Chaotic parameter control in Differential Evolution
DOI:
https://doi.org/10.63671/ijsesr.v2i4.178Keywords:
Differential evolution, Chaotic maps, Population diversity, Scaling factor, Crossover probability, CEC 2014Abstract
Differential Evolution (DE) is a popular meta-heuristic algorithm that works on the differences between the vectors of a population. It was developed by Kenneth Price and Rainer Storn in the mid-1990s.The scaling factor F and the crossover probability CR are two key control parameters of DE. Differential Evolution (DE) works well on many optimization problems, but its results depend a great deal on how the scaling factor F and the crossover probability CR are set. In this paper, the concepts of dynamical systems (chaotic maps) and population diversity are applied to the control parameters F and CR. We replace the fixed values of these two parameters with sequences drawn from ten chaotic maps: Chebyshev, circle, Gauss, iterative, logistic, piecewise, sine, Singer, sinusoidal and tent. A diversity checks on the population decides when the chaotic values are used; otherwise, F = 0.5 and CR = 0.4 are kept. We tried each map on F alone, on CR alone, and then in pairs chosen for each class of problems. All variants were run on the 30 CEC 2014 functions and compared with standard DE. No single map won everywhere. These findings can help in choosing a chaotic map to suit the type of problem at hand.
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