Mapping, Order-Independent Genes and the Knapsack Problem

This paper uses the simple structure of the knapsack problem to study the issues of mapping and representation for genetic algorithms. Two genetic algorithms using different mappings were implemented to solve the problem. In one of these neither the order or position of genes is significant. Both of the genetic algorithms perform well on the problem, and we attribute the divergent parameter settings to the different mappings. Both GAs performs well on the problems. The parameter settings for the two GAs differ markedly and this can be attributed to the different mappings. The GA where neither the position or order of the genes in the chromosome are significant is shown to be viable, although the current theory of schemata does not cover this type of GA. 2. The Knapsack Problem