A HYBRID OF ROUGH SETS AND GENETIC ALGORITHMS FOR SOLVING THE 0-1 MULTIDIMENSIONAL KNAPSACK PROBLEM

The multidimensional 0-1 knapsack problem (MKP) is a well-known NPhard combinatorial optimization problem. This paper uses a methodology that integrates a reduct of rough sets (RS) into the crossover operator of a genetic algorithm (GA) to solve the MKP. Two algorithms are presented in this paper; one selects the crossover points either randomly or via the reduct, whereas the other selects the crossover points solely by the reduct. The performance of these two algorithms was compared with a standard GA using test cases from the literature. According to the experimental results, this integration obtains both better quality and more clustered solutions, and could possibly improve the performance if some mechanisms are developed in the algorithm. The results justify the integration and demonstrate an alternative for improving the performance of the GA.

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