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Linear Mixed Integer Program Solver

version 1.1 (9.08 KB) by

Solve linear mixed integer problems with a branch and bound method.

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Solves the mixed integer linear problem:

min c'*x

s.t. A*x <= b
s.t. Aeq*x == beq
s.t. lb <= x <= ub
x(yidx) integer

where yidx is a logical index vector.

This program solves linear mixed integer problems with a branch and bound method. It is highly recommended to use a different solver than linprog for solving the lp-relaxations. There are three good alternatives
available online with pre-compiled mex files:
1. CLP by the COIN-OR project.
  MEX interface can be found at:
  http://control.ee.ethz.ch/~joloef/clp.php
2. BPMPD by Csaba Mészáros
  MEX interface can be found at:
  http://www.pserc.cornell.edu/bpmpd/
3. QSOPT by David Applegate, William Cook, Sanjeeb Dash, and Monika Mevenkamp
  MEX interface can be found at:
  http://control.ee.ethz.ch/~joloef/mexqsopt.msql
 
Functions:
miprog - Solve the linear mip problem
mipoptions - Loads default options, see source for explanation
lpr - Solves the lp relaxation
miptest - Runs a tiny test problem
Other:
testproblem.mat - Contains a small testproblem
 
Further work:
Add heuristics to create a good initial integer solution
Add cuts to the problem (branch and cut method)
 
Some testing with the problem shows that it works well with up to
around 30 integer variables and 10000 lp variables if you use qsopt or
clp. However, the performance is far from that of commercial solvers;
this program is intended for educational purposes.

Comments and Ratings (6)

Christos

Note the updated links for CLP and QSOPT solvers:
1. CLP by the COIN-OR project.
  MEX interface can be found at:
  http://control.ee.ethz.ch/~johanl/clp.php
3. QSOPT by David Applegate, William Cook, Sanjeeb Dash, and Monika Mevenkamp
  MEX interface can be found at:
  http://control.ee.ethz.ch/~johanl/mexqsopt.msql

BIG Y.

BIG Y. (view profile)

I like to use this file for the folowing mathematical model but I have never used Matlab before. Can some one help please?

Minimize Somme of X(ik(i)) for i=1 to k

subject to:

 X(ik)- T(ijk) >= X(ih)
 X(pk)- X(ik)+ H *[1-Y(ipk)] >= T(pqk)
 X(ik)- X(pk)+ H *[Y(ipk)] >= T(ijk)
 X(ik)>=0
 Y(ipk)= 0 or 1

 

  

its a good implementation for MINLP

Mariano

Thanks for your work.
I have a question: why " It is highly recommended to use a different solver than linprog for solving the lp-relaxations" ?

Petter

Petter (view profile)

Why use this instead of YALMIP?

Updates

1.1

Added better description

MATLAB Release
MATLAB 7.9 (R2009b)
Acknowledgements

Inspired: MINLP: Mixed Integer Nonlinear Programming

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