A hybrid genetic algorithm with solution archive for the discrete $$(r|p)$$ ( r | p ) -centroid problem

Abstract

In this article we propose a hybrid genetic algorithm for the discrete $$(r|p)$$(r|p)-centroid problem. We consider the competitive facility location problem where two non-cooperating companies enter a market sequentially and compete for market share. The first decision maker, called the leader, wants to maximize his market share knowing that a follower will enter the same market. Thus, for evaluating a leader's candidate solution, a corresponding follower's subproblem needs to be solved, and the overall problem therefore is a bi-level optimization problem. This problem is $$\Sigma _2^P$$Σ2P-hard, i.e., harder than any problem in NP (if $$\hbox {P}\not =\hbox {NP}$$P?NP). A heuristic approach is employed which is based on a genetic algorithm with tabu search as local improvement procedure and a complete solution archive. The archive is used to store and convert already visited solutions in order to avoid costly unnecessary re-evaluations. Different solution evaluation methods are combined into an effective multi-level evaluation scheme. The algorithm is tested on well-known benchmark sets of both Euclidean and non-Euclidean instances as well as on larger newly created instances. Especially on the Euclidean instances our algorithm is able to exceed previous state-of-the-art heuristic approaches in solution quality and running time in most cases.