br>r_41: x4 + x10  <= 1 <br>r_42: x4 + x11  <= 1 <br>r_43: x4 + x12  <= 1 <br>r_44: x4 + x13  <= 1 <br>r_45: x4 + x14  <= 1 <br>r_46: x4 + x15  <= 1 <br>r_47: x4 + x16  <= 1 <br>r_48: x4 + x17  <= 1 <br>r_49: x5 + x6  <= 1 <br>r_50: x5 + x8  <= 1 <br>r_51: x5 + x9  <= 1 <br>r_52: x5 + x10  <= 1 <br>r_53: x5 + x11  <= 1 <br>r_54: x5 + x12  <= 1 <br>r_55: x5 + x13  <= 1 <br>r_56: x5 + x14  <= 1 <br>r_57: x5 + x16  <= 1 <br>r_58: x5 + x17  <= 1 <br>r_59: x6 + x7  <= 1 <br>r_60: x6 + x8  <= 1 <br>r_61: x6 + x9  <= 1 <br>r_62: x6 + x10  <= 1 <br>r_63: x6 + x11  <= 1 <br>r_64: x6 + x12  <= 1 <br>r_65: x6 + x13  <= 1 <br>r_66: x6 + x14  <= 1 <br>r_67: x6 + x15  <= 1 <br>r_68: x6 + x16  <= 1 <br>r_69: x6 + x17  <= 1 <br>r_70: x7 + x8  <= 1 <br>r_71: x7 + x9  <= 1 <br>r_72: x7 + x10  <= 1 <br>r_73: x7 + x11  <= 1 <br>r_74: x7 + x13  <= 1 <br>r_75: x7 + x14  <= 1 <br>r_76: x7 + x15  <= 1 <br>r_77: x7 + x16  <= 1 <br>r_78: x7 + x17  <= 1 <br>r_79: x8 + x9  <= 1 <br>r_80: x8 + x10  <= 1 <br>r_81: x8 + x12  <= 1 <br>r_82: x8 + x13  <= 1 <br>r_83: x8 + x14  <= 1 <br>r_84: x8 + x15  <= 1 <br>r_85: x8 + x16  <= 1 <br>r_86: x8 + x17  <= 1 <br>r_87: x9 + x10  <= 1 <br>r_88: x9 + x11  <= 1 <br>r_89: x9 + x12  <= 1 <br>r_90: x9 + x13  <= 1 <br>r_91: x9 + x14  <= 1 <br>r_92: x9 + x15  <= 1 <br>r_93: x9 + x16  <= 1 <br>r_94: x9 + x17  <= 1 <br>r_95: x10 + x11  <= 1 <br>r_96: x10 + x12  <= 1 <br>r_97: x10 + x13  <= 1 <br>r_98: x10 + x14  <= 1 <br>r_99: x10 + x15  <= 1 <br>r_100: x10 + x16  <= 1 <br>r_101: x10 + x17  <= 1 <br>r_102: x11 + x12  <= 1 <br>r_103: x11 + x13  <= 1 <br>r_104: x11 + x14  <= 1 <br>r_105: x11 + x15  <= 1 <br>r_106: x11 + x16  <= 1 <br>r_107: x11 + x17  <= 1 <br>r_108: x12 + x13  <= 1 <br>r_109: x12 + x14  <= 1 <br>r_110: x12 + x15  <= 1 <br>r_111: x12 + x16  <= 1 <br>r_112: x12 + x17  <= 1 <br>r_113: x13 + x14  <= 1 <br>r_114: x13 + x15  <= 1 <br>r_115: x13 + x16  <= 1 <br>r_116: x13 + x17  <= 1 <br>r_117: x14 + x15  <= 1 <br>r_118: x14 + x16  <= 1 <br>r_119: x14 + x17  <= 1 <br>r_120: x15 + x16  <= 1 <br>r_121: x15 + x17  <= 1 <br>r_122: x16 + x17  <= 1 <br>bin x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 <br><br>End <br><br />minimize <br>z: -0.067526 x1 -0.443697 x2 -0.245652 x3 -0.039244 x4 -0.170053 x5 -0.107182 x6 -0.164309 x7 -0.079877 x8 -0.083525 x9 -0.042542 x10 -0.149721 x11 -0.073411 x12 -0.062683 x13 -0.041302 x14 -0.090979 x15 -0.046144 x16 -0.025028 x17 <br>subject to <br>bw: 9 x1 + 8 x2 + 8 x3 + 8 x4 + 8 x5 + 8 x6 + 8 x7 + 8 x8 + 8 x9 + 8 x10 + 8 x11 + 8 x12 + 8 x13 + 8 x14 + 8 x15 + 8 x16 + 8 x17  >= 9 <br>r_1: x1 + x2  <= 1 <br>r_2: x1 + x3  <= 1 <br>r_3: x1 + x4  <= 1 <br>r_4: x1 + x5  <= 1 <br>r_5: x1 + x6  <= 1 <br>r_6: x1 + x7  <= 1 <br>r_7: x1 + x9  <= 1 <br>r_8: x1 + x10  <= 1 <br>r_9: x1 + x11  <= 1 <br>r_10: x1 + x12  <= 1 <br>r_11: x1 + x13  <= 1 <br>r_12: x1 + x14  <= 1 <br>r_13: x1 + x15  <= 1 <br>r_14: x1 + x16  <= 1 <br>r_15: x1 + x17  <= 1 <br>r_16: x2 + x3  <= 1 <br>r_17: x2 + x4  <= 1 <br>r_18: x2 + x5  <= 1 <br>r_19: x2 + x8  <= 1 <br>r_20: x2 + x10  <= 1 <br>r_21: x2 + x12  <= 1 <br>r_22: x2 + x13  <= 1 <br>r_23: x2 + x16  <= 1 <br>r_24: x2 + x17  <= 1 <br>r_25: x3 + x4  <= 1 <br>r_26: x3 + x6  <= 1 <br>r_27: x3 + x7  <= 1 <br>r_28: x3 + x8  <= 1 <br>r_29: x3 + x9  <= 1 <br>r_30: x3 + x10  <= 1 <br>r_31: x3 + x11  <= 1 <br>r_32: x3 + x12  <= 1 <br>r_33: x3 + x14  <= 1 <br>r_34: x3 + x15  <= 1 <br>r_35: x3 + x16  <= 1 <br>r_36: x4 + x5  <= 1 <br>r_37: x4 + x6  <= 1 <br>r_38: x4 + x7  <= 1 <br>r_39: x4 + x8  <= 1 <br>r_40: x4 + x9  <= 1 <br>r_41: x4 + x10  <= 1 <br>r_42: x4 + x11  <= 1 <br>r_43: x4 + x12  <= 1 <br>r_44: x4 + x13  <= 1 <br>r_45: x4 + x14  <= 1 <br>r_46: x4 + x15  <= 1 <br>r_47: x4 + x16  <= 1 <br>r_48: x4 + x17  <= 1 <br>r_49: x5 + x6  <= 1 <br>r_50: x5 + x8  <= 1 <br>r_51: x5 + x9  <= 1 <br>r_52: x5 + x10  <= 1 <br>r_53: x5 + x11  <= 1 <br>r_54: x5 + x12  <= 1 <br>r_55: x5 + x13  <= 1 <br>r_56: x5 + x14  <= 1 <br>r_57: x5 + x16  <= 1 <br>r_58: x5 + x17  <= 1 <br>r_59: x6 + x7  <= 1 <br>r_60: x6 + x8  <= 1 <br>r_61: x6 + x9  <= 1 <br>r_62: x6 + x10  <= 1 <br>r_63: x6 + x11  <= 1 <br>r_64: x6 + x12  <= 1 <br>r_65: x6 + x13  <= 1 <br>r_66: x6 + x14  <= 1 <br>r_67: x6 + x15  <= 1 <br>r_68: x6 + x16  <= 1 <br>r_69: x6 + x17  <= 1 <br>r_70: x7 + x8  <= 1 <br>r_71: x7 + x9  <= 1 <br>r_72: x7 + x10  <= 1 <br>r_73: x7 + x11  <= 1 <br>r_74: x7 + x13  <= 1 <br>r_75: x7 + x14  <= 1 <br>r_76: x7 + x15  <= 1 <br>r_77: x7 + x16  <= 1 <br>r_78: x7 + x17  <= 1 <br>r_79: x8 + x9  <= 1 <br>r_80: x8 + x10  <= 1 <br>r_81: x8 + x12  <= 1 <br>r_82: x8 + x13  <= 1 <br>r_83: x8 + x14  <= 1 <br>r_84: x8 + x15  <= 1 <br>r_85: x8 + x16  <= 1 <br>r_86: x8 + x17  <= 1 <br>r_87: x9 + x10  <= 1 <br>r_88: x9 + x11  <= 1 <br>r_89: x9 + x12  <= 1 <br>r_90: x9 + x13  <= 1 <br>r_91: x9 + x14  <= 1 <br>r_92: x9 + x15  <= 1 <br>r_93: x9 + x16  <= 1 <br>r_94: x9 + x17  <= 1 <br>r_95: x10 + x11  <= 1 <br>r_96: x10 + x12  <= 1 <br>r_97: x10 + x13  <= 1 <br>r_98: x10 + x14  <= 1 <br>r_99: x10 + x15  <= 1 <br>r_100: x10 + x16  <= 1 <br>r_101: x10 + x17  <= 1 <br>r_102: x11 + x12  <= 1 <br>r_103: x11 + x13  <= 1 <br>r_104: x11 + x14  <= 1 <br>r_105: x11 + x15  <= 1 <br>r_106: x11 + x16  <= 1 <br>r_107: x11 + x17  <= 1 <br>r_108: x12 + x13  <= 1 <br>r_109: x12 + x14  <= 1 <br>r_110: x12 + x15  <= 1 <br>r_111: x12 + x16  <= 1 <br>r_112: x12 + x17  <= 1 <br>r_113: x13 + x14  <= 1 <br>r_114: x13 + x15  <= 1 <br>r_115: x13 + x16  <= 1 <br>r_116: x13 + x17  <= 1 <br>r_117: x14 + x15  <= 1 <br>r_118: x14 + x16  <= 1 <br>r_119: x14 + x17  <= 1 <br>r_120: x15 + x16  <= 1 <br>r_121: x15 + x17  <= 1 <br>r_122: x16 + x17  <= 1 <br><br>bounds <br>0<=x1<=1 <br>0<=x2<=1 <br>0<=x3<=1 <br>0<=x4<=1 <br>0<=x5<=1 <br>0<=x6<=1 <br>0<=x7<=1 <br>0<=x8<=1 <br>0<=x9<=1 <br>0<=x10<=1 <br>0<=x11<=1 <br>0<=x12<=1 <br>0<=x13<=1 <br>0<=x14<=1 <br>0<=x15<=1 <br>0<=x16<=1 <br>0<=x17<=1 <br><br>End <br><br /><br>lpx_read_cpxlp: 123 rows, 17 columns, 261 non-zeros <br>lpx_read_cpxlp: 17 integer columns, all of which are binary <br>lpx_read_cpxlp: 129 lines were read <br>ipp_basic_tech:  0 row(s) and 0 column(s) removed <br>ipp_reduce_bnds: 1 pass(es) made, 0 bound(s) reduced <br>ipp_basic_tech:  0 row(s) and 0 column(s) removed <br>ipp_reduce_coef: 1 pass(es) made, 0 coefficient(s) reduced <br>lpx_intopt: presolved MIP has 123 rows, 17 columns, 261 non-zeros <br>lpx_intopt: 17 integer columns, all of which are binary <br>lpx_adv_basis: size of triangular part = 123 <br>Solving LP relaxation... <br>      0:   objval =   0.000000000e+00   infeas =   1.000000000e+00 (0) <br>      1:   objval =  -6.752600000e-02   infeas =   0.000000000e+00 (0) <br>*     1:   objval =  -6.752600000e-02   infeas =   0.000000000e+00 (0) <br>*    28:   objval =  -9.664375000e-01   infeas =   0.000000000e+00 (0) <br>OPTIMAL SOLUTION FOUND <br>Integer optimization begins... <br>+    28: mip =     not found yet >=              -inf        (1; 0) <br>+    57: mip =  -5.508790000e-01 >=  -9.664375000e-01  75.4% (10; 0) <br>+    85: mip =  -5.934180000e-01 >=  -7.280825000e-01  22.7% (6; 4) <br>+    90: mip =  -6.080060000e-01 >=  -6.825930000e-01  12.3% (3; 8) <br>+    94: mip =  -6.080060000e-01 >=     tree is empty   0.0% (0; 19) <br>INTEGER OPTIMAL SOLUTION FOUND <br>mip_x1= 0.000000 <br>mip_x2= 1.000000 <br>mip_x3= 0.000000 <br>mip_x4= 0.000000 <br>mip_x5= 0.000000 <br>mip_x6= 0.000000 <br>mip_x7= 1.000000 <br>mip_x8= 0.000000 <br>mip_x9= 0.000000 <br>mip_x10= 0.000000 <br>mip_x11= 0.000000 <br>mip_x12= 0.000000 <br>mip_x13= 0.000000 <br>mip_x14= 0.000000 <br>mip_x15= 0.000000 <br>mip_x16= 0.000000 <br>mip_x17= 0.000000 <br><br>The maximum reliability is 0.753399 with a bandwidth of 16.000000 <br>Press Enter to continue! <br>                                      <br><br /><br>lpx_read_cpxlp: 123 rows, 17 columns, 261 non-zeros <br>lpx_read_cpxlp: 147 lines were read <br>lpx_interior: original LP problem has 123 rows and 17 columns <br>lpx_interior: transformed LP problem has 140 rows and 157 columns <br>lpx_interior: A has 418 non-zeros <br>lpx_interior: S has 2170 non-zeros (upper triangle) <br>lpx_interior: minimal degree ordering... <br>lpx_interior: computing Cholesky factorization... <br>lpx_interior: U has 5794 non-zeros <br>lpx_interior: guessing initial point... <br>Optimization begins... <br>  0: obj =  -1.731631825e+00; rpi =  7.9e+00; rdi =  4.9e-01; gap =  6.3e-01 <br>  1: obj =  -5.196580854e-01; rpi =  1.0e+00; rdi =  4.9e-02; gap =  1.0e+00 <br>  2: obj =  -5.227116817e-01; rpi =  2.1e-01; rdi =  2.5e-02; gap =  6.1e-01 <br>  3: obj =  -6.436771531e-01; rpi =  1.0e-01; rdi =  1.2e-02; gap =  4.2e-01 <br>  4: obj =  -7.601544184e-01; rpi =  2.5e-02; rdi =  4.4e-03; gap =  2.1e-01 <br>  5: obj =  -8.501360191e-01; rpi =  8.6e-03; rdi =  1.5e-03; gap =  9.8e-02 <br>  6: obj =  -9.355881835e-01; rpi =  2.1e-03; rdi =  1.6e-04; gap =  2.4e-02 <br>  7: obj =  -9.627362019e-01; rpi =  2.6e-04; rdi =  1.7e-05; gap =  2.8e-03 <br>  8: obj =  -9.660661130e-01; rpi =  2.6e-05; rdi =  1.7e-06; gap =  2.8e-04 <br>  9: obj =  -9.664003600e-01; rpi =  2.6e-06; rdi =  1.7e-07; gap =  2.8e-05 <br> 10: obj =  -9.664337860e-01; rpi =  2.6e-07; rdi =  1.7e-08; gap =  2.8e-06 <br> 11: obj =  -9.664371286e-01; rpi =  2.6e-08; rdi =  1.7e-09; gap =  2.8e-07 <br> 12: obj =  -9.664374629e-01; rpi =  2.6e-09; rdi =  1.7e-10; gap =  2.8e-08 <br> 13: obj =  -9.664374963e-01; rpi =  2.6e-10; rdi =  1.7e-11; gap =  2.8e-09 <br>OPTIMAL SOLUTION FOUND <br>prim_ipt_x1= 0.500000 <br>prim_ipt_x2= 0.500000 <br>prim_ipt_x3= 0.500000 <br>prim_ipt_x4= 0.500000 <br>prim_ipt_x5= 0.500000 <br>prim_ipt_x6= 0.500000 <br>prim_ipt_x7= 0.500000 <br>prim_ipt_x8= 0.500000 <br>prim_ipt_x9= 0.500000 <br>prim_ipt_x10= 0.500000 <br>prim_ipt_x11= 0.500000 <br>prim_ipt_x12= 0.500000 <br>prim_ipt_x13= 0.500000 <br>prim_ipt_x14= 0.500000 <br>prim_ipt_x15= 0.500000 <br>prim_ipt_x16= 0.500000 <br>prim_ipt_x17= 0.500000 <br><br>The max. rel= 0.891965 with a bandwidth= 68.499999(prim) 0.000000(dual) <br>Press Enter to continue! <br>                                                  <br><br />_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26537881&i=4" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26533136 Re: Re: GLPK MingW build files and PyGLPK 2009-11-26T09:35:53Z 2009-11-26T09:35:53Z Andrew Makhorin > I've build glpsol.exe with MSYS and cygwin. <br>> Besides it's useful, the binary file has more than double sized and the <br>> solver looks like quite slower. <br><br>Under cygwin gcc is run with default options '-g' (that includes <br>debugging info into the executable) and '-O2'. On my 32-bit windows <br>machine I build glpk using 'make