A Multi-Objective Evolutionary Algorithm for Finding Efficient Solutions to a Competitive Facility Location Problem

Abstract

This chapter investigates the performance of several Multi-Objective Evolutionary Algorithms (MOEAs) in discovering solutions to the Competitive Facility Location (CFL) problem and a sensitivity analysis of the solutions related to input parameters. In terms of the optimality, the MOEAs are able to find Pareto-optimal solutions in the discrete-valued objective (captured weights) search space but show inferior Pareto-optimal solutions to the real-valued objective (facility quality). In terms of runtime complexity, the MOEAs run in polynomial time but are computationally expensive in terms of repeated executions for sensitivity analysis. The sensitivity analyses show that the mutation rate causes much of the variation in the output and requires a high probability value in order to generate CFL solutions near the Pareto-optimal front. The section on robustness examined the effects of changing the area location in finding solutions to the competitive facility location problem while preserving a small set of previously effective GA-parameter combinations. The results show that there is no single GA-parameter combination that dictates the generation of best solutions. TheMOEA in this case, is robust as long as the mutation probability and the bit-turn probability are set to a probability of more than 60 % while keeping the crossover probability low.