Linear Mixed Integer Program Solver 1.0 Description

Description: 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 MdoTeszdodAros 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.

This function solves the mixed integer linear programming problems. It uses the linprog.m function that comes with the optimization toolbox of MATLAB. It employs the branch and bound algorithm. It uses depth first search

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