A Swarm Intelligence Approach to the Quadratic Multiple Knapsack Problem

In this paper we present an artificial bee colony (ABC) algorithm to solve the quadratic multiple knapsack problem (QMKP) which can be considered as an extension of two well known knapsack problems viz. multiple knapsack problem and quadratic knapsack problem. In QMKP, 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 total profit if both objects of the pair belong to the same knapsack. The objective of this problem is to assign each object to at most one knapsack in such a way that the total weight of the objects in each knapsack should not exceed knapsack's capacity and the total profit of all the objects included into the knapsacks is maximized. We have compared our approach with three genetic algorithms and a stochastic hill climber. Computational results show the effectiveness of our approach.

[1]  Dervis Karaboga,et al.  A survey: algorithms simulating bee swarm intelligence , 2009, Artificial Intelligence Review.

[2]  Alok Singh,et al.  A swarm intelligence approach to the quadratic minimum spanning tree problem , 2010, Inf. Sci..

[3]  Alok Singh,et al.  A New Grouping Genetic Algorithm for the Quadratic Multiple Knapsack Problem , 2007, EvoCOP.

[4]  Tugba Saraç,et al.  A Genetic Algorithm for the Quadratic Multiple Knapsack Problem , 2007, BVAI.

[5]  Emanuel Falkenauer,et al.  Genetic Algorithms and Grouping Problems , 1998 .

[6]  D. Karaboga,et al.  On the performance of artificial bee colony (ABC) algorithm , 2008, Appl. Soft Comput..

[7]  Jens Gottlieb,et al.  Evolutionary Computation in Combinatorial Optimization , 2006, Lecture Notes in Computer Science.

[8]  Mehmet Fatih Tasgetiren,et al.  A discrete artificial bee colony algorithm for the lot-streaming flow shop scheduling problem , 2011, Inf. Sci..

[9]  Bryant A. Julstrom,et al.  The quadratic multiple knapsack problem and three heuristic approaches to it , 2006, GECCO.

[10]  Dervis Karaboga,et al.  AN IDEA BASED ON HONEY BEE SWARM FOR NUMERICAL OPTIMIZATION , 2005 .

[11]  Alok Singh,et al.  An artificial bee colony algorithm for the leaf-constrained minimum spanning tree problem , 2009, Appl. Soft Comput..

[12]  Francesco Ventriglia,et al.  Advances in Brain, Vision, and Artificial Intelligence, Second International Symposium, BVAI 2007, Naples, Italy, October 10-12, 2007, Proceedings , 2007, BVAI.