An effective GRASP and tabu search for the 0-1 quadratic knapsack problem

Authors:
Zhen Yang;Guoqing Wang;Feng Chu
Affiliations:
Management School, Jinan University, 601# Huangpu W. Road, Guangzhou, China;Management School, Jinan University, 601# Huangpu W. Road, Guangzhou, China;Laboratoire d'Informatique, Biologie Intégrative et Systèmes Complexes (IBISC), EA 4526, Université d'Evry Val d'Essonne, 40 Rue du Pelvoux, CE1455 Courcouronnes, 91020 Evry Cedex, ...
Venue:
Computers and Operations Research
Year:
2013

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Abstract

As a generalization of the classical 0-1 knapsack problem, the 0-1 Quadratic Knapsack Problem (QKP) that maximizes a quadratic objective function subject to a linear capacity constraint is NP-hard in strong sense. In this paper, we propose a memory based Greedy Randomized Adaptive Search Procedures (GRASP) and a tabu search algorithm to find near optimal solution for the QKP. Computational experiments on benchmarks and on randomly generated instances demonstrate the effectiveness and the efficiency of the proposed algorithms, which outperforms the current state-of-the-art heuristic Mini-Swarm in computational time and in the probability to achieve optimal solutions. Numerical results on large-sized instances with up to 2000 binary variables have also been reported.