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The Univariate Marginal Distribution Algorithm Copes Well with Deception and Epistasis.

Benjamin Doerr¹, Martin S Krejca²

¹Laboratoire d'Informatique (LIX), CNRS, École Polytechnique, Institut Polytechnique de Paris, Palaiseau, France doerr@lix.polytechnique.fr.

Evolutionary Computation

|October 8, 2021

Summary

The univariate marginal distribution algorithm (UMDA) can efficiently solve deceptive problems when population sizes are large enough to prevent genetic drift. This contrasts with previous findings suggesting limitations in evolutionary computation.

Keywords:

Estimation-of-distribution algorithm epistasis runtime analysis theory.univariate marginal distribution algorithm

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Area of Science:

Artificial Intelligence
Computational Intelligence
Evolutionary Computation

Background:

Previous research indicated the univariate marginal distribution algorithm (UMDA) struggles with deceptive problems due to exponential time complexity.
This suggested limitations in univariate Estimation of Distribution Algorithms (EDAs) concerning deception and epistasis.

Purpose of the Study:

To re-evaluate the performance of the UMDA on the DeceptiveLeadingBlocks (DLB) problem.
To demonstrate that appropriate parameter settings, specifically larger population sizes, overcome previous performance limitations.

Main Methods:

Analysis of UMDA performance with population sizes sufficient to prevent genetic drift.
Derivation of fitness evaluation bounds for UMDA optimization of the DLB problem.
Comparison of UMDA runtime with classic evolutionary algorithms like the (1+1) EA.

Main Results:

UMDA optimizes the DLB problem with high probability using O(n^2 log n) fitness evaluations when genetic drift is prevented.
This performance is significantly better than the O(n^3) bound for classic evolutionary algorithms.
The study confirms that running EDAs in a genetic drift regime leads to substantial performance degradation.

Conclusions:

The UMDA, with adequate population sizes, effectively handles deception and epistasis, contrary to prior conclusions.
UMDA demonstrates superior performance in navigating local optima compared to many classic evolutionary algorithms.
This work rigorously establishes the critical role of population size in EDA performance and highlights the risks of genetic drift.