Fast Estimations of Hitting Time of Elitist Evolutionary Algorithms from Fitness Levels

TL;DR

This paper introduces a subset level method that improves the estimation of hitting times for elitist evolutionary algorithms on non-level-based fitness functions, validated through knapsack problem instances.

Contribution

A novel subset level method that extends fitness level analysis to non-level-based functions using drift analysis and explicit lower bound expressions.

Findings

The method provides quick lower bound estimates for hitting times.

It applies to non-level-based fitness functions, broadening previous scope.

Validated on six knapsack problem instances.

Abstract

The fitness level method is a widely used technique for estimating the mean hitting time of elitist evolutionary algorithms on level-based fitness functions. However, this paper identifies its main limitation: the linear lower bound derived from traditional fitness level partitioning is not tight when applied to many non-level-based fitness functions. A new subset level method is introduced to address this limitation. It selects a subset of non-optimal solutions, partitions them into levels, and then estimates linear bound coefficients based on drift analysis. Explicit expressions are proposed to compute the lower bound on the mean hitting time of elitist evolutionary algorithms. The proposed method is validated using six instances of the knapsack problem. Results show that the new method can be used to quickly estimate the lower bound on the mean hitting time of elitist evolutionary algorithms. This expands the application scope of the fitness level method to non-level-based functions.