Multi-Objective EAs And Game Theory

Abstract

The traditional way to address the problem of multiple objective optimization is to associate a scalar objective, generally obtained through some linear combination of weighted objectives. Such an approach may be of interest in some cases—particularly if the weight of each criterion is known beforehand—but besides its ad hoc character, it has several drawbacks since there is a loss of information and a need to define the weights associated to each objective. Moreover, the behavior of the algorithm is very sensitive and is biased by the values of these weights. Schaffer was the first to propose a Genetic Algorithm approach in 1985 for multiple objectives through his Vector Evaluated Genetic Algorithms, but it was biased towards the extrema of each objective. Goldberg proposed a solution to this particular problem with both non-dominance Pareto-ranking and sharing, in order to distribute the solutions over the entire Pareto front. All of these approaches are based on Pareto ranking and use either sharing or mating restrictions to ensure diversity. In the following, a first section presents a Pareto-based multi -objective algorithm inspired by Non-dominated Sorting Genetic Algorithm. It is a cooperative approach which gives a whole set of non-dominated solutions—the Pareto front.