On Benchmarking Stochastic Global Optimization Algorithms

Amultitude of heuristic stochastic optimization algorithms have been described in literature to obtain good solutions of the box-constrained global optimization problem often with a limit on the number of used function evaluations. In the larger question of which algorithms behave well on which type of instances, our focus is here on the benchmarking of the behavior of algorithms by applying experiments on test instances. We argue that a good minimum performance benchmark is due to pure random search; i.e. algorithms should do better. We introduce the concept of the cumulative distribution function of the record value as a measure with the benchmark of pure random search and the idea of algorithms being dominated by others. The concepts are illustrated using frequently used algorithms.