Comparative Analysis of the Bacterial Foraging Algorithm and Differential Evolution in Global Optimization Problems

Abstract

There are bio-inspired metaheuristics in nature rarely used in areas where there is not domain or knowledge of computational algorithms, to mention some, medicine, finance and administration. TS-MBFOA, a bacteria-based algorithm and the Differential Evolution Algorithm (DEA), are metaheuristic algorithms proposed for the optimization of complex problems mathematically modeled as linear or non-linear problems. In this paper, these algorithms are implemented to analyze their performance in the search for better solutions in constrained optimization problems. Tests were conducted on four optimization problems known in the literature as benchmark problems. Both algorithms were run in 30 independent executions for each problem with the same number of generations and evaluations. Although the parameters of each algorithm are different, the number of evaluations was selected for a fair comparison. Results are similar for both algorithms, however, DEA obtains better results for the problem with the larger number of constraints. Additionally, DEA generates solutions in less time than TS-MBFOA. The nonparametric Wilcoxon Signed Rank Test indicates significant differences in only 3 problems. The convergence graph of both algorithms for each problem shows that after 50 generations, both algorithms are close to the best known solution in the state of the art.