On the Optimal Convergence Probability of Univariate Estimation of Distribution Algorithms

TL;DR

This paper derives bounds and conditions for the probability of convergence to the optimal solution in univariate Estimation of Distribution Algorithms like cGA and PBIL, providing insights into their parameter settings for guaranteed convergence.

Contribution

It offers new bounds and sufficient conditions for convergence of cGA and PBIL, along with parameter ranges ensuring high-confidence convergence to optimal solutions.

Findings

Derived bounds on convergence probability

Identified parameter ranges for guaranteed convergence

Provided sufficient conditions for convergence

Abstract

In this paper, we obtain bounds on the probability of convergence to the optimal solution for the compact Genetic Algorithm (cGA) and the Population Based Incremental Learning (PBIL). We also give a sufficient condition for convergence of these algorithms to the optimal solution and compute a range of possible values of the parameters of these algorithms for which they converge to the optimal solution with a confidence level.