Multi-objective evolutionary computation and fuzzy optimization

In fuzzy optimization it is desirable that all fuzzy solutions under consideration be attainable, so that the decision maker will be able to make ‘‘a posteriori’’ decisions according to current decision environments. No additional optimization runs will be needed when the decision environment changes or when the decision maker needs to evaluate several decisions to establish the most appropriate ones. In this sense, multi-objective optimization is similar to fuzzy optimization, since it is also desirable to capture the Pareto front composing the solution. The Pareto front in a multi-objective problem can be interpreted as the fuzzy solution for a fuzzy problem. Multi-objective evolutionary algorithms have been shown in the last few years to be powerful techniques in solving 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 constraints, 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 considered here are given. 2006 Elsevier Inc. All rights reserved.