Opposition-Based Differential Evolution

TLDR

Evolutionary algorithms are popular for nonlinear optimization but are computationally expensive due to slow evolutionary processes. This paper proposes a novel opposition-based differential evolution algorithm to accelerate DE. The proposed ODE uses opposition-based learning for initialization and generation jumping, incorporates opposite numbers to speed convergence, and is evaluated on 58 benchmark functions across various dimensions, population sizes, jumping rates, and mutation strategies, with comparisons to fuzzy adaptive DE. Experimental results show that ODE outperforms both the original DE and FADE in convergence speed and solution accuracy, confirming the empirical benefit of opposite numbers.

Abstract

Evolutionary algorithms (EAs) are well-known optimization approaches to deal with nonlinear and complex problems. However, these population-based algorithms are computationally expensive due to the slow nature of the evolutionary process. This paper presents a novel algorithm to accelerate the differential evolution (DE). The proposed opposition-based DE (ODE) employs opposition-based learning (OBL) for population initialization and also for generation jumping. In this work, opposite numbers have been utilized to improve the convergence rate of DE. A comprehensive set of 58 complex benchmark functions including a wide range of dimensions is employed for experimental verification. The influence of dimensionality, population size, jumping rate, and various mutation strategies are also investigated. Additionally, the contribution of opposite numbers is empirically verified. We also provide a comparison of ODE to fuzzy adaptive DE (FADE). Experimental results confirm that the ODE outperforms the original DE and FADE in terms of convergence speed and solution accuracy.