Solving a Fuzzy Nonlinear Optimization Problem by an “ad hoc” Multi-objective Evolutionary Algorithm

A fuzzy optimization problem arising in some import-export companies in the south of Spain is presented. In Fuzzy Optimization is desirable that fuzzy solutions can be really attained because then the decision maker will be able of making a decision “a posteriori” according to the current decision environment. In this way, no more runs of the optimization technique are needed when decision environment changes or when decision maker requires check out several decisions in order to establish the more appropriates. Multi-objective optimization can obtain the solution of a fuzzy optimization problem, since capturing the Pareto front we are able composing the solution fuzzy. Multi-objective Evolutionary algorithms have been shown in the last few years as powerful techniques to solve multi-objective optimization problems because they can search for multiple Pareto solutions in a single run of the algorithm. In this contribution we first introduce a multi-objective approach for nonlinear constrained optimization problems with fuzzy costs, and then an “ad hoc” multi-objective evolutionary algorithm to solve the former problem. A case-study of a fuzzy optimization problem is analyzed and the proposed solutions from the evolutionary algorithm here considered are shown.