Reviewing and Benchmarking Parameter Control Methods in Differential Evolution

Abstract

Many Differential Evolution (DE) algorithms with various parameter control methods (PCMs) have been proposed. However, previous studies usually considered PCMs to be an integral component of a complex DE algorithm. Thus the characteristics and performance of each method are poorly understood. We present an in-depth review of 24 PCMs for the scale factor and crossover rate in DE and a large scale benchmarking study. We carefully extract the 24 PCMs from their original, complex algorithms and describe them according to a systematic manner. Our review facilitates the understanding of similarities and differences between existing, representative PCMs. The performance of DEs with the 24 PCMs and 16 variation operators is investigated on 24 black-box benchmark functions. Our benchmarking results reveal which methods exhibit high performance when embedded in a standardized framework under 16 different conditions, independent from their original, complex algorithms. We also investigate how much room there is for further improvement of PCMs by comparing the 24 methods with an oracle-based model, which can be considered to be a conservative lower bound on the performance of an optimal method.

An Approach to Chance Constrained Problems Based on Huge Data Sets Using Weighted Stratified Sampling and Adaptive Differential Evolution

“…The performance of DE depends on control parameters, namely the scale factor F ∈ [0.1, 1] in (19) and the crossover rate CR ∈ [0, 1] in (20). Therefore, various parameter adaptation mechanisms have been reported [28,29,31]. ADEP employs an adaptive parameter control mechanism in which feedback from the evolutionary search is used to dynamically change the control parameters [19].…”

“…A full data set B ⊆ 3 , |B| = 10 7 is generated randomly as shown in (31) and (32). For the probabilityp(x, B) in (26), a non-linear function g(x, ξ ) is defined as…”

“…We suppose that the amount of rainfall ξ ∈ Ω in (37) is given as "big data". For convenience, the full data set ξ = (ξ 1 , ξ 2 , ξ 3 ) ∈ B ⊆ Ω is generated randomly by using the truncated normal distribution shown in (31). Please notice that ξ ∈ B denotes the amount of rainfall in one period, but the river flow depending on an actual time.…”

Analyzing adaptive parameter landscapes in parameter adaptation methods for differential evolution

“…Parameter control methods in EAs can be classified into deterministic, adaptive, and self-adaptive control methods [12]. Although some DE algorithms with deterministic and self-adaptive approaches have been proposed (e.g., [32,48]), adaptive approaches have mainly been studied in the DE community [45].…”

“…While "an adaptive DE" is a complex algorithm that consists of multiple components, "a PAM" is a single component only for adaptively adjusting F and C values. As explained in [45], "L-SHADE" [46] is "an adaptive DE" that mainly consists of the following four components: (a) the current-to-pbest/1 mutation strategy [53], (b) the binomial crossover, (c) the "PAM" in SHADE [42], and (d) the linear population size reduction strategy. In this paper, we are interested in (c) the "PAM" in SHADE, rather than L-SHADE.…”