Introducing Competitive Mechanism to Differential Evolution for Numerical Optimization

TL;DR

The paper tackles numerical optimization by enhancing differential evolution with a competitive mechanism, yielding the DE/winner-to-best/1 mutation that selects a base vector from a competing individual or the current vector. It employs $F_1,F_2 \sim \mathcal{N}(0.5,0.3)$ and $Cr \sim \mathcal{N}(0.5,0.3)$ to promote balanced exploration and exploitation. Comprehensive experiments on the CEC2017 benchmark and six engineering design problems compare CDE against CMA-ES, JADE, L-SHADE, GTDE, and other DE variants, with 30 runs and Holm statistical analysis confirming competitive performance. The results demonstrate CDE’s strong exploitation, robustness across diverse landscapes, and practical potential for real-world optimization tasks, offering a lightweight yet effective improvement to standard DE. The study highlights that simple competitive mechanisms can significantly boost DE without substantial computational overhead.

Abstract

This paper introduces a novel competitive mechanism into differential evolution (DE), presenting an effective DE variant named competitive DE (CDE). CDE features a simple yet efficient mutation strategy: DE/winner-to-best/1. Essentially, the proposed DE/winner-to-best/1 strategy can be recognized as an intelligent integration of the existing mutation strategies of DE/rand-to-best/1 and DE/cur-to-best/1. The incorporation of DE/winner-to-best/1 and the competitive mechanism provide new avenues for advancing DE techniques. Moreover, in CDE, the scaling factor $F$ and mutation rate $Cr$ are determined by a random number generator following a normal distribution, as suggested by previous research. To investigate the performance of the proposed CDE, comprehensive numerical experiments are conducted on CEC2017 and engineering simulation optimization tasks, with CMA-ES, JADE, and other state-of-the-art optimizers and DE variants employed as competitor algorithms. The experimental results and statistical analyses highlight the promising potential of CDE as an alternative optimizer for addressing diverse optimization challenges.

Figures (3)

• Figure 1: The flowchart of CDE.
• Figure 2: The demonstration of engineering simulation tasks.
• Figure 3: Convergence curves of eight algorithms on six engineering simulation optimization tasks.