The Barrier Tree Benchmark: Many Basins and Double Funnels

The Barrier Tree Benchmark (BTB) is a principled generator of continuous real-valued landscapes: problems of known topography/critical point structure can be systematically designed and deployed in algorithm comparison studies. A previous BTB study focused on a single funnel and a double basin. This work demonstrates algorithm performance on BTB instances with many basins, and on double funnels. A methodology for principled algorithm comparison on families of problems of similar complexity and structure is proposed. It is hoped that the BTB will address a parameter tuning pathology of current problem benchmarks, namely, that common optimisation algorithms require widely different control parameter settings for optimal performance on differing problem classes. This pathology is traced to the irregular and arbitrary composition of standard benchmarks.