A Binary Differential Evolution with adaptive parameters applied to the Multiple Knapsack Problem

Abstract

This paper introduces an adaptive Binary Differential Evolution (aBDE) that self adjusts two parameters of the algorithm: perturbation and mutation rates. The well-known 0-1 Multiple Knapsack Problem (MKP) is addressed to validate the performance of the method. The MKP is a NP-hard optimization problem and the aim is to maximize the total profit subjected to the total weight in each knapsack that must be less than or equal to a given limit. Results were obtained using 11 instances of the problem with different degrees of complexity. The results were compared using aBDE, BDE, a standard Genetic Algorithm (GA), and its adaptive version (aGA). The results show that aBDE obtained better results than the other algorithms. This indicates that the proposed approach is an interesting and promising strategy for control of parameters and for optimization of complex problems.