In this study, we use Genetic Programming (GP) to compose new optimization benchmark functions. Optimization benchmarks have the important role of showing the differences between evolutionary algorithms, making it possible for further analysis and comparisons. We show that the benchmarks generated by GP are able to differentiate algorithms better than human-made benchmark functions. The fitness measure of the GP is the Wasserstein distance of the solutions found by a pair of optimizers. Additionally, we use MAP-Elites to both enhance the search power of the GP and also illustrate how the difference between optimizers changes by various landscape features. Our approach provides a novel way to automate the design of benchmark functions and to compare evolutionary algorithms.

翻译：本研究采用遗传编程(Genetic Programming, GP)方法构建新型优化基准函数。优化基准函数在揭示进化算法差异性方面具有关键作用，可为算法后续分析与比较提供支持。研究表明，GP生成的基准函数比人工设计的基准函数更能有效区分不同算法。GP的适应度度量采用一对优化器所得解之间的Wasserstein距离。此外，我们引入MAP-Elites方法，既增强了GP的搜索能力，又揭示了不同景观特征如何影响优化器间的差异。本方法为自动化设计基准函数及比较进化算法提供了全新途径。