Island models meet rumor spreading

Island models in evolutionary computation solve problems by a careful interplay of independently running evolutionary algorithms on the island and an exchange of good solutions between the islands. In this work, we conduct rigorous run time analyses for such island models trying to simultaneously obtain good run times and low communication effort. We improve the existing upper bounds for the communication effort (i) by improving the run time bounds via a careful analysis, (ii) by setting the balance between individual computation and communication in a more appropriate manner, and (iii) by replacing the usual communicate-with-all-neighbors approach with randomized rumor spreading, where each island contacts a randomly chosen neighbor. This epidemic communication paradigm is known to lead to very fast and robust information dissemination in many applications. Our results concern islands running simple (1+1) evolutionary algorithms, we regard d-dimensional tori and complete graphs as communication topologies, and optimize the classic test functions OneMax and LeadingOnes.

[1]  Thomas Jansen,et al.  On the analysis of the (1+1) evolutionary algorithm , 2002, Theor. Comput. Sci..

[2]  Carsten Witt,et al.  Optimizing Linear Functions with Randomized Search Heuristics - The Robustness of Mutation , 2012, STACS.

[3]  Wilfried Sihn,et al.  Parallel Evolutionary Algorithms , 2002, ESM.

[4]  Erick Cantú-Paz,et al.  A Survey of Parallel Genetic Algorithms , 2000 .

[5]  Carsten Witt,et al.  On the Utility of Island Models in Dynamic Optimization , 2015, GECCO.

[6]  Daniel Johannsen,et al.  Random combinatorial structures and randomized search heuristics , 2010 .

[7]  Pietro Simone Oliveto,et al.  On the effectiveness of crossover for migration in parallel evolutionary algorithms , 2011, GECCO '11.

[8]  Marvin Künnemann,et al.  Optimizing linear functions with the (1+λ) evolutionary algorithm - Different asymptotic runtimes for different instances , 2015, Theor. Comput. Sci..

[9]  Xin Yao,et al.  A study of drift analysis for estimating computation time of evolutionary algorithms , 2004, Natural Computing.

[10]  Carsten Witt,et al.  Tight Bounds on the Optimization Time of a Randomized Search Heuristic on Linear Functions† , 2013, Combinatorics, Probability and Computing.

[11]  Enrique Alba,et al.  Parallel evolutionary algorithms can achieve super-linear performance , 2002, Inf. Process. Lett..

[12]  Per Kristian Lehre,et al.  Black-box Complexity of Parallel Search with Distributed Populations , 2015, FOGA.

[13]  Per Kristian Lehre,et al.  Black-Box Search by Unbiased Variation , 2010, GECCO '10.

[14]  Marvin Künnemann,et al.  Tight Analysis of Randomized Rumor Spreading in Complete Graphs , 2014, ANALCO.

[15]  Benjamin Doerr,et al.  Optimal Parameter Settings for the (1 + λ, λ) Genetic Algorithm , 2016, GECCO.

[16]  Mahmoud Fouz,et al.  Asymptotically Optimal Randomized Rumor Spreading , 2010, Electron. Notes Discret. Math..

[17]  Dario Izzo,et al.  On the impact of the migration topology on the Island Model , 2010, Parallel Comput..

[18]  Dirk Sudholt,et al.  Design and Analysis of Schemes for Adapting Migration Intervals in Parallel Evolutionary Algorithms , 2015, Evolutionary Computation.

[19]  Enrique Alba,et al.  Parallel metaheuristics: recent advances and new trends , 2012, Int. Trans. Oper. Res..

[20]  Benjamin Doerr,et al.  Multiplicative Drift Analysis , 2010, GECCO '10.

[21]  Carsten Witt,et al.  Optimal Mutation Rates for the (1+λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}) EA on One , 2017, Algorithmica.

[22]  Dirk Sudholt,et al.  General Upper Bounds on the Runtime of Parallel Evolutionary Algorithms* , 2014, Evolutionary Computation.

[23]  Ingo Wegener,et al.  Theoretical Aspects of Evolutionary Algorithms , 2001, ICALP.