MetaDE: Evolving Differential Evolution by Differential Evolution

TL;DR

This work tackles the challenge of hyperparameter configuration in Differential Evolution by introducing MetaDE, a two-tier meta-evolutionary framework that uses DE itself to evolve a Parameterized Differential Evolution (PDE) and its variants. PDE expands DE with six tunable components ($F$, $CR$, $bl$, $br$, $dn$, $cs$), enabling a vast space of mutation and crossover strategies; a DE-based evolver optimizes PDE’s six parameters, while multiple PDE executors solve the target problem in parallel, all implemented on a GPU-accelerated EvoX platform. The approach is evaluated on the CEC2022 single-objective benchmark and robotic-control tasks via evolutionary reinforcement learning, showing competitive or superior convergence and efficiency versus strong baselines, especially under strict wall-clock and large-population settings. The results highlight the potential of self-adaptive meta-optimization for robust, high-concurrency optimization and offer insights into optimal DE configurations across problem landscapes, with public code available for reproducibility.

Abstract

As a cornerstone in the Evolutionary Computation (EC) domain, Differential Evolution (DE) is known for its simplicity and effectiveness in handling challenging black-box optimization problems. While the advantages of DE are well-recognized, achieving peak performance heavily depends on its hyperparameters such as the mutation factor, crossover probability, and the selection of specific DE strategies. Traditional approaches to this hyperparameter dilemma have leaned towards parameter tuning or adaptive mechanisms. However, identifying the optimal settings tailored for specific problems remains a persistent challenge. In response, we introduce MetaDE, an approach that evolves DE's intrinsic hyperparameters and strategies using DE itself at a meta-level. A pivotal aspect of MetaDE is a specialized parameterization technique, which endows it with the capability to dynamically modify DE's parameters and strategies throughout the evolutionary process. To augment computational efficiency, MetaDE incorporates a design that leverages parallel processing through a GPU-accelerated computing framework. Within such a framework, DE is not just a solver but also an optimizer for its own configurations, thus streamlining the process of hyperparameter optimization and problem-solving into a cohesive and automated workflow. Extensive evaluations on the CEC2022 benchmark suite demonstrate MetaDE's promising performance. Moreover, when applied to robot control via evolutionary reinforcement learning, MetaDE also demonstrates promising performance. The source code of MetaDE is publicly accessible at: https://github.com/EMI-Group/metade.

Figures (19)

• Figure 1: Parameter delineation of PDE and their respective domains. PDE comprehensively parameterizes DE, endorsing unrestricted parameter and strategy modifications. In this schema, $F$ and $CR$ are continuous parameters, whereas others are categorical. The dashed-line boxes exhibit their specific value ranges. The mutation function is derived from the base vector left, base vector right, and difference number parameters.
• Figure 2: Architecture of MetaDE. Within this architecture, a conventional DE algorithm operates as an evolver, where its individual $\mathbf{x}_i$ represents a distinct parameter configuration $\mathbf{\theta}_i$. These configurations are relayed to PDE to instantiate diverse DE variants as the executors. Each executor then evolves its distinct population and returns the best fitness $y^*$ as identified, which is subsequently set as the fitness of $\mathbf{x}_i$.
• Figure 3: Convergence curves on 10D problems in CEC2022 benchmark suite. The peer DE variants are set with population size of 100.
• Figure 4: Convergence curves on 20D problems in CEC2022 benchmark suite. The peer DE variants are set with population size of 100.
• Figure 5: The number of FEs achieved by each algorithm within 60s. The results are averaged on all 10D and 20D problems in the CEC2022 benchmark suite.