CFLAGS=-O3', and the code is about <br>30% faster than the one built with MSVS 2010 'cl -O3'. <br><br><br><br>_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26533136&i=0" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26528336 Gusek : a GLPK IDE for Windows - 0.2.7 2009-11-26T03:54:28Z 2009-11-26T03:54:28Z Luiz Bettoni Hi, All. <br><br>I've updated the Gusek project on SourceForge: <br>    <a href="http://gusek.sourceforge.net" target="_top" rel="nofollow">http://gusek.sourceforge.net</a><br><br><br>Release 0.2.7 changes: <br>  - GLPK updated to 4.40 - now GUSEK uses GLPK for Windows <br>    pre-build GLPK binaries (thanks to Xypron). <br>  - Added tips folder (gusek_tips), introducing useful <br>    samples to gusek users. <br>  - Added python files support (as in native SciTE) for <br>    PyMathProg modelling (testing). <br><br><br>Gusek provide an open source LP/MILP IDE for Win32, <br>packing a custom version of the SciTE editor linked to the <br>GLPK standalone solver (glpsol.exe). <br><br>Best Regards, <br>Luiz Bettoni <br><br><br><br><br><br>_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26528336&i=0" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26527551 Re: Re: Re: GLPK MingW build files and PyGLPK 2009-11-26T03:47:00Z 2009-11-26T03:47:00Z Luiz Bettoni <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> </head> <body bgcolor="#ffffff" text="#000000"> Hi, Nigel, Andrew.<br> <br> I've build glpsol.exe with MSYS and cygwin.<br> Besides it's useful, the binary file has more than double sized and the solver looks like quite slower.<br> <br> So, for my testing purposes, I'll use my own MingW build files. <br> In Gusek package I'll use Xypron pre-built files.<br> <br> Thanks, guys!<br> Luiz<br> <br> <br> At 16:59, Nigel Galloway wrote: <blockquote id="mid_%3C20091106120803_CBB5B7BD6E_ws5-10_us4_outblaze_com%3E" cite="mid:%3C20091106120803.CBB5B7BD6E@ws5-10.us4.outblaze.com%3E" type="cite"> <pre wrap="">You should probably add the MSYS extensions to MingW, these include a make utility compatible with Linux. This is what I usually use to compile glpk on windows using NetBeans rather than Visual C++ as the IDE. I make no changes. Good Luck, Nigel </pre> <blockquote id="StationeryCiteGenerated_1" type="cite"> <pre wrap="">----- Original Message ----- From: "Andrew Makhorin" <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26527551&i=0" target="_top" rel="nofollow">mao@...</a> To: "Luiz Bettoni" <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26527551&i=1" target="_top" rel="nofollow">bettoni@...</a> Cc: "help-glpk" <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26527551&i=2" target="_top" rel="nofollow">help-glpk@...</a> Subject: [Help-glpk] Re: GLPK MingW build files and PyGLPK Date: Thu, 5 Nov 2009 20:40:50 +0300 </pre> <blockquote id="StationeryCiteGenerated_2" type="cite"> <pre wrap="">You do not intend to include MingW w32 build files in GLPK package anymore? </pre> </blockquote> <blockquote id="StationeryCiteGenerated_3" type="cite"> <pre wrap="">On every GLPK launch i've patched them and sent to the list, but if no-one uses mingw to build GLPK (I'm alone? U), it's wast effort. </pre> </blockquote> <blockquote id="StationeryCiteGenerated_4" type="cite"> <pre wrap="">If MingW build files isn't util anymore, I'm planning replace Gusek glpsol binaries by winglpk pre-build ones. </pre> </blockquote> <pre wrap="">If you build only the glpsol executable, why not to use Cygwin? It allows configuring and building the package in the standard way. Is there anything