On Proportions of Fit Individuals in Population of Evolutionary Algorithm with Tournament Selection

TL;DR

This paper models the proportion of fit individuals in a non-elitist EA with tournament selection, showing how tournament size affects performance and providing bounds on runtime for specific problems.

Contribution

It introduces a fitness-level model with bounds for non-elitist EAs, highlighting the impact of tournament size and deriving runtime bounds for certain problem classes.

Findings

Increasing tournament size improves EA performance.

Provides exponential tail bounds for local search on unimodal functions.

Establishes polynomial runtime bounds for EAs on 2-SAT and Set Cover problems.

Abstract

In this paper, we consider a fitness-level model of a non-elitist mutation-only evolutionary algorithm (EA) with tournament selection. The model provides upper and lower bounds for the expected proportion of the individuals with fitness above given thresholds. In the case of so-called monotone mutation, the obtained bounds imply that increasing the tournament size improves the EA performance. As corollaries, we obtain an exponentially vanishing tail bound for the Randomized Local Search on unimodal functions and polynomial upper bounds on the runtime of EAs on 2-SAT problem and on a family of Set Cover problems proposed by E. Balas.