Usage of Summation in LP Solve

[stanleyy_2000]

Hi,

I'm a new user of lp_solve version 5.5.0.15.

It looks incredibly user-friendly and easy to use, but I am not sure if there is a way, without using external language, to key in constraints involving summation?

More specifically, a few of my constraints involve something like Summation (from i = 1 to i = 30) * Summation (from j = 1 to j = 20) * function

For the above case, also, how do I declare "i" and "j", knowing that they are just subscripts to variables, (i.e. Fi = ki + ....)

There doesn't seem to have an issue addressing summation in th lp_solve refernce guide and I do not know the names for "i" and "j"so I have difficulty searching for help regarding this issue too.

Many thanks in advance.

Stan

[William H. Patton]

See the references to GNU Mathprog from the search page of the online docs.

It is a model description language that includes sets and summation and data
separation from structure.

http://lpsolve.sourceforge.net/5.5/

http://lpsolve.sourceforge.net/5.5/MathProg.htm

http://lpsolve.sourceforge.net/5.5/XLI.htm

 

It is easiest to use via the solver IDE.

http://lpsolve.sourceforge.net/5.5/IDE.htm

 

Here is an example

/* QUEENS, a classic combinatorial optimization problem */

 

/* Written in GNU MathProg by Andrew Makhorin <mao@...> */

 

/* The Queens Problem is to place as many queens as possible on the 8x8

   (or more generally, nxn) chess board in a way that they do not fight

   each other. This problem is probably as old as the chess game itself,

   and thus its origin is not known, but it is known that Gauss studied

   this problem. */

 

param n, integer, > 0, default 8;

/* size of the chess board */

 

var x{1..n, 1..n}, binary;

/* x[i,j] = 1 means that a queen is placed in square [i,j] */

 

s.t. a{i in 1..n}: sum{j in 1..n} x[i,j] <= 1;

/* at most one queen can be placed in each row */

 

s.t. b{j in 1..n}: sum{i in 1..n} x[i,j] <= 1;

/* at most one queen can be placed in each column */

 

s.t. c{k in 2-n..n-2}: sum{i in 1..n, j in 1..n: i-j == k} x[i,j] <= 1;

/* at most one queen can be placed in each "\"-diagonal */

 

s.t. d{k in 3..n+n-1}: sum{i in 1..n, j in 1..n: i+j == k} x[i,j] <= 1;

/* at most one queen can be placed in each "/"-diagonal */

 

maximize obj: sum{i in 1..n, j in 1..n} x[i,j];

/* objective is to place as many queens as possible */

 

/* solve the problem */

solve;

 

end

 

 

  _____  

From: lp_solve@... [mailto:lp_solve@...] On Behalf
Of stanleyy_2000
Sent: Saturday, October 24, 2009 4:49 AM
To: lp_solve@...
Subject: [lp_solve] Usage of Summation in LP Solve

 

 

Hi,

I'm a new user of lp_solve version 5.5.0.15.

It looks incredibly user-friendly and easy to use, but I am not sure if
there is a way, without using external language, to key in constraints
involving summation?

More specifically, a few of my constraints involve something like Summation
(from i = 1 to i = 30) * Summation (from j = 1 to j = 20) * function

For the above case, also, how do I declare "i" and "j", knowing that they
are just subscripts to variables, (i.e. Fi = ki + ....)

There doesn't seem to have an issue addressing summation in th lp_solve
refernce guide and I do not know the names for "i" and "j"so I have
difficulty searching for help regarding this issue too.

Many thanks in advance.

Stan

[jcabetas]

All summation of a summation can be developed as a single summation, and hence, a linear equation...

--- In lp_solve@..., "stanleyy_2000" <stanleyy_2000@...> wrote:

>
> Hi,
>
> I'm a new user of lp_solve version 5.5.0.15.
>
> It looks incredibly user-friendly and easy to use, but I am not sure if there is a way, without using external language, to key in constraints involving summation?
>
> More specifically, a few of my constraints involve something like Summation (from i = 1 to i = 30) * Summation (from j = 1 to j = 20) * function
>
> For the above case, also, how do I declare "i" and "j", knowing that they are just subscripts to variables, (i.e. Fi = ki + ....)
>
> There doesn't seem to have an issue addressing summation in th lp_solve refernce guide and I do not know the names for "i" and "j"so I have difficulty searching for help regarding this issue too.
>
> Many thanks in advance.
>
> Stan
>

[Peter Notebaert-2]

And an alternative is ZIMPL, used in the same way as MathProg.

Peter

On Sat, Oct 24, 2009 at 4:44 PM, William H. Patton <pattonwh@...>wrote:

