Hybrid Differential Evolution for Knapsack Problem

Abstract

A hybrid Differential Evolution algorithm with double population was proposed for 0-1 knapsack problem. The two populations play different roles during the process of evolution with the floating-point population as an engine while the binary population guiding the search direction. Each gene of every chromosome in the floating-point encoding population is restricted to the range [-1, 1], while each gene of every chromosome in the binary encoding population is zero or one. A new mapping operation based on sign function was proposed to generate the binary population from the floating-point population. And a local refining operation called discarding operation was employed in the new algorithm to fix up the solutions which are infeasible. Three benchmarks of 0-1 knapsack problem with different sizes were used to verify the new algorithm and the performance of the new algorithm was also compared with that of other evolutionary algorithms. The simulation results show it is an effective and efficient way for the 0-1 Knapsack problem.