Drift Analysis

Drift analysis is one of the major tools for analysing evolutionary algorithms and nature-inspired search heuristics. In this chapter we give an introduction to drift analysis and give some examples of how to use it for the analysis of evolutionary algorithms.

[1]  B. Hajek Hitting-time and occupation-time bounds implied by drift analysis with applications , 1982, Advances in Applied Probability.

[2]  Andrew M. Sutton,et al.  The Benefit of Recombination in Noisy Evolutionary Search , 2015, ISAAC.

[3]  Ingo Wegener,et al.  Randomized local search, evolutionary algorithms, and the minimum spanning tree problem , 2004, Theor. Comput. Sci..

[4]  Benjamin Doerr,et al.  Edge-based representation beats vertex-based representation in shortest path problems , 2010, GECCO '10.

[5]  Véronique Ladret Asymptotic hitting time for a simple evolutionary model of protein folding , 2003, math/0308237.

[6]  Timo Kötzing Concentration of First Hitting Times Under Additive Drift , 2015, Algorithmica.

[7]  Dirk Sudholt,et al.  Update Strength in EDAs and ACO: How to Avoid Genetic Drift , 2016, GECCO.

[8]  G. Grimmett,et al.  Probability and random processes , 2002 .

[9]  Timo Kötzing,et al.  Optimizing expected path lengths with ant colony optimization using fitness proportional update , 2013, FOGA XII '13.

[10]  Benjamin Doerr,et al.  Multiplicative drift analysis , 2010, GECCO.

[11]  Pietro Simone Oliveto,et al.  Erratum: Simplified Drift Analysis for Proving Lower Bounds in Evolutionary Computation , 2008, PPSN.

[12]  Benjamin Doerr,et al.  Drift analysis and linear functions revisited , 2010, IEEE Congress on Evolutionary Computation.

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

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

[15]  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.

[16]  Rajeev Motwani,et al.  Randomized Algorithms , 1995, SIGA.

[17]  Benjamin Doerr,et al.  Static and Self-Adjusting Mutation Strengths for Multi-valued Decision Variables , 2018, Algorithmica.

[18]  Dirk Sudholt,et al.  A few ants are enough: ACO with iteration-best update , 2010, GECCO '10.

[19]  Carsten Witt,et al.  A Runtime Analysis of Parallel Evolutionary Algorithms in Dynamic Optimization , 2016, Algorithmica.

[20]  Serguei Popov,et al.  Non-homogeneous Random Walks: Lyapunov Function Methods for Near-Critical Stochastic Systems , 2016 .

[21]  Benjamin Doerr,et al.  The Impact of Random Initialization on the Runtime of Randomized Search Heuristics , 2015, Algorithmica.

[22]  Dirk Sudholt,et al.  The choice of the offspring population size in the (1, λ) evolutionary algorithm , 2014, Theor. Comput. Sci..

[23]  Duc-Cuong Dang,et al.  Level-Based Analysis of Genetic Algorithms and Other Search Processes , 2014, bioRxiv.

[24]  Duc-Cuong Dang,et al.  Simplified Runtime Analysis of Estimation of Distribution Algorithms , 2015, GECCO.

[25]  Jens Jägersküpper,et al.  A Blend of Markov-Chain and Drift Analysis , 2008, PPSN.

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

[27]  Duc-Cuong Dang,et al.  Efficient Optimisation of Noisy Fitness Functions with Population-based Evolutionary Algorithms , 2015, FOGA.

[28]  Dirk Sudholt,et al.  Towards a Runtime Comparison of Natural and Artificial Evolution , 2015, Algorithmica.

[29]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[30]  Carsten Witt,et al.  The Interplay of Population Size and Mutation Probability in the ($$1+\lambda $$1+λ) EA on OneMax , 2016, Algorithmica.

[31]  Carsten Witt,et al.  Runtime analysis of ant colony optimization on dynamic shortest path problems , 2013, GECCO '13.

[32]  Timo Kötzing,et al.  ACO Beats EA on a Dynamic Pseudo-Boolean Function , 2012, PPSN.

[33]  Benjamin Doerr,et al.  Non-existence of linear universal drift functions , 2010, Theor. Comput. Sci..

[34]  Per Kristian Lehre,et al.  General Drift Analysis with Tail Bounds , 2013, ArXiv.

[35]  Tobias Friedrich,et al.  Island models meet rumor spreading , 2017, GECCO.

[36]  Carsten Witt,et al.  MMAS Versus Population-Based EA on a Family of Dynamic Fitness Functions , 2014, Algorithmica.

[37]  Duc-Cuong Dang,et al.  Self-adaptation of Mutation Rates in Non-elitist Populations , 2016, PPSN.

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

[39]  Carsten Witt,et al.  The Interplay of Population Size and Mutation Probability in the (1+λ) EA on OneMax , 2017, Algorithmica.

[40]  Per Kristian Lehre,et al.  Theoretical Analysis of Stochastic Search Algorithms , 2017, Handbook of Heuristics.

[41]  Benjamin Doerr,et al.  Bounding bloat in genetic programming , 2017, GECCO.

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

[43]  Duc-Cuong Dang,et al.  Runtime Analysis of Non-elitist Populations: From Classical Optimisation to Partial Information , 2016, Algorithmica.

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

[45]  Andrew M. Sutton,et al.  Robustness of Ant Colony Optimization to Noise , 2015, GECCO.

[46]  Timo Kötzing,et al.  Robustness of Populations in Stochastic Environments , 2014, Algorithmica.

[47]  Dirk Sudholt,et al.  The choice of the offspring population size in the (1,λ) EA , 2012, GECCO '12.

[48]  Andrew M. Sutton,et al.  The Compact Genetic Algorithm is Efficient Under Extreme Gaussian Noise , 2017, IEEE Transactions on Evolutionary Computation.

[49]  Duc-Cuong Dang,et al.  Populations Can Be Essential in Tracking Dynamic Optima , 2016, Algorithmica.

[50]  Pietro Simone Oliveto,et al.  Simplified Drift Analysis for Proving Lower Bounds in Evolutionary Computation , 2008, Algorithmica.

[51]  Per Kristian Lehre,et al.  Concentrated Hitting Times of Randomized Search Heuristics with Variable Drift , 2014, ISAAC.

[52]  Jonathan E. Rowe,et al.  Theoretical analysis of local search strategies to optimize network communication subject to preserving the total number of links , 2009, Int. J. Intell. Comput. Cybern..

[53]  Angelika Steger,et al.  Drift Analysis and Evolutionary Algorithms Revisited , 2016, Combinatorics, Probability and Computing.

[54]  Per Kristian Lehre,et al.  Improved runtime bounds for the univariate marginal distribution algorithm via anti-concentration , 2017, GECCO.

[55]  Pietro Simone Oliveto,et al.  Improved time complexity analysis of the Simple Genetic Algorithm , 2015, Theor. Comput. Sci..

[56]  Mahmoud Fouz,et al.  Sharp bounds by probability-generating functions and variable drift , 2011, GECCO '11.

[57]  D. Down,et al.  Stability of Queueing Networks , 1994 .

[58]  Benjamin Doerr,et al.  Ants easily solve stochastic shortest path problems , 2012, GECCO '12.

[59]  R. Tweedie Criteria for classifying general Markov chains , 1976, Advances in Applied Probability.