>
>
>  See the references to GNU Mathprog from the search page of the online
> docs.
>
> It is a model description language that includes sets and summation and
> data separation from structure.
>
> http://lpsolve.sourceforge.net/5.5/
>
> http://lpsolve.sourceforge.net/5.5/MathProg.htm
>
> http://lpsolve.sourceforge.net/5.5/XLI.htm
>
>
>
> It is easiest to use via the solver IDE.
>
> http://lpsolve.sourceforge.net/5.5/IDE.htm
>
>
>
> Here is an example
>
> /* QUEENS, a classic combinatorial optimization problem */
>
>
>
> /* Written in GNU MathProg by Andrew Makhorin <mao@...> */
>
>
>
> /* The Queens Problem is to place as many queens as possible on the 8x8
>
>    (or more generally, nxn) chess board in a way that they do not fight
>
>    each other. This problem is probably as old as the chess game itself,
>
>    and thus its origin is not known, but it is known that Gauss studied
>
>    this problem. */
>
>
>
> param n, integer, > 0, default 8;
>
> /* size of the chess board */
>
>
>
> var x{1..n, 1..n}, binary;
>
> /* x[i,j] = 1 means that a queen is placed in square [i,j] */
>
>
>
> s.t. a{i in 1..n}: sum{j in 1..n} x[i,j] <= 1;
>
> /* at most one queen can be placed in each row */
>
>
>
> s.t. b{j in 1..n}: sum{i in 1..n} x[i,j] <= 1;
>
> /* at most one queen can be placed in each column */
>
>
>
> s.t. c{k in 2-n..n-2}: sum{i in 1..n, j in 1..n: i-j == k} x[i,j] <= 1;
>
> /* at most one queen can be placed in each "\"-diagonal */
>
>
>
> s.t. d{k in 3..n+n-1}: sum{i in 1..n, j in 1..n: i+j == k} x[i,j] <= 1;
>
> /* at most one queen can be placed in each "/"-diagonal */
>
>
>
> maximize obj: sum{i in 1..n, j in 1..n} x[i,j];
>
> /* objective is to place as many queens as possible */
>
>
>
> /* solve the problem */
>
> solve;
>
>
>
> end
>
>
>
>
>  ------------------------------
>
> *From:* lp_solve@... [mailto:lp_solve@...] *On
> Behalf Of *stanleyy_2000
> *Sent:* Saturday, October 24, 2009 4:49 AM
> *To:* lp_solve@...
> *Subject:* [lp_solve] Usage of Summation in LP Solve
>
>
>
>
>
> Hi,
>
> I'm a new user of lp_solve version 5.5.0.15.
>
> It looks incredibly user-friendly and easy to use, but I am not sure if
> there is a way, without using external language, to key in constraints
> involving summation?
>
> More specifically, a few of my constraints involve something like Summation
> (from i = 1 to i = 30) * Summation (from j = 1 to j = 20) * function
>
> For the above case, also, how do I declare "i" and "j", knowing that they
> are just subscripts to variables, (i.e. Fi = ki + ....)
>
> There doesn't seem to have an issue addressing summation in th lp_solve
> refernce guide and I do not know the names for "i" and "j"so I have
> difficulty searching for help regarding this issue too.
>
> Many thanks in advance.
>
> Stan
>
>
>

[Sisira Jayasinghe]

I tried to solve the example from the help page for integer variables using
LPSolve IDE 5.5.0.15.

 

min: -x1 -2 x2 +0.1 x3 +3 x4;

r_1: +x1 +x2 <= 5;

r_2: +2 x1 -x2 >= 0;

r_3: -x1 +3 x2 >= 0;

r_4: +x3 +x4 >= 0.5;

x3 >= 1.1;

 

int x3;

 

The solution I get for x3 is 1.1 .

 

What am I doing wrong? Please help.

 

Sisira

 

 

 

[Peter Notebaert-2]

I can only imagine that you checked the checkbox to ignore integer restrictions in the settings of the IDE.

Peter

--- In lp_solve@..., "Sisira Jayasinghe" <sisirajaya@...> wrote:

>
> I tried to solve the example from the help page for integer variables using
> LPSolve IDE 5.5.0.15.
>
>  
>
> min: -x1 -2 x2 +0.1 x3 +3 x4;
>
> r_1: +x1 +x2 <= 5;
>
> r_2: +2 x1 -x2 >= 0;
>
> r_3: -x1 +3 x2 >= 0;
>
> r_4: +x3 +x4 >= 0.5;
>
> x3 >= 1.1;
>
>  
>
> int x3;
>
>  
>
> The solution I get for x3 is 1.1 .
>
>  
>
> What am I doing wrong? Please help.
>
>  
>
> Sisira
>

[Sisira Jayasinghe]

Hi Peter:

You are correct that setting was checked. But that was by default, out of
the box. I did not make any settings changes.

 

Thank you very much for your quick help.

Sisira

 

 

From: lp_solve@... [mailto:lp_solve@...] On Behalf
Of peter_notebaert
Sent: Tuesday, November 03, 2009 9:32 AM
To: lp_solve@...
Subject: [lp_solve] Re: integer variables

 

 

I can only imagine that you checked the checkbox to ignore integer
restrictions in the settings of the IDE.

Peter

--- In lp_solve@... <mailto:lp_solve%40yahoogroups.com> ,
"Sisira Jayasinghe" <sisirajaya@...> wrote:
>
> I tried to solve the example from the help page for integer variables
using

> LPSolve IDE 5.5.0.15.
>
>
>
> min: -x1 -2 x2 +0.1 x3 +3 x4;
>
> r_1: +x1 +x2 <= 5;
>
> r_2: +2 x1 -x2 >= 0;
>
> r_3: -x1 +3 x2 >= 0;
>
> r_4: +x3 +x4 >= 0.5;
>
> x3 >= 1.1;
>
>
>
> int x3;
>
>
>
> The solution I get for x3 is 1.1 .
>
>
>
> What am I doing wrong? Please help.
>
>
>
> Sisira
>