A Parametric Mixed-Integer Optimization Algorithm for Multiobjective Engineering Problems Involving Discrete Decisions

Abstract

An iterative, decomposition-based algorithm is proposed in this paper, for the solution of convex parametric MINLP problems and, in extension, the identification of the noninferior solution set in multiobjective problems involving continuous and discrete decisions. The parametric optimal solution is constructed via an upper- and lower-bound procedure. Parametric upper bounds are identified with the solution of parametric NLP problems, while the parametric lower bound is updated in each iteration via the solution of a parametric MILP Master problem, which involves only the binary variables of the initial problem. Convergence properties and computational requirements are discussed in example problems from process synthesis under uncertainty and simultaneous product/process design.