Ant Colony Optimization and Multiple Knapsack Problem

The ant colony optimization algorithms and their applications on the multiple knapsack problem (MKP) are introduced. The MKP is a hard combinatorial optimization problem with wide application. Problems from different industrial fields can be interpreted as a knapsack problem including financial and other management. The MKP is represented by a graph, and solutions are represented by paths through the graph. Two pheromone models are compared: pheromone on nodes and pheromone on arcs of the graph. The MKP is a constraint problem which provides possibilities to use varied heuristic information. The purpose of the chapter is to compare a variety of heuristic and pheromone models and different variants of ACO algorithms on MKP.

[1]  L. Lönnstedt.  The Use of Operational Research in Twelve Companies Quoted on the Stockholm Stock Exchange , 1973 .

[2]  Francisco Herrera,et al.  Analysis of the Best-Worst Ant System and Its Variants on the QAP , 2002, Ant Algorithms.

[3]  Z. Michalewicz,et al.  A new version of ant system for subset problems , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[4]  Luca Maria Gambardella,et al.  Ant Algorithms for Discrete Optimization , 1999, Artificial Life.

[5]  Stefka Fidanova,et al.  ACO Algorithm for MKP Using Various Heuristic Information , 2002, Numerical Methods and Application.

[6]  Thomas Stützle,et al.  A short convergence proof for a class of ant colony optimization algorithms , 2002, IEEE Trans. Evol. Comput..

[7]  Thomas Stützle,et al.  MAX-MIN Ant System , 2000, Future Gener. Comput. Syst..

[8]  M Dorigo,et al.  Ant colonies for the quadratic assignment problem , 1999, J. Oper. Res. Soc..

[9]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[10]  Stefka Fidanova.  ACO Algorithm with Additional Reinforcement , 2002, Ant Algorithms.

[11]  Luca Maria Gambardella,et al.  Ant colony system: a cooperative learning approach to the traveling salesman problem , 1997, IEEE Trans. Evol. Comput..

[12]  Stefka Fidanova.  Convergence Proof for a Monte Carlo Method for Combinatorial Optimization Problems , 2004, International Conference on Computational Science.

[13]  Whitfield Diffie,et al.  New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.