Evolving Benchmark Functions to Compare Evolutionary Algorithms via Genetic Programming

Abstract

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.