Incorporating the Notion of Relative Importance of Objectives in Evolutionary Multiobjective Optimization

This paper describes the use of decision maker preferences in terms of the relative importance of objectives in evolutionary multiobjective optimization. A mathematical model of the relative importance of objectives and an elicitation algorithm are proposed, and three methods of incorporating explicated preference information are described and applied to standard test problems in an empirical study. The axiomatic model proposed here formalizes the notion of relative importance of objectives as a partial order that supports strict preference, equality of importance, and incomparability between objective pairs. Unlike most approaches, the proposed model does not encode relative importance as a set of real-valued parameters. Instead, the approach provides a functional correspondence between a coherent overall preference with a subset of the Pareto-optimal front. An elicitation algorithm is also provided to assist a human decision maker in constructing a coherent overall preference. Besides elicitation of a priori preference, an interactive facility is also furnished to enable modification of overall preference while the search progresses. Three techniques of integrating explicated preference information into the well-known Non-dominated Sorting Genetic Algorithm (NSGA)-II are also described and validated in a set of empirical investigation. The approach allows a focus on a subset of the Pareto-front. Validations on test problems demonstrate that the preference-based algorithm gained better convergence as the dimensionality of the problems increased.

I. Introduction

Multiobjective optimization problems (MOP) involve multiple conflicting, incomparable, and noncommensurable objective functions. The conflict, incomparability, and noncommensurability of the objectives imply that an MOP corresponds to a nonsingular set of Pareto-optimal solutions characterized by trade-off in the performance in various objectives [1]. Improvement in one objective is gained only with degradation in another such that in the objective space of the MOP at hand, the corresponding Pareto-optimal set form a nondominated front, the Pareto-front.