Benchmarking Stochastic Algorithms for Global Optimization Problems by Visualizing Confidence Intervals.

The popular performance profiles and data profiles for benchmarking deterministic optimization algorithms are extended to benchmark stochastic algorithms for global optimization problems. A general confidence interval is employed to replace the significance test, which is popular in traditional benchmarking methods but suffering more and more criticisms. Through computing confidence bounds of the general confidence interval and visualizing them with performance profiles and (or) data profiles, our benchmarking method can be used to compare stochastic optimization algorithms by graphs. Compared with traditional benchmarking methods, our method is synthetic statistically and therefore is suitable for large sets of benchmark problems. Compared with some sample-mean-based benchmarking methods, e.g., the method adopted in black-box-optimization-benchmarking workshop/competition, our method considers not only sample means but also sample variances. The most important property of our method is that it is a distribution-free method, i.e., it does not depend on any distribution assumption of the population. This makes it a promising benchmarking method for stochastic optimization algorithms. Some examples are provided to illustrate how to use our method to compare stochastic optimization algorithms.