Generating evenly distributed equitably efficient solutions in multi-objective optimization problems

Abstract

We consider multi-objective optimization (MOP) problems where the decision maker (DM) has equity concerns. We assume that the preference model of the DM satisfies properties related to inequity-aversion, hence we focus on finding efficient solutions in line with the properties of inequity-averse preferences, namely the equitably efficient solutions. We discuss two algorithms for finding good subsets of equitably efficient solutions. In the first approach, we propose an algorithm that generates an evenly distributed subset of the set of equitably efficient solutions to be considered further by the DM. The second approach is an extension of an interactive approach developed for finding efficient solutions in the rational dominance sense and finds equitably efficient solutions in the preferred region of the DM. We illustrate these algorithms on equitable multi-objective knapsack problems that fund projects in di erent categories subject to a limited budget. We perform experiments to show and discuss the performances of the algorithms for three and five criteria settings. The experiments show that the first algorithm generates an evenly distributed subset in reasonable time, hence is advantageous in terms of solution time, compared to an approach that aims to find the whole set of equitably efficient solutions. The second approach is also shown to be a computationally efficient one that could be used in settings where the DM is willing to provide preference information.