A framework for incorporating trade-off information using multi-objective evolutionary algorithms

Since their inception, multi-objective evolutionary algorithms have been adequately applied in finding a diverse approximation of efficient fronts of multi-objective optimization problems. In contrast, if we look at the rich history of classical multi-objective algorithms, we find that incorporation of user preferences has always been a major thrust of research. In this paper, we provide a general structure for incorporating preference information using multi-objective evolutionary algorithms. This is done in an NSGA-II scheme and by considering trade-off based preferences that come from so called proper Pareto-optimal solutions. We argue that finding proper Pareto-optimal solutions requires a set to compare with and hence, population based approaches should be a natural choice. Moreover, we suggest some practical modifications to the classical notion of proper Pareto-optimality. Computational studies on a number of test problems of varying complexity demonstrate the efficiency of multi-objective evolutionary algorithms in finding the complete preferred region for a large class of complex problems. We also discuss a theoretical justification for our NSGA-II based framework.