Genetic Algorithm Based on the Orthogonal Design for Multidimensional Knapsack Problems

In this paper, a genetic algorithm based on the orthogonal design for solving the multidimensional knapsack problems is proposed. The orthogonal design with the factor analysis, an experimental design method, is applied to the genetic algorithm, to make the algorithm be more robust, statistically sound and quickly convergent. A crossover operator formed by the orthogonal array and the factor analysis is presented. First, this crossover operator can generate a small, but representative sample of points as offspring. After all of the better genes of these offspring are selected, an optimal offspring better than its parents is then generated in the end. Moreover, a check-and-repair operator is adopted to make the infeasible chromosomes generated by the crossover and mutation operators feasible, and make the feasible chromosomes better. The simulation results show that the proposed algorithm can find optimal or close-to-optimal solutions with less computation burden.