MINLP: Mixed Integer Nonlinear Programming

Mixed Integer Nonlinear Programming Solver with APM MATLAB

Solves the mixed integer nonlinear problem:

min p(x,y)

s.t. f(x,y) <= 0
s.t. g(x,y) == 0
s.t. lb <= x <= ub
s.t. nlb <= y <= nub
x(yidx) integer where yidx is a logical index vector
y continuous variables

This program solves nonlinear mixed integer problems with a branch and bound method. NLP relaxations are solved with IPOPT or APOPT.

Files:
minlp.m - Solve the example MINLP problem
minlp.apm - MINLP problem definition
Other:
APM Function Library (v.0.5.6) in folder
Further work:
Add heuristics to create a good initial integer solution
Add cuts to the problem (branch and cut method)

Some testing shows that it works well with up to around 30 integer variables and 10000 NLP variables. Solutions to NLP relaxations are solved as a web-service. With the network communication overhead, the solution time may be slower than other MINLP solvers such as DICOPT, BONMIN, etc. This program is intended for educational purposes and to attract collaborators for future developments. The release notes and development roadmap are listed at the APMonitor.com web-site:

http://apmonitor.com/wiki/index.php/Main/ProductRoadmap