Automated and Surrogate Multi-Resolution Approaches in Genetic Algorithms

Abstract

Recent work on multi-resolution optimisation (varying the fidelity of a design during a search) has developed approaches for automated resolution change depending on the population characteristics. This used the standard deviation of the population, or the marginal probability density estimation per variable, to automatically determine the resolution to apply to a design in the next generation. Here we build on this methodology in a number of new directions. We investigate the use of a complete estimated probability density function for resolution determination, enabling the dependencies between variables to be represented. We also explore the use of the multi-resolution transformation to assign a surrogate fitness to population members, but without modifying their location, and discuss the fitness landscape implications of this approach. Results are presented on a range of popular uni-objective continuous test-functions. These demonstrate the performance improvements that can be gained using an automated multi-resolution approach, and surprisingly indicate the simplest resolution indicator is often the most effective, but that relative performance is often problem dependant. We also observe how population duplicates grow in multi-resolution approaches, and discuss the implications of this when comparing algorithms (and efficiently implementing them).