Assessment of a hybrid approach for nonconvex constrained MINLP problems

Abstract

A methodology to solve nonconvex constrained mixed-integer nonlinear programming (MINLP) problems is presented. A MINLP problem is one where some of the variables must have only integer values. Since in most applications of the industrial processes, some problem variables are restricted to take discrete values only, there are real practical problems that are modeled as nonconvex constrained MINLP problems. An efficient deterministic method for solving nonconvex constrained MINLP may be obtained by using a clever extension of Branch-and-Bound (B&B) method. When solving the relaxed nonconvex nonlinear programming subproblems that arise in the nodes of a tree in a B&B algorithm, using local search methods, only convergence to local optimal solutions is guaranteed. Pruning criteria cannot be used to avoid an exhaustive search in the search space. To address this issue, we propose the use of a genetic algorithm to promote convergence to a global optimum of the relaxed nonconvex NLP subproblem. We present some numerical experiments with the proposed algorithm.