A hybrid genetic algorithm with solution archive for the discrete -centroid problem

作者：Biesinger Benjamin^*; Hu Bin; Raidl Guenther

来源：Journal of Heuristics, 2015, 21(3): 391-431.

DOI：10.1007/s10732-015-9282-5

• Combinatorial optimization
• Competitive facility location
• Discrete (r vertical bar p)-centroid problem
• Metaheuristics
• Solution archive
• Bi-level optimization

In this article we propose a hybrid genetic algorithm for the discrete -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 -hard, i.e., harder than any problem in NP (if ). 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.

• 出版日期2015-6