In Search of Equitable Solutions Using Multi-objective Evolutionary Algorithms

Abstract

Over the last two decades, evolutionary algorithms have been applied in solving multi-objective optimization problems. Most of these algorithms use the concept of Pareto-optimality to drive their search. However, many real-world multi-objective applications, in particular from location theory and general resource allocation models, require finding so-called equitably efficient points. These solutions form a subset of the Pareto-optimal set. In equitable efficiency, objective functions are considered impartial which makes the distribution of outcomes more important rather than assignment of several outcomes to an objective. In literature, we found two classical approaches to compute an equitably efficient point. These approaches rely on either solving a problem which is always non-differentiable or on solving a more difficult problem. In this paper, for the first time, a multi-objective evolutionary approach to this problem is proposed. The approach finds a diverse set of equitably optimal solutions and, in addition, tackles the nondifferentiability which is inherently present in the classical approach. It is shown that even for simple differentiable problems, which belong to the realm of classical techniques, the evolutionary approach is a better choice than the classical ones. Computational studies on a number of test problems of varying complexity demonstrate the efficiency of the evolutionary approach in solving a large class of both simple and complex equitable multi-objective optimization problems.