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

• Published in: Journal of heuristics Vol. 21; no. 3; pp. 391 - 431
• Main Authors: Biesinger, Benjamin, Hu, Bin, Raidl, Günther
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2015; Springer Nature B.V
• Subjects: Archives & records; Artificial Intelligence; Calculus of Variations and Optimal Control; Optimization; Competition; Customers; Genetic algorithms; Heuristic; Linear programming; Management Science; Market shares; Mathematics; Mathematics and Statistics; Operations Research; Operations Research/Decision Theory; Optimization; Turnover; Solution archive; Bi-level optimization; Metaheuristics; centroid problem; Discrete; Combinatorial optimization; Competitive facility location
• ISSN: 1381-1231; 1572-9397
• DOI: 10.1007/s10732-015-9282-5

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 Σ 2 P -hard, i.e., harder than any problem in NP (if 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.