Journal of Heuristics

, Volume 21, Issue 3, pp 391–431 | Cite as

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

Article

Abstract

In this article we propose a hybrid genetic algorithm for the discrete \((r|p)\)-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 \(\Sigma _2^P\)-hard, i.e., harder than any problem in NP (if \(\hbox {P}\not =\hbox {NP}\)). 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.

Keywords

Combinatorial optimization Competitive facility location Discrete \((r|p)\)-centroid problem Metaheuristics  Solution archive Bi-level optimization 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Institute of Computer Graphics and AlgorithmsVienna University of TechnologyViennaAustria

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