Assessment of a Hybrid Approach for Nonconvex Constrained MINLP Problems
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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.
