Particle Swarm Optimization for the Multidimensional Knapsack Problem

The multidimensional 0/1 knapsack problem is a classical problem of discrete optimization. There are several approaches for solving the different variations of such problem, including mathematical programming and stochastic heuristic methods. This paper presents the application of Particle Swarm Optimization (PSO) for the problem, using selected instances of ORLib. For the instances tested, results were very close or equal to the optimal solution known, even considering that the parameters of PSO were not optimized. The analysis of the results suggests the potential of a simple PSO for this class of combinatorial problems.

[1]  Arild Hoff,et al.  Genetic Algorithms for 0/1 Multidimensional Knapsack Problems , 2005 .

[2]  Thomas Bäck,et al.  The zero/one multiple knapsack problem and genetic algorithms , 1994, SAC '94.

[3]  Ioan Cristian Trelea,et al.  The particle swarm optimization algorithm: convergence analysis and parameter selection , 2003, Inf. Process. Lett..

[4]  Wei Shih,et al.  A Branch and Bound Method for the Multiconstraint Zero-One Knapsack Problem , 1979 .

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

[6]  Leandro dos Santos Coelho,et al.  Particle Swarn Optimization with Fast Local Search for the Blind Traveling Salesman Problem , 2005, Fifth International Conference on Hybrid Intelligent Systems (HIS'05).

[7]  John E. Beasley,et al.  A Genetic Algorithm for the Multidimensional Knapsack Problem , 1998, J. Heuristics.

[8]  S. Senju,et al.  An Approach to Linear Programming with 0--1 Variables , 1968 .

[9]  Heitor Silvério Lopes,et al.  Self-Adapting Evolutionary Parameters: Encoding Aspects for Combinatorial Optimization Problems , 2005, EvoCOP.

[10]  Paolo Toth,et al.  Knapsack Problems: Algorithms and Computer Implementations , 1990 .

[11]  Yuhui Shi,et al.  Particle swarm optimization: developments, applications and resources , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[12]  M. Clerc,et al.  The swarm and the queen: towards a deterministic and adaptive particle swarm optimization , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[13]  Russell C. Eberhart,et al.  Comparison between Genetic Algorithms and Particle Swarm Optimization , 1998, Evolutionary Programming.