A comparison of various optimization algorithms on a multilevel problem

Abstract

In many problems in science and engineering, there are often a number of computational models that can be used to simulate the problem at hand. Models of physical systems can differ according to computational cost, accuracy and precision. This paper presents the concept of multilevel optimization, where different models of the problem are used in combination. This initial study compares several strategies for combining fast evaluations of limited accuracy with a few accurate calculations. It also attempts to show how different optimizers work under these different combination strategies. A specially designed test function is used to carry out these comparisons. Of the proposed strategies and optimisers, a sequential mixing strategy applied to a genetic algorithm with clustering gives the best results. This paper highlights the need to develop specialized optimization algorithms for this kind of problem