Unleashing the Potential of Differential Evolution through Individual-Level Strategy Diversity

TL;DR

This work addresses DE’s sensitivity to strategy choice by introducing iStratDE, which assigns fixed per-individual mutation and crossover strategies at initialization to create persistent behavioral diversity and enable fully parallel GPU execution. It provides a convergence analysis under standard assumptions and demonstrates, through extensive benchmarks on CEC2022 and Brax-based robotic control tasks, that iStratDE matches or outperforms strong adaptive DE variants while maintaining scalability. The key findings show that structural diversity at the individual level, enabled by a rich strategy pool (192 configurations) and large populations, yields robust exploration and asynchronous convergence without feedback or archives. The results suggest that minimal, decentralized diversity mechanisms can offer competitive performance and scalability, motivating broader adoption of per-individual design principles in evolutionary algorithms.

Abstract

Since Differential Evolution (DE) is sensitive to strategy choice, most existing variants pursue performance through adaptive mechanisms or intricate designs. While these approaches focus on adjusting strategies over time, the structural benefits that static strategy diversity may bring remain largely unexplored. To bridge this gap, we study the impact of individual-level strategy diversity on DE's search dynamics and performance, and introduce iStratDE (DE with individual-level strategies), a minimalist variant that assigns mutation and crossover strategies independently to each individual at initialization and keeps them fixed throughout the evolutionary process. By injecting diversity at the individual level without adaptation or feedback, iStratDE cultivates persistent behavioral heterogeneity that is especially effective with large populations. Moreover, its communication-free construction possesses intrinsic concurrency, thereby enabling efficient parallel execution and straightforward scaling for GPU computing. We further provide a convergence analysis of iStratDE under standard reachability assumptions, which establishes the almost-sure convergence of the best-so-far fitness. Extensive experiments on the CEC2022 benchmark suite and robotic control tasks demonstrate that iStratDE matches or surpasses established adaptive DE variants. These results highlight individual-level strategy assignment as a straightforward yet effective mechanism for enhancing DE's performance. The source code of iStratDE is publicly accessible at: https://github.com/EMI-Group/istratde.

Figures (19)

• Figure 1: Framework of iStratDE. Each individual is initialized with a unique combination of mutation strategy $S_i$ and control parameters $P_i$. During reproduction, mutation and crossover are applied according to these assigned configurations, producing a trial vector $\boldsymbol{u}_i$ that competes with its parent solution $\boldsymbol{x}_i$; the fitter candidate survives into the next generation. Although the solution vector $\boldsymbol{x}_i$ and its fitness $y_i$ evolve over time, the assigned strategy $S_i$ and parameters $P_i$ remain fixed, thereby sustaining persistent diversity across the population.
• Figure 1: Convergence curves on 10D problems in CEC2022 benchmark suite. The peer DE variants are set with population size of 100.
• Figure 2: Convergence curves on 10D problems in the CEC2022 benchmark suite.
• Figure 2: Convergence curves on 20D problems in CEC2022 benchmark suite. The peer DE variants are set with population size of 100.
• Figure 3: Average number of function evaluations (FEs) completed within 60s on 10D and 20D problems in the CEC2022 benchmark suite.