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Probabilistic properties of fitness-based quasi-reflection in evolutionary algorithms |
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| Affiliation: | 1. Department of Biomedical Engineering, Case Western Reserve University, Cleveland, OH, United States;2. Fluid Physics and Transport Processes Branch, NASA Glenn Research Center, Cleveland, OH, United States;3. Center for Space Medicine, Baylor College of Medicine, Houston, TX, United States;4. Institute for Science and Technology in Medicine, Keele University, UK;5. Department of Mechanical Engineering, Fenn College of Engineering, Cleveland State University, Cleveland, OH, United States;6. Orchard Kinetics, LLC, Cleveland, OH, United States;7. Cleveland Functional Electrical Stimulation (FES) Center, Cleveland, OH, United States;8. Louis Stokes Cleveland Veterans Administration Medical Center, Cleveland, OH, United States;9. MetroHealth Medical Center, Cleveland, OH, United States;1. Department of Chemical and Biomedical Engineering, Cleveland State University, Cleveland, OH 44141, USA;2. Department of Mechanical Engineering, The City College of New York, New York, NY 10031, USA;1. CORIA-UMR 6614 - Normandie Université CNRS-Université et INSA de Rouen Campus Universitaire du Madrillet, 76800 Saint-Etienne-du Rouvray, France;2. Department of Physics, Cleveland State University, Cleveland, OH 44115, USA;1. Chemical and Biomedical Engineering Department, Cleveland State University, Cleveland, OH 44114, United States;2. Materials Science and Engineering Department, The University of Arizona, Tuscan, AZ 85721, United States;3. NASA-Marshall Space Flight Space Center, Huntsville, AL 35811, United States |
| Abstract: | 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. |
| Keywords: | Evolutionary algorithms Continuous optimization Opposition Fitness-based quasi-reflection |
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