Comparison of Monte Carlo and deterministic methods for non-adaptive optimization

Abstract

In this paper we compare the average performance of Monte Carlo methods for global optimization with non-adaptive deterministic alternatives. We analyze the behavior of the algorithms under the assumption of Wiener measure on the space of continuous functions on the unit interval. In this setting we show that the primary strength of the Monte Carlo methods (compositeness) is outweighed by the primary weakness (random gap size) when compared to efficient deterministic methods.