Dimension improvements based adaptation of control parameters in Differential Evolution: A fitness-value-independent approach

Abstract

In this paper, we proposed a novel fitness-value-independent Differential Evolution to tackle complex real-parameter single-objective optimization. There were three innovations in the algorithm: First, dimension improvements based adaptation schemes for control parameters F and CR were advanced in this paper. Different from those fitness value improvements based parameter control in the recent winner DE variants, our algorithm has fitness-value-independent characteristic, therefore, it can be applied in much wider optimization scenarios especially for those that the exact fitness values of the objectives are unavailable. Second, a combined parabolic–linear reduction scheme for population size is employed in the algorithm based on the observation that the slower reduction of population size at the earlier stage of the evolution usually helps to get better perception of the objectives while a linear reduction of population size in the later stage helps to get better exploitation. Third, an indicator is proposed to monitor the diversity of the population and a corresponding population enhancement technique is launched when the diversity is detected bad. The first two innovations have the Parameter adaptive characteristic of the DE algorithm while the third innovation refers to population enhancement technique, therefore, we name our algorithm “the PaDE-pet algorithm”. Then, the algorithm is validated under a larger test suite containing 88 benchmarks from CEC2013, CEC2014 and CEC2017 test suites for real-parameter single objective optimization, which may avoid over-fitting problem in comparison with employing a test suite containing a small number of benchmarks. The experiments support the superiority of the novel PaDE-pet algorithm in comparison with several recently proposed powerful DE variants.