specific in Gusek that requires Mingw? </pre> </blockquote> <pre wrap=""> </pre> <pre wrap=""> </pre> </blockquote> </body> </html> <br />_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26527551&i=3" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26525179 glpk and glpk-java 2009-11-25T23:12:17Z 2009-11-25T23:12:17Z Torben-5 Hi <br><br>I am using Ubuntu 9.04 and I have installed the glpk version 4.39. I <br>would like to install the java interface glpk-java version 1.0.6 <br>(<a href="http://sourceforge.net/projects/glpk-java/" target="_top" rel="nofollow">http://sourceforge.net/projects/glpk-java/</a>). When trying to compile the <br>package I get the compiler error: <br><br><br><br>mkdir -p src/java <br>mkdir -p java/org/gnu/glpk <br>swig -I/usr/local/include -I/usr/include -java -package org.gnu.glpk -o <br>src/java/glpk_wrap.c -outdir java/org/gnu/glpk glpk.i <br>libtool --mode=compile gcc -c -fPIC src/java/glpk_wrap.c <br>libtool: compile: gcc -c -fPIC src/java/glpk_wrap.c -fPIC -DPIC -o <br>.libs/glpk_wrap.o <br>src/java/glpk_wrap.c: In function ‘Java_org_gnu_glpk_GLPKJNI_glp_1vprintf’: <br>src/java/glpk_wrap.c:7672: error: incompatible types in assignment <br>make: *** [all] Error 1 <br><br><br>I am not an experienced c/c++ programmer, and can not immediately see <br>the problem. The source code for the function <br>Java_org_gnu_glpk_GLPKJNI_glp_1vprintf <br><br>SWIGEXPORT void JNICALL Java_org_gnu_glpk_GLPKJNI_glp_1vprintf(JNIEnv <br>*jenv, jclass jcls, jstring jarg1, jlong jarg2) { <br>char *arg1 = (char *) 0 ; <br>va_list arg2 ; <br>va_list *argp2 ; <br><br>(void)jenv; <br>(void)jcls; <br>arg1 = 0; <br>if (jarg1) { <br>arg1 = (char *)(*jenv)->GetStringUTFChars(jenv, jarg1, 0); <br>if (!arg1) return ; <br>} <br>argp2 = *(va_list **)&jarg2; <br>if (!argp2) { <br>SWIG_JavaThrowException(jenv, SWIG_JavaNullPointerException, "Attempt to <br>dereference null va_list"); <br>return ; <br>} <br>arg2 = *argp2; <br>glp_vprintf((char const *)arg1,arg2); <br>if (arg1) (*jenv)->ReleaseStringUTFChars(jenv, jarg1, (const char *)arg1); <br>} <br><br>and line 7672 is <br>arg2 = *argp2; <br><br>Any ideas to what is wrong, would be appreciated. <br><br>Best regards <br>Torben <br><br><br>_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26525179&i=0" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26518234 Re: Linear Programming Relaxation 2009-11-25T10:48:55Z 2009-11-25T10:48:55Z Andrew Makhorin > What does actually "2-approximation" "3-approximation" or <br>> "6-approximation" means? <br><br>See: <br><a href="http://en.wikipedia.org/wiki/Approximation_algorithm" target="_top" rel="nofollow">http://en.wikipedia.org/wiki/Approximation_algorithm</a><br><br><br><br>_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26518234&i=0" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26514147 Re: Linear Programming Relaxation 2009-11-25T07:00:42Z 2009-11-25T07:00:42Z Paul Loh <html><head></head><body><div style="font-family:arial, helvetica, sans-serif;font-size:18pt"><DIV>Hi David,</DIV> <DIV> </DIV> <DIV>Thank you very much for your reply. </DIV> <DIV> </DIV> <DIV>I hope you can help me on another question that I could not find the answer from the Internet.</DIV> <DIV> </DIV> <DIV>I read some papers that stated "2-approximation" "3-approximation" or "6-approximation" for example the paper titled:</DIV> <DIV> </DIV> <DIV>"Massaging a linear programming solution to give a 2-approximation for a generalization of the vertex cover problem"<BR></DIV> <DIV>What does actually "2-approximation" "3-approximation" or "6-approximation" means?