Is there an algorithm to transform an arbitrary Mixed Integer Programming problem into the corresponding formulation for Particle Swarm Optimization? I have found some information related to the use of penalty functions to avoid violation of constraints, but not a well defined procedure to convert the objective function and each of the constraints as required for a PSO solution.
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$\begingroup$ Note that MIP is a problem formulation and PSO is a heuristic. So what you mean is that you're asking how to solve an MIP using PSO. $\endgroup$ – Suresh Venkat Jun 21 '11 at 21:21
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$\begingroup$ Suresh, I am not asking how to solve the MIP problem using PSO: I know how PSO works and I have already implemented in C and MPI parallel versions of PSO to solve other problems. What I am asking for is how to translate the MIP problem in the corresponding PSO function whose fitness must be optimized. $\endgroup$ – Massimo Cafaro Jun 22 '11 at 11:06
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Ok, I have found how to do this by reading Introduction to Mathematical Optimization: From Linear Programming to Metaheuristics. Chapters 7 and 10 clearly explain the possibilities, essentially the penalty method and the use of Lagrange multipliers coupled with Kuhn-Tucker conditions if necessary.
