Benchmarking Parameter Control Methods in Differential Evolution for Mixed-Integer Black-Box Optimization

Abstract

Differential evolution (DE) generally requires parameter control methods (PCMs) for the scale factor and crossover rate. Although a better understanding of PCMs provides a useful clue to designing an efficient DE, their effectiveness is poorly understood in mixed-integer black-box optimization. In this context, this paper benchmarks PCMs in DE on the mixed-integer black-box optimization benchmarking function (bbob-mixint) suite in a component-wise manner. First, we demonstrate that the best PCM significantly depends on the combination of the mutation strategy and repair method. Although the PCM of SHADE is state-of-the-art for numerical black-box optimization, our results show its poor performance for mixed-integer black-box optimization. In contrast, our results show that some simple PCMs (e.g., the PCM of CoDE) perform the best in most cases. Then, we demonstrate that a DE with a suitable PCM performs significantly better than CMA-ES with integer handling for larger budgets of function evaluations. Finally, we show how the adaptation in the PCM of SHADE fails.

arXiv commentThis is an accepted version of a paper published in the proceedings of GECCO 2024

References in corpus (5)

• COCO: A Platform for Comparing Continuous Optimizers in a Black-Box Setting
• Automated Algorithm Selection on Continuous Black-Box Problems By Combining Exploratory Landscape Analysis and Machine Learning
• Reviewing and Benchmarking Parameter Control Methods in Differential Evolution
• CMA-ES with Margin: Lower-Bounding Marginal Probability for Mixed-Integer Black-Box Optimization
• TPAM: A Simulation-Based Model for Quantitatively Analyzing Parameter Adaptation Methods