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The Univariate Marginal Distribution Algorithm Copes Well with Deception and Epistasis

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Evolutionary Computation in Combinatorial Optimization (EvoCOP 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12102))

Abstract

In their recent work, Lehre and Nguyen (FOGA 2019) show that the univariate marginal distribution algorithm (UMDA) needs time exponential in the parent populations size to optimize the DeceivingLeadingBlocks (DLB) problem. They conclude from this result that univariate EDAs have difficulties with deception and epistasis.

In this work, we show that this negative finding is caused by an unfortunate choice of the parameters of the UMDA. When the population sizes are chosen large enough to prevent genetic drift, then the UMDA optimizes the DLB problem with high probability with at most \(\lambda (\frac{n}{2} + 2 e \ln n)\) fitness evaluations. Since an offspring population size \(\lambda \) of order \(n \log n\) can prevent genetic drift, the UMDA can solve the DLB problem with \(O(n^2 \log n)\) fitness evaluations. In contrast, for classic evolutionary algorithms no better run time guarantee than \(O(n^3)\) is known, so our result rather suggests that the UMDA can cope well with deception and epistatis.

Together with the result of Lehre and Nguyen, our result for the first time rigorously proves that running EDAs in the regime with genetic drift can lead to drastic performance losses.

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References

  1. Chen, T., Lehre, P.K., Tang, K., Yao, X.: When is an estimation of distribution algorithm better than an evolutionary algorithm? In: Proceedings of CEC 2009, pp. 1470–1477 (2009). https://doi.org/10.1109/CEC.2009.4983116

  2. Dang, D., et al.: Escaping local optima with diversity mechanisms and crossover. In: Proceedings of GECCO 2016, pp. 645–652 (2016). https://doi.org/10.1145/2908812.2908956

  3. Dang, D., et al.: Escaping local optima using crossover with emergent diversity. IEEE Trans. Evol. Comput. 22(3), 484–497 (2018). https://doi.org/10.1109/TEVC.2017.2724201

    Article  Google Scholar 

  4. Dang, D., Lehre, P.K.: Simplified runtime analysis of estimation of distribution algorithms. In: Proceedings of GECCO 2015, pp. 513–518 (2015). https://doi.org/10.1145/2739480.2754814

  5. Doerr, B.: Analyzing randomized search heuristics via stochastic domination. Theor. Comput. Sci. 773, 115–137 (2019). https://doi.org/10.1016/j.tcs.2018.09.024

    Article  MathSciNet  MATH  Google Scholar 

  6. Doerr, B.: A tight runtime analysis for the cGA on jump functions: EDAs can cross fitness valleys at no extra cost. In: Proceedings of GECCO 2019, pp. 1488–1496 (2019). https://doi.org/10.1145/3321707.3321747

  7. Doerr, B.: Probabilistic tools for the analysis of randomized optimization heuristics. In: Doerr, B., Neumann, F. (eds.) Theory of Evolutionary Computation. NCS, pp. 1–87. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-29414-4_1. https://arxiv.org/abs/1801.06733

    Chapter  Google Scholar 

  8. Doerr, B., Krejca, M.S.: Significance-based estimation-of-distribution algorithms. In: Proceedings of GECCO 2018, pp. 1483–1490 (2018). https://doi.org/10.1145/3205455.3205553

  9. Doerr, B., Künnemann, M.: Optimizing linear functions with the (1+\(\lambda \)) evolutionary algorithm - different asymptotic runtimes for different instances. Theor. Comput. Sci. 561, 3–23 (2015). https://doi.org/10.1016/j.tcs.2014.03.015

    Article  MathSciNet  MATH  Google Scholar 

  10. Doerr, B., Zheng, W.: Sharp bounds for genetic drift in EDAs. CoRR abs/1910.14389 (2019). https://arxiv.org/abs/1910.14389

  11. Droste, S.: A rigorous analysis of the compact genetic algorithm for linear functions. Nat. Comput. 5(3), 257–283 (2006). https://doi.org/10.1007/s11047-006-9001-0

    Article  MathSciNet  MATH  Google Scholar 

  12. Droste, S., Jansen, T., Wegener, I.: On the analysis of the (1+1) evolutionary algorithm. Theor. Comput. Sci. 276(1–2), 51–81 (2002). https://doi.org/10.1016/S0304-3975(01)00182-7

    Article  MathSciNet  MATH  Google Scholar 

  13. Hasenöhrl, V., Sutton, A.M.: On the runtime dynamics of the compact genetic algorithm on jump functions. In: Proceedings of GECCO 2018, pp. 967–974 (2018). https://doi.org/10.1145/3205455.3205608

