A new grouping genetic algorithm for the quadratic multiple knapsack problem

Authors:
Alok Singh;Anurag Singh Baghel
Affiliations:
J. K. Institute of Applied Physics and Technology, Faculty of Science, University of Allahabad, Allahabad, UP, India;Department of Electronics and Communication, Jaipur, Rajasthan, India
Venue:
EvoCOP'07 Proceedings of the 7th European conference on Evolutionary computation in combinatorial optimization
Year:
2007

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Abstract

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.