Theoretical Study of Optimizing Rugged Landscapes with the cGA

TL;DR

This paper provides a theoretical analysis showing that the compact genetic algorithm (cGA) outperforms classical local search algorithms like RLS and (1+1) EA on rugged, noisy fitness landscapes such as a noisy OneMax problem.

Contribution

The paper offers a theoretical comparison demonstrating the robustness of the cGA in rugged landscapes with noise, unlike traditional local search methods.

Findings

cGA finds near-optimal solutions even with high noise variance

RLS and (1+1) EA are limited to solutions with about half the optimal number of 1s

Theoretical insights into EDAs' suitability for rugged fitness landscapes

Abstract

Estimation of distribution algorithms (EDAs) provide a distribution - based approach for optimization which adapts its probability distribution during the run of the algorithm. We contribute to the theoretical understanding of EDAs and point out that their distribution approach makes them more suitable to deal with rugged fitness landscapes than classical local search algorithms. Concretely, we make the OneMax function rugged by adding noise to each fitness value. The cGA can nevertheless find solutions with n(1 - \epsilon) many 1s, even for high variance of noise. In contrast to this, RLS and the (1+1) EA, with high probability, only find solutions with n(1/2+o(1)) many 1s, even for noise with small variance.