</DIV> <DIV> </DIV> <DIV>Thank-you.</DIV> <DIV> </DIV> <DIV>Rdgs,</DIV> <DIV>Paul</DIV> <DIV> </DIV> <DIV style="FONT-FAMILY: arial, helvetica, sans-serif; FONT-SIZE: 18pt"><BR> <DIV style="FONT-FAMILY: arial, helvetica, sans-serif; FONT-SIZE: 13px"><FONT size=2 face=Tahoma> <HR SIZE=1> <B><SPAN style="FONT-WEIGHT: bold">From:</SPAN></B> David Bremner <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26514147&i=0" target="_top" rel="nofollow">bremner@...</a>><BR><B><SPAN style="FONT-WEIGHT: bold">To:</SPAN></B> RC Loh <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26514147&i=1" target="_top" rel="nofollow">rc_loh@...</a>><BR><B><SPAN style="FONT-WEIGHT: bold">Cc:</SPAN></B> <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26514147&i=2" target="_top" rel="nofollow">help-glpk@...</a><BR><B><SPAN style="FONT-WEIGHT: bold">Sent:</SPAN></B> Wednesday, 25 November 2009 8:54:12<BR><B><SPAN style="FONT-WEIGHT: bold">Subject:</SPAN></B> Re: [Help-glpk] Linear Programming Relaxation<BR></FONT><BR>RC Loh wrote:<BR><BR><BR>>Just to confirm on question (2). I understand that GLPK also uses<BR>>Interior Point method. Isn't the Interior Point method a polynomial<BR>>time method?<BR><BR>Yes it is, but for linear programming, not for integer or mixed<BR>integer programming.<BR><BR>>So with the Linear Programming Relaxation, the GLPK still does not<BR>>runs in polynomial time?<BR><BR>A MIP solver needs to solve a whole search tree where each node is an<BR>LP relaxation, and in general the number of LP relaxations solved is<BR>not bounded by a polynomial in the input size.  There are many books<BR>where this is explained; I happen to know "A First Course in<BR>Combinatorial Optimization" by Jon Lee, see Chapters 6 and 7.  <BR><BR>David<BR><BR></DIV></DIV></div><br> <hr size=1> <a href="http://sg.rd.yahoo.com/sg/mail/domainchoice/mail/signature/*http://mail.promotions.yahoo.com/newdomains/sg/" target="_top" rel="nofollow"> New Email names for you! </a> <br> Get the Email name you've always wanted on the new @ymail and @rocketmail.<br> Hurry before someone else does!</body></html><br />_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26514147&i=3" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26512164 Re: Linear Programming Relaxation 2009-11-25T04:54:12Z 2009-11-25T04:54:12Z David Bremner-4 RC Loh wrote: <br><br><br>>Just to confirm on question (2). I understand that GLPK also uses <br>>Interior Point method. Isn't the Interior Point method a polynomial <br>>time method? <br><br>Yes it is, but for linear programming, not for integer or mixed <br>integer programming. <br><br>>So with the Linear Programming Relaxation, the GLPK still does not <br>>runs in polynomial time? <br><br>A MIP solver needs to solve a whole search tree where each node is an <br>LP relaxation, and in general the number of LP relaxations solved is <br>not bounded by a polynomial in the input size.  There are many books <br>where this is explained; I happen to know "A First Course in <br>Combinatorial Optimization" by Jon Lee, see Chapters 6 and 7.   <br><br>David <br><br><br><br>_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26512164&i=0" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26510109 Callbacks in C# 2009-11-25T01:59:26Z 2009-11-25T01:59:26Z jezambranos Hi <br><br>Has anyone have used GLPKSharp to implement cut callbacks , is there a place where i can see an example ? <br><br><br>Sorry for the english <br><br>Regards <br>Javier <br />Hi<br /><br />Has anyone have used GLPKSharp to implement cut callbacks , is there a place where i can see an example ?