A Novel Hybrid Grey Wolf Differential Evolution Algorithm

TL;DR

This work addresses the limitations of Grey Wolf Optimizer (GWO) and Differential Evolution (DE) by introducing a hybrid GWO-DE algorithm that leverages DE/best/1/bin and the self-adaptive jDE variant with a switching mechanism to counter stagnation. The approach dynamically selects among base optimizers based on recent performance, maintaining a per-iteration complexity of $O(NPD + NPF)$. Extensive experiments on eleven classic numerical functions and the CEC 2017 benchmark across $D=30$, $50$, and $100$ demonstrate that GWO-DE often achieves the best or top-ranked performance, with Friedman tests confirming superior average ranking. The results indicate that the hybrid algorithm offers improved robustness and convergence speed for high-dimensional global optimization tasks in engineering and related fields.

Abstract

Grey wolf optimizer (GWO) is a nature-inspired stochastic meta-heuristic of the swarm intelligence field that mimics the hunting behavior of grey wolves. Differential evolution (DE) is a popular stochastic algorithm of the evolutionary computation field that is well suited for global optimization. In this part, we introduce a new algorithm based on the hybridization of GWO and two DE variants, namely the GWO-DE algorithm. We evaluate the new algorithm by applying various numerical benchmark functions. The numerical results of the comparative study are quite satisfactory in terms of performance and solution quality.

Figures (8)

• Figure 1: Box plots of log error distribution for the common benchmark functions, $D=30$, a) Ackley, b) generalized Griewank, c) Generalized Penalized $f_{13}$, d) Rosenbrock.
• Figure 2: Convergence rate plots of log mean error distribution for the common benchmark functions, $D=30$, a) Ackley, b) generalized Griewank, c) Generalized Penalized $f_{13}$, d) Rosenbrock.
• Figure 3: Box plots of log error distribution for CEC 2017 benchmark functions, $D=30$, a) $f_1$, b) $f_4$, c) $f_{11}$, d) $f_{21}$.
• Figure 4: Convergence rate plots of log mean error distribution for CEC 2017 benchmark functions, $D=30$, a) $f_1$, b) $f_4$, c) $f_{11}$, d) $f_{21}$.
• Figure 5: Box plots of log error distribution for CEC 2017 benchmark functions, $D=50$, a) $f_1$, b) $f_4$, c) $f_{11}$, d) $f_{21}$.