Sharp bounds for genetic drift in estimation of distribution algorithms (Hot-off-the-press track at GECCO 2020)

Estimation of distribution algorithms (EDAs) are a successful branch of evolutionary algorithms (EAs) that evolve a probabilistic model instead of a population. Analogous to genetic drift in EAs, EDAs also encounter the phenomenon that the random sampling in the model update can move the sampling frequencies to boundary values not justified by the fitness. This can result in a considerable performance loss. This work gives the first tight quantification of this effect for three EDAs and one ant colony optimizer, namely for the univariate marginal distribution algorithm, the compact genetic algorithm, population-based incremental learning, and the max-min ant system with iteration-best update. Our results allow to choose the parameters of these algorithms in such a way that within a desired runtime, no sampling frequency approaches the boundary values without a clear indication from the objective function. This paper for the Hot-off-the-Press track at GECCO 2020 summarizes the work "Sharp Bounds for Genetic Drift in Estimation of Distribution Algorithms" by B. Doerr and W. Zheng, which has been accepted for publication in the IEEE Transactions on Evolutionary Computation [5].

[1]  Y. Svirezhev,et al.  Diffusion Models of Population Genetics , 1990 .

[2]  Weijie Zheng,et al.  Sharp Bounds for Genetic Drift in Estimation of Distribution Algorithms , 2020, IEEE Transactions on Evolutionary Computation.

[3]  Carsten Witt,et al.  Lower Bounds on the Run Time of the Univariate Marginal Distribution Algorithm on OneMax , 2017, FOGA '17.

[4]  Thomas Bäck,et al.  Theory of Evolutionary Computation: Recent Developments in Discrete Optimization , 2020, Theory of Evolutionary Computation.

[5]  Motoo Kimura,et al.  Diffusion models in population genetics , 1964, Journal of Applied Probability.

[6]  Heinz Mühlenbein,et al.  On the Mean Convergence Time of Evolutionary Algorithms without Selection and Mutation , 1994, PPSN.

[7]  Dirk Sudholt,et al.  On the Choice of the Update Strength in Estimation-of-Distribution Algorithms and Ant Colony Optimization , 2018, Algorithmica.

[8]  Carsten Witt,et al.  Theory of estimation-of-distribution algorithms , 2018, GECCO.

[9]  Weijie Zheng,et al.  From understanding genetic drift to a smart-restart parameter-less compact genetic algorithm , 2020, GECCO.

[10]  Tobias Friedrich,et al.  EDAs cannot be Balanced and Stable , 2016, GECCO.

[11]  Carsten Witt,et al.  Upper Bounds on the Running Time of the Univariate Marginal Distribution Algorithm on OneMax , 2018, Algorithmica.

[12]  Dirk Sudholt,et al.  Medium step sizes are harmful for the compact genetic algorithm , 2018, GECCO.

[13]  Dirk P. Kroese,et al.  Convergence properties of the cross-entropy method for discrete optimization , 2007, Oper. Res. Lett..

[14]  Xin Yao,et al.  Drift analysis and average time complexity of evolutionary algorithms , 2001, Artif. Intell..

[15]  Benjamin Doerr,et al.  The Univariate Marginal Distribution Algorithm Copes Well with Deception and Epistasis , 2020, Evolutionary Computation.

[16]  Stefan Droste,et al.  A rigorous analysis of the compact genetic algorithm for linear functions , 2006, Natural Computing.

[17]  Per Kristian Lehre,et al.  On the limitations of the univariate marginal distribution algorithm to deception and where bivariate EDAs might help , 2019, FOGA '19.

[18]  Pedro Larrañaga,et al.  The Convergence Behavior of the PBIL Algorithm: A Preliminary Approach , 2001 .