<br /><br /><br />Sorry for the english<br /><br />Regards <br />Javier<br />_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26510109&i=0" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26507626 Re: Linear Programming Relaxation 2009-11-24T21:08:34Z 2009-11-24T21:08:34Z Paul Loh <html><head></head><body><div style="font-family:arial, helvetica, sans-serif;font-size:18pt"><DIV>Hi Andrew,</DIV> <DIV> </DIV> <DIV>Thank you very much for your reply.</DIV> <DIV> </DIV> <DIV>Just to confirm on question (2). I understand that GLPK also uses Interior Point method. Isn't the Interior Point method a polynomial time method?</DIV> <DIV> </DIV> <DIV>So with the Linear Programming Relaxation, the GLPK still does not runs in polynomial time?</DIV> <DIV> </DIV> <DIV>Rdgs,</DIV> <DIV>Paul</DIV> <DIV> </DIV> <DIV><BR> </DIV> <DIV style="FONT-FAMILY: arial, helvetica, sans-serif; FONT-SIZE: 18pt"><BR> <DIV style="FONT-FAMILY: arial, helvetica, sans-serif; FONT-SIZE: 13px"><FONT size=2 face=Tahoma> <HR SIZE=1> <B><SPAN style="FONT-WEIGHT: bold">From:</SPAN></B> Andrew Makhorin <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26507626&i=0" target="_top" rel="nofollow">mao@...</a>><BR><B><SPAN style="FONT-WEIGHT: bold">To:</SPAN></B> RC Loh <<a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26507626&i=1" target="_top" rel="nofollow">rc_loh@...</a>><BR><B><SPAN style="FONT-WEIGHT: bold">Cc:</SPAN></B> <a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26507626&i=2" target="_top" rel="nofollow">help-glpk@...</a><BR><B><SPAN style="FONT-WEIGHT: bold">Sent:</SPAN></B> Tuesday, 24 November 2009 11:10:13<BR><B><SPAN style="FONT-WEIGHT: bold">Subject:</SPAN></B> Re: [Help-glpk] Linear Programming Relaxation<BR></FONT><BR>> I have an Integer Program and I run the GLPK to solve it. I noticed<BR>> that the GLPK automatically turns ON the Linear Programming Relaxation<BR>> without me specifying it. I have 4 questions:<BR><BR>> 1) Can I turned OFF the Linear Programming Relaxation? Because I want<BR>> to let the GLPK run without the relaxation to see how long does the<BR>> program takes to produce a result.<BR><BR>Solving LP relaxation to optimality is needed to start the MIP<BR>search.<BR><BR>> 2) Can I say that we the Linear Programming Relaxation turns ON, the<BR>> program runs in polynomial time?<BR><BR>No. Neither the simplex method nor the branch-and-bound method is<BR>a polynomial time algorithm.<BR><BR>> 3) I understand that with the Linear Programming Relaxation turns on,<BR>> the programs actually produce an approximate result. But GLPK actually<BR>> corrected the approximated results automatically. Can I turn OFF the<BR>> correction of the approximation? Because I want to see the results<BR>> without the correction.<BR><BR>> 4) How GLPK correct the approximated results?<BR><BR>Optimal solution to LP relaxation is not an approximation to MIP<BR>solution, because it may be integer infeasible; it gives a global<BR>bound to MIP optimum.<BR><BR></DIV></DIV></div><br> <hr size=1> <a href="http://sg.rd.yahoo.com/sg/mail/domainchoice/mail/signature/*http://mail.promotions.yahoo.com/newdomains/sg/" target="_top" rel="nofollow"> New Email names for you! </a> <br> Get the Email name you've always wanted on the new @ymail and @rocketmail.<br> Hurry before someone else does!