Classical Benchmark Functions, But Harder

We explore the hardness evolvability of 12 well-known continuous benchmark test functions such as Schwefel, Griewank and Goldstein-Price, by evolutionarily retuning their numeric parameters. Evaluation is done by assessing the hardness of optimzation for the plant propagation algorithm (PPA), a crossoverless evolutionary method. The evolutionary process has a significant effect on a function’s objective landscape (“Fitness landscape” is the more common term, but “objective landscape” is correcter, as some algorithms actively process objective values into fitness values.) and the resulting hardness for PPA. When assessing at the resulting landscapes, three distinct patterns of evolution are observed: concave-to-convex inversion, global minimum narrowing, and increase in ruggedness. Conclusively, many of these traditional benchmark functions are not nearly as hard as the could be, at least for one metaheuristic optimization algorithm. As it turns out, traditional benchmark functions can be made much more challenging by only retuning a few of their constants. Some limitations and future options are discussed.