Solving the 0-1 Knapsack Problem with EDAs

In this chapter we present several approaches to the 0-1 knapsack problem based on Estimation of Distribution Algorithms. These approaches use two different types of representation, three methods for obtaining the initial population and two different methods for handling the problem’s constraints. Experimental results for problems of different sizes are given.

[1]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[2]  E. Costa,et al.  An Evolutionary Approach to the Zero/One Knapsack Problem: Testing Ideas from Biology , 2001 .

[3]  David Pisinger,et al.  Core Problems in Knapsack Algorithms , 1999, Oper. Res..

[4]  Anne L. Olsen Penalty functions and the knapsack problem , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[5]  L. Darrell Whitley,et al.  A note on the performance of genetic algorithms on zero-one knapsack problems , 1994, SAC '94.

[6]  S. Baluja An Empirical Comparison of Seven Iterative and Evolutionary Function Optimization Heuristics , 1995 .

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

[8]  Shumeet Baluja,et al.  Fast Probabilistic Modeling for Combinatorial Optimization , 1998, AAAI/IAAI.

[9]  S. Martello,et al.  A New Algorithm for the 0-1 Knapsack Problem , 1988 .

[10]  G. Ingargiola,et al.  Reduction Algorithm for Zero-One Single Knapsack Problems , 1973 .

[11]  Egon Balas,et al.  An Algorithm for Large Zero-One Knapsack Problems , 1980, Oper. Res..

[12]  Robert Hinterding Mapping, order-independent genes and the knapsack problem , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

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