Pure Strategy or Mixed Strategy?

TL;DR

This paper provides a theoretical analysis of mixed versus pure strategy evolutionary algorithms, showing conditions under which mixed strategies outperform pure strategies in terms of convergence and hitting time.

Contribution

It proves that mixed strategy (1+1) EAs are at least as good as the worst pure strategy, and can outperform all pure strategies if mutation operators are mutually complementary.

Findings

Mixed strategies are not worse than the worst pure strategy.

Mutually complementary mutation operators enable better performance.

Performance is measured by asymptotic convergence rate and hitting time.

Abstract

Mixed strategy EAs aim to integrate several mutation operators into a single algorithm. However few theoretical analysis has been made to answer the question whether and when the performance of mixed strategy EAs is better than that of pure strategy EAs. In theory, the performance of EAs can be measured by asymptotic convergence rate and asymptotic hitting time. In this paper, it is proven that given a mixed strategy (1+1) EAs consisting of several mutation operators, its performance (asymptotic convergence rate and asymptotic hitting time)is not worse than that of the worst pure strategy (1+1) EA using one mutation operator; if these mutation operators are mutually complementary, then it is possible to design a mixed strategy (1+1) EA whose performance is better than that of any pure strategy (1+1) EA using one mutation operator.