Comparative efficiency of dimensionality reduction schemes in global optimization

Abstract

This work presents results of a comparative efficiency for global optimization methods based on ideas of reducing the dimensionality of the multiextremal optimization problems. Two approaches to the dimensionality reduction are considered. One of them applies Peano-type space filling curves for reducing the multidimensional problem to an equivalent univariate one. The second approach is based on the nested optimization scheme that transforms the multidimensional problem to a family of one-dimensional subproblems connected recursively. In the frameworks of both approaches, the so-called characteristical algorithms are used for executing the univariate optimization. The efficiency of the compared global search methods is evaluated experimentally on the well-known GKLS test class generator being at present a classical tool for testing global optimization algorithms. Results for problems of different dimensions demonstrate a convincing advantage of the adaptive nested optimization scheme used in combination with the information-statistical univariate algorithm over its rivals.