Probabilistic GRASP-Tabu Search algorithms for the UBQP problem

Authors:
Yang Wang;Zhipeng Lü;Fred Glover;Jin-Kao Hao
Affiliations:
LERIA, Université d'Angers, 2 Boulevard Lavoisier, 49045 Angers, France;School of Computer Science and Technology, Huazhong University of Science and Technology, 430074 Wuhan, China;OptTek Systems, Inc., 2241 17th Street Boulder, CO 80302, USA;LERIA, Université d'Angers, 2 Boulevard Lavoisier, 49045 Angers, France
Venue:
Computers and Operations Research
Year:
2013

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Abstract

This paper presents two algorithms combining GRASP and Tabu Search for solving the Unconstrained Binary Quadratic Programming (UBQP) problem. We first propose a simple GRASP-Tabu Search algorithm working with a single solution and then reinforce it by introducing a population management strategy. Both algorithms are based on a dedicated randomized greedy construction heuristic and a tabu search procedure. We show extensive computational results on two sets of 31 large random UBQP instances and one set of 54 structured instances derived from the MaxCut problem. Comparisons with state-of-the-art algorithms demonstrate the efficacy of our proposed algorithms in terms of both solution quality and computational efficiency. It is noteworthy that the reinforced GRASP-Tabu Search algorithm is able to improve the previous best known results for 19 MaxCut instances.