Strategic oscillation for the quadratic multiple knapsack problem
- 399 Downloads
The quadratic multiple knapsack problem (QMKP) consists in assigning a set of objects, which interact through paired profit values, exclusively to different capacity-constrained knapsacks with the aim of maximising total profit. Its many applications include the assignment of workmen to different tasks when their ability to cooperate may affect the results.
Strategic oscillation (SO) is a search strategy that operates in relation to a critical boundary associated with important solution features (such as feasibility). Originally proposed in the context of tabu search, it has become widely applied as an efficient memory-based methodology. We apply strategic oscillation to the quadratic multiple knapsack problem, disclosing that SO effectively exploits domain-specific knowledge, and obtains solutions of particularly high quality compared to those obtained by current state-of-the-art algorithms.
KeywordsStrategic oscillation Tabu search Quadratic multiple knapsack problem Empirical study
This work was supported by the research projects TIN2009-07516, TIN2012-35632-C02, TIN2012-37930-C02-01, and P08-TIC-4173.
- 1.Hiley, A., Julstrom, B.: The quadratic multiple knapsack problem and three heuristic approaches to it. In: Proc. of the Genetic and Evolutionary Computation Conference (GECCO’06), pp. 547–552 (2006) Google Scholar
- 3.Sundar, S., Singh, A.: A swarm intelligence approach to the quadratic multiple knapsack problem. In: ICONIP. LNCS, vol. 6443, pp. 626–633 (2010) Google Scholar
- 4.Saraç, T., Sipahioglu, A.: A genetic algorithm for the quadratic multiple knapsack problem. In: BVAI. LNCS, vol. 4729, pp. 490–498 (2007) Google Scholar
- 5.Singh, A., Baghel, A.: A new grouping genetic algorithm for the quadratic multiple knapsack problem. In: EvoCOP. LNCS, vol. 4446, pp. 210–218 (2007) Google Scholar
- 14.Glover, F.: Tabu search and adaptive memory programming—advances, applications and challenges. In: Barr, Helgason, Kennington (eds.) Interfaces in Computer Science and Operations Research, pp. 1–75. Kluwer Academic, Dordrecht (1996) Google Scholar
- 18.Zar, J.H.: Biostatistical Analysis. Prentice Hall, New York (1999) Google Scholar
- 20.Iman, R., Davenport, J.: Approximations of the critical region of the Friedman statistic. In: Commun. Stat., pp. 571–595 (1980) Google Scholar
- 22.Wilcoxon, F.: Individual comparisons by ranking methods. Biomaterials 1, 80–83 (1945) Google Scholar