A Survey on Recent Progress in the Theory of Evolutionary Algorithms for Discrete Optimization

The theory of evolutionary computation for discrete search spaces has made significant progress since the early 2010s. This survey summarizes some of the most important recent results in this research area. It discusses fine-grained models of runtime analysis of evolutionary algorithms, highlights recent theoretical insights on parameter tuning and parameter control, and summarizes the latest advances for stochastic and dynamic problems. We regard how evolutionary algorithms optimize submodular functions, and we give an overview over the large body of recent results on estimation of distribution algorithms. Finally, we present the state of the art of drift analysis, one of the most powerful analysis technique developed in this field.

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[2]  Dirk Sudholt,et al.  Time Complexity Analysis of Randomized Search Heuristics for the Dynamic Graph Coloring Problem , 2021, Algorithmica.

[3]  Andrew M. Sutton,et al.  Runtime analysis of RLS and the (1+1) EA for the chance-constrained knapsack problem with correlated uniform weights , 2021, GECCO.

[4]  Frank Neumann,et al.  Advanced Ore Mine Optimisation under Uncertainty Using Evolution , 2021, ArXiv.

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[13]  Benjamin Doerr,et al.  Bivariate estimation-of-distribution algorithms can find an exponential number of optima , 2020, GECCO.

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[15]  Benjamin Doerr,et al.  First Steps Towards a Runtime Analysis When Starting With a Good Solution , 2020, PPSN.

[16]  Frank Neumann,et al.  Optimising Monotone Chance-Constrained Submodular Functions Using Evolutionary Multi-Objective Algorithms , 2020, PPSN.

[17]  Benjamin Doerr,et al.  Runtime Analysis of a Heavy-Tailed (1+(λ, λ)) Genetic Algorithm on Jump Functions , 2020, PPSN.

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[21]  Frank Neumann,et al.  Specific single- and multi-objective evolutionary algorithms for the chance-constrained knapsack problem , 2020, GECCO.

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[51]  Andreas Krause,et al.  Adaptive Sequence Submodularity , 2019, NeurIPS.

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[53]  Frank Neumann,et al.  Pareto Optimization for Subset Selection with Dynamic Cost Constraints , 2018, AAAI.

[54]  Frank Neumann,et al.  Greedy Maximization of Functions with Bounded Curvature under Partition Matroid Constraints , 2018, AAAI.

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

[63]  Duc-Cuong Dang,et al.  Level-Based Analysis of the Univariate Marginal Distribution Algorithm , 2018, Algorithmica.

[64]  Adrian Kosowski,et al.  Brief Announcement: Population Protocols Are Fast , 2018, PODC.

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[66]  Markus Wagner,et al.  Escaping large deceptive basins of attraction with heavy-tailed mutation operators , 2018, GECCO.

[67]  Dorian Nogneng,et al.  A new analysis method for evolutionary optimization of dynamic and noisy objective functions , 2018, GECCO.

[68]  Dirk Sudholt,et al.  On the robustness of evolutionary algorithms to noise: refined results and an example where noise helps , 2018, GECCO.

[69]  Benjamin Doerr,et al.  A tight runtime analysis for the (μ + λ) EA , 2018, GECCO.

[70]  Weijie Zheng,et al.  Working principles of binary differential evolution , 2018, GECCO.

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

[72]  Andrew M. Sutton,et al.  On the runtime dynamics of the compact genetic algorithm on jump functions , 2018, GECCO.

[73]  Pietro Simone Oliveto,et al.  On the runtime analysis of selection hyper-heuristics with adaptive learning periods , 2018, GECCO.

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

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

[76]  Martin S. Krejca,et al.  Intuitive Analyses via Drift Theory , 2018 .

[77]  Frank Neumann,et al.  Reoptimization Time Analysis of Evolutionary Algorithms on Linear Functions Under Dynamic Uniform Constraints , 2018, Algorithmica.

[78]  Jonathan E. Rowe,et al.  Linear multi-objective drift analysis , 2018, Theor. Comput. Sci..

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[80]  Anne Auger,et al.  Drift theory in continuous search spaces: expected hitting time of the (1 + 1)-ES with 1/5 success rule , 2018, GECCO.

