Probabilistic properties of fitness-based quasi-reflection in evolutionary algorithms

Evolutionary algorithms (EAs) excel in optimizing systems with a large number of variables. Previous mathematical and empirical studies have shown that opposition-based algorithms can improve EA performance. We review existing opposition-based algorithms and introduce a new one. The proposed algorithm is named fitness-based quasi-reflection and employs the relative fitness of solution candidates to generate new individuals. We provide the probabilistic analysis to prove that among all the opposition-based methods that we investigate, fitness-based quasi-reflection has the highest probability of being closer to the solution of an optimization problem. We support our theoretical findings via Monte Carlo simulations and discuss the use of different reflection weights. We also demonstrate the benefits of fitness-based quasi-reflection on three state-of-the-art EAs that have competed at IEEE CEC competitions. The experimental results illustrate that fitness-based quasi-reflection enhances EA performance, particularly on problems with more challenging solution spaces. We found that competitive DE (CDE) which was ranked tenth in CEC 2013 competition benefited the most from opposition. CDE with fitness-based quasi-reflection improved on 21 out of the 28 problems in the CEC 2013 test suite and achieved 100% success rate on seven more problems than CDE.