Combining Drift Analysis and Generalized Schema Theory to Design Efficient Hybrid and/or Mixed Strategy EAs

TL;DR

This paper develops a rigorous mathematical framework combining drift analysis and generalized schema theory to guide the design of efficient hybrid and mixed strategy evolutionary algorithms for complex NP-hard problems.

Contribution

It introduces a novel theoretical foundation for hybrid EAs, integrating schema theory and drift analysis to improve their design and understanding.

Findings

Framework supports the design of more effective hybrid EAs

Application to single-machine scheduling demonstrates practical utility

Provides mathematical insights into EA performance and convergence

Abstract

Hybrid and mixed strategy EAs have become rather popular for tackling various complex and NP-hard optimization problems. While empirical evidence suggests that such algorithms are successful in practice, rather little theoretical support for their success is available, not mentioning a solid mathematical foundation that would provide guidance towards an efficient design of this type of EAs. In the current paper we develop a rigorous mathematical framework that suggests such designs based on generalized schema theory, fitness levels and drift analysis. An example-application for tackling one of the classical NP-hard problems, the "single-machine scheduling problem" is presented.