Solving the 0/1 knapsack problem using rough sets and genetic algorithms

Abstract

This article proposes a methodology that introduces attribute reduction of rough sets into crossover of genetic algorithms (GAs), and then uses the methodology to develop two algorithms. The first algorithm selects the crossover points, either by attribute reduction or randomly; the second selects the crossover points solely by attribute reduction, with no crossover otherwise. We test the methodology on the solving of the 0/1 knapsack problem, due to the problem's NP-hard complexity, and we compare the experiment results to those of typical GAs. According to the results, the introduction of attribute reduction increases the mean and decreases the standard deviation of the final solutions, especially in the presence of tighter capacity, i.e. attribution reduction leads to better solution quality and more tightly clustered solutions. Moreover, the mean number of iterations required to terminate the algorithm and that required to reach maximal profits are significantly reduced.