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

• Published in: Computers & operations research Vol. 40; no. 5; pp. 1176 - 1185
• Main Authors: Yang, Zhen, Wang, Guoqing, Chu, Feng
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.05.2013; Elsevier; Pergamon Press Inc
• Subjects: 0-1 quadratic knapsack problem; Applied sciences; Computer Science; Exact sciences and technology; Flows in networks. Combinatorial problems; Heuristic; Knapsack problem; Mathematical functions; Mathematical programming; Meta-heuristic; Numerical analysis; Operational research and scientific management; Operational research. Management science; Operations Research; Optimization algorithms; Quadratic programming; Studies; 0-1 quadratic knapsack problem; Meta-heuristic; Probabilistic approach; Randomized algorithm; Search algorithm; Tabu search; Heuristic method; NP hard problem; Greedy algorithm; Capacity constraint; Objective function; Metamodel; Quadratic function
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2012.11.023

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.