Level-Based Analysis of Genetic Algorithms for Combinatorial Optimization

TL;DR

This paper analyzes the run-time of non-elitist genetic algorithms for combinatorial optimization, providing improved bounds and conditions for efficiently finding approximate solutions with guaranteed local optima.

Contribution

It introduces new upper bounds on run-time using drift analysis and establishes conditions for efficient approximation in problems with local optima.

Findings

Improved upper bounds on genetic algorithm run-time.

Conditions for efficient approximate solutions.

Application to problems with guaranteed local optima.

Abstract

The paper is devoted to upper bounds on run-time of Non-Elitist Genetic Algorithms until some target subset of solutions is visited for the first time. In particular, we consider the sets of optimal solutions and the sets of local optima as the target subsets. Previously known upper bounds are improved by means of drift analysis. Finally, we propose conditions ensuring that a Non-Elitist Genetic Algorithm efficiently finds approximate solutions with constant approximation ratio on the class of combinatorial optimization problems with guaranteed local optima (GLO).