Fuzzy optimization with multi-objective evolutionary algorithms: A case study

This paper outlines a real-world industrial problem for product-mix selection involving 8 decision variables and 21 constraints with fuzzy coefficients. On one hand, a multi-objective optimization approach to solve the fuzzy problem is proposed. Modified S-curve membership functions are considered. On the other hand, an ad hoc Pareto-based multi-objective evolutionary algorithm to capture multiple non dominated solutions in a single run of the algorithm is described. Solutions in the Pareto front corresponds with the fuzzy solution of the former fuzzy problem expressed in terms of the group of three (x→, μ, α), i.e., optimal solution - level of satisfaction - vagueness factor. Decision-maker could choose, in a posteriori decision environment, the most convenient optimal solution according to his level of satisfaction and vagueness factor. The proposed algorithm has been evaluated with the existing methodologies in the field and the results have been compared with the well-known multi-objective evolutionary algorithm NSGA-II. © 2007 IEEE.