A multi-objective evolutionary approach for nonlinear constrained optimization with fuzzy costs

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 the decision maker needs to check out several decisions in order to establish the more appropriates. In this sense, multi-objective optimization is similar to fuzzy optimization, since it\´s also desirable to capture the Pareto front composing the solution. 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 arising in some import-export companies in the south of Spain is analyzed and the proposed solutions from the evolutionary algorithm here considered are shown.