A Fuzzy Adaptive Differential Evolution Algorithm

Abstract

The differential evolution algorithm is a floating-point encoded evolutionary algorithm for global optimization over continuous spaces. The algorithm has so far used empirically chosen values for its search parameters that are kept fixed through an optimization process. The objective of this paper is to introduce a new version of the Differential Evolution algorithm with adaptive control parameters -the fuzzy adaptive differential evolution algorithm, which uses fuzzy logic controllers to adapt the search parameters for the mutation operation and crossover operation. The control inputs incorporate the relative objective function values and individuals of the successive generations. The emphasis of this paper is analysis of the dynamics and behavior of the algorithm. Experimental results, provided by the proposed algorithm for a set of standard test functions, outperformed those of the standard differential evolution algorithm for optimization problems with higher dimensionality.

Self-adaptive randomized and rank-based differential evolution for multimodal problems

“…For all experiments, unless mentioned otherwise, the utilized settings for the parameters are given by -F = 0.5 (as in [1,5,15,26,35,42]) -C r = 0.9 (as in [1,5,15,26,35,42]) -mutation strategy: DE/rand/1/bin (classic DE) (as in [5,21,24,26,35,36]…”

“…As in previous experiments, for each setting, we manually adapt the optimal population size to reach the robustness condition and to minimize the MFE number at the same time. On Rastrigin and Zeldasine, there is a strong sensitivity on C r , where small values for C r tend to improve the convergence speed, although it is generally advised to set C r = 0.9 [1,5,15,26,35,42]. This is because both functions are separable, but this property is a special case and in general functions are not expected to be separable.…”

“…In two different works, Liu and Lampinen [15] and Brest et al [5], introduce methods for on-line self-adaptation of DE's control parameters for mutation and crossover. Another self-adaptive DE is proposed in [20].…”

Training Artificial Neural Network Using Modification of Differential Evolution Algorithm

“…Liu and J. Lampinen [11] present an algorithm based on the Fuzzy Logic Control (FLC) in which the step-length was controlled using a single FLC. Its two inputs were: linearly depressed parameter vector change and function value change over the whole population members between the current generation and the last generation.…”

Gradual and Cumulative Improvements to the Classical Differential Evolution Scheme through Experiments

“…Initial efforts have been put into finding guidelines for choosing proper DE control parameters for different kinds of optimization problems, see for example the pioneering work of R. Storn et al [2], [3], J. Liu and J. Lampinen [4], or in the attempt to mathematically derive good DE parameters, see the pioneering work of D. Zaharie [5]. Another research direction has been devoted to eliminating the need for manual parameter tuning altogether, by automatically perturbing or adapting the control parameters during optimization based on feedback from the search, see the pioneering work of J. Liu and J. Lampinen [6], A.K. Qin et al [7] [8], and J. Brest et al [9].…”