Elitism Levels Traverse Mechanism For The Derivation of Upper Bounds on Unimodal Functions

TL;DR

This paper introduces an Elitism Levels Traverse Mechanism to derive upper bounds on the performance of population-based evolutionary algorithms solving unimodal functions, with theoretical proofs and empirical testing on the OneMax function.

Contribution

It presents a novel mechanism for analyzing evolutionary algorithms, providing theoretical bounds and demonstrating its effectiveness on a standard benchmark.

Findings

Proves the efficiency of the mechanism theoretically.

Derives bounds cμn log n - O(μn) for the OneMax function.

Applicable to algorithms using tournament selection and single-bit operators.

Abstract

In this article we present an Elitism Levels Traverse Mechanism that we designed to find bounds on population-based Evolutionary algorithms solving unimodal functions. We prove its efficiency theoretically and test it on OneMax function deriving bounds c{\mu}n log n - O({\mu} n). This analysis can be generalized to any similar algorithm using variants of tournament selection and genetic operators that flip or swap only 1 bit in each string.