</body></html><br />_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26507626&i=3" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26498065 Re: Linear Programming Relaxation 2009-11-24T07:10:13Z 2009-11-24T07:10:13Z Andrew Makhorin > I have an Integer Program and I run the GLPK to solve it. I noticed <br>> that the GLPK automatically turns ON the Linear Programming Relaxation <br>> without me specifying it. I have 4 questions: <br><br>> 1) Can I turned OFF the Linear Programming Relaxation? Because I want <br>> to let the GLPK run without the relaxation to see how long does the <br>> program takes to produce a result. <br><br>Solving LP relaxation to optimality is needed to start the MIP <br>search. <br><br>> 2) Can I say that we the Linear Programming Relaxation turns ON, the <br>> program runs in polynomial time? <br><br>No. Neither the simplex method nor the branch-and-bound method is <br>a polynomial time algorithm. <br><br>> 3) I understand that with the Linear Programming Relaxation turns on, <br>> the programs actually produce an approximate result. But GLPK actually <br>> corrected the approximated results automatically. Can I turn OFF the <br>> correction of the approximation? Because I want to see the results <br>> without the correction. <br><br>> 4) How GLPK correct the approximated results? <br><br>Optimal solution to LP relaxation is not an approximation to MIP <br>solution, because it may be integer infeasible; it gives a global <br>bound to MIP optimum. <br><br><br><br>_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26498065&i=0" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p> tag:old.nabble.com,2006:post-26496144 Linear Programming Relaxation 2009-11-24T05:45:06Z 2009-11-24T05:45:06Z Paul Loh <html><head></head><body><div style="font-family:arial, helvetica, sans-serif;font-size:18pt;color:#407f00;"><DIV>Hi,</DIV> <DIV> </DIV> <DIV>I have an Integer Program and I run the GLPK to solve it. I noticed that the GLPK automatically turns ON the Linear Programming Relaxation without me specifying it. I have 4 questions:</DIV> <DIV> </DIV> <DIV>1) Can I turned OFF the Linear Programming Relaxation? Because I want to let the GLPK run without the relaxation to see how long does the program takes to produce a result.</DIV> <DIV> </DIV> <DIV>2) Can I say that we the Linear Programming Relaxation turns ON, the program runs in polynomial time?</DIV> <DIV> </DIV> <DIV>3) I understand that with the Linear Programming Relaxation turns on, the programs actually produce an approximate result. But GLPK actually corrected the approximated results automatically. Can I turn OFF the correction of the approximation? Because I want to see the results without the correction.</DIV> <DIV> </DIV> <DIV>4) How GLPK correct the approximated results?</DIV> <DIV> </DIV> <DIV>Thank you.</DIV> <DIV> </DIV> <DIV>Rdgs,</DIV> <DIV>Paul</DIV> <DIV> </DIV></div><br> <hr size=1> <a href="http://sg.rd.yahoo.com/sg/mail/domainchoice/mail/signature/*http://mail.promotions.yahoo.com/newdomains/sg/" target="_top" rel="nofollow"> Get your new Email address! </a> <br> Grab the Email name you've always wanted before someone else does!</body></html><br />_______________________________________________ <br>Help-glpk mailing list <br><a href="http://old.nabble.com/user/SendEmail.jtp?type=post&post=26496144&i=0" target="_top" rel="nofollow">Help-glpk@...</a> <br><a href="http://lists.gnu.org/mailman/listinfo/help-glpk" target="_top" rel="nofollow">http://lists.gnu.org/mailman/listinfo/help-glpk</a><br><p>From forum: <a href="http://old.nabble.com/Gnu---GLPK---Help-f1654.html" embed="fixTarget[1654]" target="_top" >Gnu - GLPK - Help</a></p>