Evolutionary Multiobjective Optimization Using a Fuzzy-based Dominance Concept

One aspect that is often disregarded in evolutionary multiobjective research is the fact that the solution of a problem involves not only search but decision making. Most of approaches concentrate on adapting an evolutionary algorithm to generate the Pareto frontier. In this work we present a new idea to incorporate preferences in MOEA. We introduce a binary fuzzy preference relation that expresses the degree of truth of the predicate “x is at least as good as y”. On this basis, a strict preference relation with a reasonable high degree of credibility can be established on any population. An alternative x is not strictly outranked if and only if there does not exist an alternative y which is strictly preferred to x. It is easy to prove that the best solution is not strictly outranked. We used the Nondominated Sorting Genetic Algorithm II (NSGA-II), but replacing dominance by the above non-outranked concept. So, we search for the nostrictly outranked frontier that is a proper subset of the Pareto frontier. In several instances of a nineobjective knapsack problem our proposal clearly outperforms the standard NSGA-II, achieving non-outranked solutions which are in an obvious privileged zone of the Pareto frontier.