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<h1 align="left"><u>Zimpl</u></h1>
<p>Zimpl is a language to translate the mathematical model of a problem into a linear or (mixed-) integer mathematical program expressed in .lp or .mps file format which can be read and (hopefully) solved by a LP or MIP solver.</p>
<p>See <a href="http://www.zib.de/koch/zimpl/">http://www.zib.de/koch/zimpl/</a> for the home page of this tool and examples.</p>
<p>On the above page, a command line tool is provided to read a model written in the Zimpl language and it creates a CPLEX lp file.
lp_solve is able to read this generated CPLEX lp file via the xli_CPLEX XLI driver, but that would require an extra step.<br>
lp_solve can read/write and solve these Zimpl models directly via the xli_Zimpl XLI driver (see <a href="XLI.htm">External Language Interfaces</a>).
It reads such a model in above format and can solve it then.<br>
Also note that the XLI driver depends on an external dll: zlib1.dll. When it cannot be found on the system, an appropriate
message will be given. This dll must be in a directory specified by the Path environment variable. A common place
is c:\windows\system32. The dll is distributed with the package. The latest version can be found at <a href="http://www.zlib.net/">http://www.zlib.net/</a><br>
<br>
For example:</p>
<pre>
lp_solve -rxli xli_Zimpl <a href="#chvatal_diet.zpl">chvatal_diet.zpl</a>
</pre>
<p>This gives as result:</p>
<pre>
Value of objective function: 97
Actual values of the variables:
x$Oatmeal 4
x$Chicken 0
x$Eggs 0
x$Milk 5
x$Pie 2
x$Pork 0
</pre>
<h4>Options</h4>
<p>The XLI accepts several options:</p>
<pre>
-b Enable Bison (Lex parser) debugging output.
-D name=value Sets the parameter name to the specified value.
This is equivalent with having this line in the ZIMPL program: param name:=val.
-f enable flex debugging output.
-n cm|cn|cf name column make/name/full
-O Try to reduce the generated LP by doing some presolve analysis.
-s seed Positive seed number for the random number generator.
-v[0-5] Set the verbosity level. 0 is quiet, 1 is default, 2 is verbose, 3 and 4 are chatter, and 5 is debug.
-V show version info
</pre>
<p>These options are the same as the stand-alone zimpl program.</p>
<p>The <a href="lp_solve.htm">lp_solve command</a> line program can provide these parameters via the -rxliopt argument.<br>
<br>
For example:</p>
<pre>
lp_solve -rxli xli_Zimpl <a href="#chvatal_diet.zpl">chvatal_diet.zpl</a> -rxliopt "-v0 -O"
</pre>
<h4>Generating ZIMPL models</h4>
<p>The XLI can also create a ZIMPL model, however it doesn't use the strength of the language.
Constraints are written out line per line. But it can be a starter.
For example:</p>
<pre>
lp_solve <a href="#model.lp">model.lp</a> -wxli xli_Zimpl model.zpl
</pre>
<p>This gives as model.zpl:</p>
<pre>
# Variable definitions
var x >= 0;
var y >= 0;
# Objective function
maximize obj: +143*x +60*y;
# Constraints
subto R1: +120*x +210*y <= 15000;
subto R2: +110*x +30*y <= 4000;
subto R3: +x +y <= 75;
</pre>
<h4>API</h4>
<p>Use the lpsolve API call <a href="read_XLI.htm">read_XLI</a> to read a model
and <a href="write_XLI.htm">write_XLI</a> to write a model.
See also <a href="XLI.htm">External Language Interfaces</a>.
</p>
<h4>IDE</h4>
<p>Also from within the IDE, this XLI can be used. However, some entries
must be added in LpSolveIDE.ini (in the folder where the IDE is installed).
</p>
<p>In the [XLI] section the following must be added:</p>
<pre>
lib5=xli_ZIMPL
</pre>
<p>And a new section for the ZIMPL XLI must also be added:</p>
<pre>
[xli_ZIMPL]
extension=.zpl
language=ZIMPL
</pre>
<p>Then make sure that the xli_ZIMPL.dll is available for the IDE.
This must be done by placing this dll in the IDE folder or in the
Windows system32 folder.</p>
<h4>Example models</h4>
<a name="chvatal_diet.zpl"></a>
<h5>chvatal_diet.zpl</h5>
<pre>
# $Id: chvatal_diet.zpl,v 1.2 2003/10/02 08:20:12 bzfkocht Exp $
#
# From V. Chvatal: Linear Programming
# Chapter 1, Page 3ff.
#
# A diet problem
#
set Food := { "Oatmeal", "Chicken", "Eggs", "Milk", "Pie", "Pork" };
set Nutrients := { "Energy", "Protein", "Calcium" };
set Attr := Nutrients + {"Servings", "Price"};
param needed[Nutrients] := <"Energy"> 2000, <"Protein"> 55, <"Calcium"> 800;
param data[Food * Attr] :=
| "Servings", "Energy", "Protein", "Calcium", "Price" |
|"Oatmeal" | 4 , 110 , 4 , 2 , 3 |
|"Chicken" | 3 , 205 , 32 , 12 , 24 |
|"Eggs" | 2 , 160 , 13 , 54 , 13 |
|"Milk" | 8 , 160 , 8 , 284 , 9 |
|"Pie" | 2 , 420 , 4 , 22 , 20 |
|"Pork" | 2 , 260 , 14 , 80 , 19 |;
# (kcal) (g) (mg) (cents)
var x[<f> in Food] integer >= 0 <= data[f, "Servings"];
minimize cost: sum <f> in Food : data[f, "Price"] * x[f];
subto need :
forall <n> in Nutrients do
sum <f> in Food : data[f, n] * x[f] >= needed[n];
</pre>
<a name="model.lp"></a>
<h5>model.lp</h5>
<pre>
/* model.lp */
max: 143 x + 60 y;
120 x + 210 y <= 15000;
110 x + 30 y <= 4000;
x + y <= 75;
</pre>
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