A Set-Oriented Genetic Algorithm and the Knapsack Problem

Genetic Algorithms (GAS) have been used to solve the NP-complete problems effectively such as the knapsack problem. One difficulty in applying GA to the knapsack problem is that the bit string representation of the canonical GA chromosome does not provide the direct mapping of the problem into the GA chromosome. In this paper, a new chromosome representation of the GA is proposed which is called the “set-oriented GA”. A chromosome in the set-oriented GA is a set while it is a bit-string in the canonical GA. Crossover and mutation operators are described using the combinations of set operation such as union, intersection, and complement. Performance comparison of the canonical GA and the set-oriented GA in the knapsack problem is presented. The set-oriented GA turns out to be not only effective in representing the problem but also efficient in finding the solution.