Adaptive multiresolution search: How to beat brute force?

Abstract

Multiresolution and wavelet-based search methods are suited to problems for which acceptable solutions are in regions of high average local fitness. In this paper, two different approaches are presented. In the Markov-based approach, the sampling resolution is chosen adaptively depending on the fitness of the last sample(s). The advantage of this method, behind its simplicity, is that it allows the computation of the discovery probability of a target sample for quite large search spaces. This permits to “reverse-engineer” search-and-optimization problems. Starting from some prototypic examples of fitness functions the discovery rate can be computed as a function of the free parameters. The second approach is a wavelet-based multiresolution search using a memory to store local average values of the fitness functions. The sampling density probability is chosen per design proportional to a low-resolution approximation of the fitness function. High average fitness regions are sampled more often, and at a higher resolution, than low average fitness regions. If splines are used as scaling mother functions, a fuzzy description of the search strategy can be given within the framework of the Takagi–Sugeno model.