A Comparison of Differential Evolution Algorithm with Binary and Continuous Encoding for the MKP

Abstract

This paper provides a brief description on how continuous algorithms can be applied to binary problems. Differential Evolution is the continuous algorithm studied and two versions of this algorithm are presented: the Binary Differential Evolution with a binary encoding and the Discretized Differential Evolution with a continuous encoding. Several discretization methods are presented and the most used method in literature is implemented for the solution discretization. Benchmarks with different complexity and search space sizes of the Multiple Knapsack Problem are used to compare the performance of each Differential Evolution algorithm presented and the Genetic Algorithm with binary encoding. Results suggest that continuous methods can be very efficient when discretized for binary spaces.