A New Grouping Genetic Algorithm for the Quadratic Multiple Knapsack Problem
The quadratic multiple knapsack problem is an extension of the well known 0/1 multiple knapsack problem. In the quadratic multiple knapsack problem, profit values are associated not only with individual objects but also with pairs of objects. Profit value associated with a pair of objects is added to the overall profit if both objects of the pair belong to the same knapsack. Being an extension of the 0/1 multiple knapsack problem, this problem is also NP-Hard. In this paper, we have proposed a new steady-state grouping genetic algorithm for the quadratic multiple knapsack problem and compared our results with two recently proposed methods – a genetic algorithm and a stochastic hill climber. The results show the effectiveness of our approach.
KeywordsCombinatorial optimization grouping genetic algorithm knapsack problem quadratic multiple knapsack problem.
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- 3.Cotta, C., Troya, J.M.: A Hybrid Genetic Algorithm for the 0-1 Multiple Knapsack Problem. In: Artificial Neural Networks and Genetic algorithms, vol. 3, pp. 250–254. Springer, Berlin (1998)Google Scholar
- 6.Falkenauer, E.: New Representations and Operators for GAs Applied to Grouping Problems. Evolutionary Computation 2, 123–144 (1992)Google Scholar
- 7.Falkenauer, E.: Genetic Algorithms and Grouping Problems. John Wiley & Sons, Chicester (1998)Google Scholar
- 8.Davis, L.: Handbook of Genetic Algorithms. Van Nostrand Reinhold, New York (1991)Google Scholar
- 9.Singh, A., Gupta, A.K.: Two Heuristics for the One-Dimensional Bin-Packing Problem. To appear in OR-Spectrum (2007)Google Scholar