  14. Hoeffding, W.: Probability inequalities for sums of bounded random variables. J. Am. Stat. Assoc. 58(301), 13–30 (1963). https://doi.org/10.2307/2282952

    Article  MathSciNet  MATH  Google Scholar 

  15. Krejca, M.S., Witt, C.: Lower bounds on the run time of the univariate marginal distribution algorithm on OneMax. In: Proceedings of FOGA 2017, pp. 65–79 (2017). https://doi.org/10.1145/3040718.3040724

  16. Krejca, M.S., Witt, C.: Theory of estimation-of-distribution algorithms. In: Doerr, B., Neumann, F. (eds.) Theory of Evolutionary Computation. NCS, pp. 405–442. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-29414-4_9

    Chapter  Google Scholar 

  17. Lehre, P.K., Nguyen, P.T.H.: Improved runtime bounds for the univariate marginal distribution algorithm via anti-concentration. In: Proceedings of GECCO 2017, pp. 1383–1390 (2017). https://doi.org/10.1145/3071178.3071317

  18. Lehre, P.K., Nguyen, P.T.H.: On the limitations of the univariate marginal distribution algorithm to deception and where bivariate EDAs might help. In: Proceedings of FOGA 2019, pp. 154–168 (2019). https://doi.org/10.1145/3299904.3340316

  19. Lengler, J., Sudholt, D., Witt, C.: Medium step sizes are harmful for the compact genetic algorithm. In: Proceedings of GECCO 2018, pp. 1499–1506 (2018). https://doi.org/10.1145/3205455.3205576

  20. Mühlenbein, H., Paaß, G.: From recombination of genes to the estimation of distributions I. Binary parameters. In: Proceedings of PPSN 1996, pp. 178–187 (1996). https://doi.org/10.1007/3-540-61723-X_982

  21. Pelikan, M., Hauschild, M.W., Lobo, F.G.: Estimation of distribution algorithms. In: Kacprzyk, J., Pedrycz, W. (eds.) Springer Handbook of Computational Intelligence, pp. 899–928. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-43505-2_45

    Chapter  Google Scholar 

  22. Sudholt, D., Witt, C.: On the choice of the update strength in estimation-of-distribution algorithms and ant colony optimization. Algorithmica 81(4), 1450–1489 (2018). https://doi.org/10.1007/s00453-018-0480-z

    Article  MathSciNet  MATH  Google Scholar 

  23. Witt, C.: Domino convergence: why one should hill-climb on linear functions. In: Proceedings of GECCO 2018, pp. 1539–1546 (2018). https://doi.org/10.1145/3205455.3205581

  24. Witt, C.: Upper bounds on the running time of the univariate marginal distribution algorithm on OneMax. Algorithmica 81(2), 632–667 (2018). https://doi.org/10.1007/s00453-018-0463-0

    Article  MathSciNet  MATH  Google Scholar 

  25. Zheng, W., Yang, G., Doerr, B.: Working principles of binary differential evolution. In: Proceedings of GECCO 2018, pp. 1103–1110 (2018). https://doi.org/10.1145/3205455.3205623

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Acknowledgments

This work was supported by COST Action CA15140 and by a public grant as part of the Investissements d’avenir project, reference ANR-11-LABX-0056-LMH, LabEx LMH, in a joint call with Gaspard Monge Program for optimization, operations research and their interactions with data sciences.

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Authors and Affiliations

  1. Laboratoire d’Informatique (LIX), CNRS, École Polytechnique, Institute Polytechnique de Paris, Palaiseau, France

    Benjamin Doerr

  2. Hasso Plattner Institute, University of Potsdam, Potsdam, Germany

    Martin S. Krejca

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  1. Benjamin Doerr
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  2. Martin S. Krejca
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Correspondence to Martin S. Krejca .

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Editors and Affiliations

  1. University of Coimbra, Coimbra, Portugal

    Luís Paquete

  2. Aberystwyth University, Aberystwyth, UK

    Christine Zarges

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Doerr, B., Krejca, M.S. (2020). The Univariate Marginal Distribution Algorithm Copes Well with Deception and Epistasis. In: Paquete, L., Zarges, C. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2020. Lecture Notes in Computer Science(), vol 12102. Springer, Cham. https://doi.org/10.1007/978-3-030-43680-3_4

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  • DOI: https://doi.org/10.1007/978-3-030-43680-3_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-43679-7

  • Online ISBN: 978-3-030-43680-3

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