A New Grouping Genetic Algorithm for the Quadratic Multiple Knapsack Problem

  • Alok Singh
  • Anurag Singh Baghel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4446)


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.


Combinatorial optimization grouping genetic algorithm  knapsack problem quadratic multiple knapsack problem.  


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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Alok Singh
    • 1
  • Anurag Singh Baghel
    • 2
  1. 1.J. K. Institute of Applied Physics and Technology, Faculty of Science, University of Allahabad, Allahabad – 211002, UPIndia
  2. 2.Department of Electronics and Communication, Banasthali Vidyapith Jaipur Campus, Sarojini Marg, Jaipur – 302001, RajasthanIndia

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