Genetic Algorithms for 0–1 Programming

Abstract

In this chapter, genetic algorithms with double strings (GADS) as developed for multidimensional 0–1 knapsack problems are discussed in detail. Through the introduction of a double string representation and the corresponding decoding algorithm, it is shown that a potential solution satisfying constraints can be obtained for each individual. Then the GADS are extended to deal with more general 0–1 programming problems involving both positive and negative coefficients in the constraints. Especially, new decoding algorithms for double strings using reference solutions both without and with the reference solution updating procedure are introduced so that each individual is decoded to the corresponding feasible solution for the general 0–1 programming problems. The detailed comparative numerical experiments with a branch and bound method are also provided.