A multi-start iterated local search algorithm for the generalized quadratic multiple knapsack problem

• Published in: Computers & operations research Vol. 83; pp. 54 - 65
• Main Authors: Avci, Mustafa, Topaloglu, Seyda
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.07.2017; Pergamon Press Inc
• Subjects: Adaptive algorithms; Algorithms; Branch & bound algorithms; Generalized quadratic multiple knapsack problem; Iterated local search; Knapsack problem; Operations research; Perturbation; Perturbation mechanism; Search algorithms; Search process; Variable neighborhood descent; Perturbation mechanism; Generalized quadratic multiple knapsack problem; Variable neighborhood descent; Iterated local search
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2017.02.004

•The generalized quadratic multiple knapsack problem is studied.•A multi-start iterated local search algorithm is developed for its solution.•The algorithm combines an adaptive perturbation mechanism with local search.•35 out of 48 best known solutions are improved for large-size problem instances. The quadratic multiple knapsack problem (QMKP) is a variant of the classical knapsack problem where multiple knapsacks are considered and the objective is to maximize a quadratic objective function subject to capacity constraints. The generalized quadratic multiple knapsack problem (G-QMKP) extends the QMKP by considering the setups, assignment conditions and the knapsack preferences of the items. In this study, a multi-start iterated local search algorithm (MS-ILS) in w the variable neighborhood descent (VND) algorithm is integrated with an adaptive perturbation mechanism is proposed to solve the G-QMKP. The multi-start implementation together with the adaptive perturbation mechanism enables the search process to explore different search regions in the search space while VND is applied to obtain high-quality solutions from the examined regions. Another remarkable feature of MS-ILS is its simplicity and adaptiveness that ease its implementation. The proposed MS-ILS is tested on G-QMKP benchmark instances derived from the literature. The results indicate that the developed MS-ILS can produce high-quality solutions for the G-QMKP. Particularly, it has been observed that the developed MS-ILS has improved the best known solutions for 35 out of 48 large-size G-QMKP instances.