Crossover based on rough sets - a case of multidimensional knapsack problem

This paper uses two algorithms based on the methodology that introduces attribute reduction of rough sets into crossover of genetic algorithms (GAs). The first algorithm selects the crossover points, either by attribute reduction or randomly; the second one selects the crossover points solely by attribute reduction, with no crossover otherwise. We test the methodology on the solving of multidimensional knapsack problems using combinations of the number of items and the number of knapsacks, and compare the experiment results to those of typical GAs. According to the preliminary results, the introduction of attribute reduction has the advantage that increases the mean and decreases the standard deviation of the final solutions when the number of items is medium. Despite that the advantage appears to be less consistent when the number of items increases, the results still show that the mean number of iterations required to terminate the algorithm and the mean number of iterations required to reach maximal solutions can be decreased.