A set-oriented genetic algorithm and the knapsack problem

Genetic algorithms (GAs) have been used to solve NP-complete problems, such as the knapsack problem, effectively. One difficulty in applying GAs to the knapsack problem is that the bit-string representation of the canonical GA chromosome does not provide a direct mapping of the problem on to the GA chromosome. In this paper, a new chromosome representation of the GA is proposed, called the "set-oriented GA". A chromosome in the set-oriented GA is a set, while in the canonical GA it is a bit-string. Crossover and mutation operators are described using the combinations of set operations, such as union, intersection and complement. A performance comparison of the canonical GA and the set-oriented GA on 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.