[81]  Benjamin Doerr,et al.  Better Runtime Guarantees via Stochastic Domination , 2018, EvoCOP.

[82]  Chao Qian,et al.  Running Time Analysis of the (1+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1+1$$\end{document})-EA for OneMax an , 2017, Algorithmica.

[83]  Jason H. Moore,et al.  Investigating the parameter space of evolutionary algorithms , 2017, BioData Mining.

[84]  Gabriela Ochoa,et al.  Mapping the global structure of TSP fitness landscapes , 2017, J. Heuristics.

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

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

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[89]  Carsten Witt,et al.  The Impact of a Sparse Migration Topology on the Runtime of Island Models in Dynamic Optimization , 2017, Algorithmica.

[90]  Benjamin Doerr,et al.  Optimal Static and Self-Adjusting Parameter Choices for the (1+(λ,λ))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$( , 2017, Algorithmica.

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

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

[94]  Benjamin Doerr,et al.  Runtime analysis of the (1 + (λ, λ)) genetic algorithm on random satisfiable 3-CNF formulas , 2017, GECCO.

[95]  Benjamin Doerr,et al.  The (1+λ) evolutionary algorithm with self-adjusting mutation rate , 2017, GECCO.

[96]  Pratyusha Rakshit,et al.  Noisy evolutionary optimization algorithms - A comprehensive survey , 2017, Swarm Evol. Comput..

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[98]  Benjamin Doerr,et al.  Fast genetic algorithms , 2017, GECCO.

[99]  Andrew M. Sutton,et al.  Resampling vs Recombination: a Statistical Run Time Estimation , 2017, FOGA '17.

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

[101]  Avinatan Hassidim,et al.  Submodular Optimization under Noise , 2016, COLT.

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

[103]  Frank Neumann,et al.  Time Complexity Analysis of Evolutionary Algorithms on Random Satisfiable k-CNF Formulas , 2016, Algorithmica.

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

[105]  Benjamin Doerr,et al.  k-Bit Mutation with Self-Adjusting k Outperforms Standard Bit Mutation , 2016, PPSN.

[106]  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.

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

[108]  Benjamin Doerr,et al.  Optimal Parameter Choices via Precise Black-Box Analysis , 2016, GECCO.

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

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[111]  Yevgeniy Vorobeychik,et al.  Submodular Optimization with Routing Constraints , 2016, AAAI.

[112]  Andrew M. Sutton,et al.  Robustness of Ant Colony Optimization to Noise , 2015, Evolutionary Computation.

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

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

[121]  Holger R. Maier,et al.  Improved genetic algorithm optimization of water distribution system design by incorporating domain knowledge , 2015, Environ. Model. Softw..

[122]  Frank Neumann,et al.  On the Runtime of Randomized Local Search and Simple Evolutionary Algorithms for Dynamic Makespan Scheduling , 2015, IJCAI.

[123]  Mark Hoogendoorn,et al.  Parameter Control in Evolutionary Algorithms: Trends and Challenges , 2015, IEEE Transactions on Evolutionary Computation.

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

[126]  Carsten Witt,et al.  (1+1) EA on Generalized Dynamic OneMax , 2015, FOGA.

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

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

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

[130]  Martin Pelikan,et al.  Estimation of Distribution Algorithms , 2015, Handbook of Computational Intelligence.

[131]  Frank Neumann,et al.  Parameterized Runtime Analyses of Evolutionary Algorithms for the Planar Euclidean Traveling Salesperson Problem , 2014, Evolutionary Computation.

[132]  Per Kristian Lehre,et al.  Unbiased Black-Box Complexity of Parallel Search , 2014, PPSN.

[133]  Frank Neumann,et al.  Maximizing Submodular Functions under Matroid Constraints by Multi-objective Evolutionary Algorithms , 2014, PPSN.

[134]  Thomas Jansen,et al.  Reevaluating Immune-Inspired Hypermutations Using the Fixed Budget Perspective , 2014, IEEE Transactions on Evolutionary Computation.

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[145]  Zbigniew Michalewicz,et al.  Multi-mine Planning using a Multi-objective Evolutionary Algorithm , 2013, 2013 IEEE Congress on Evolutionary Computation.

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[147]  Thomas Jansen,et al.  Approximating vertex cover using edge-based representations , 2013, FOGA XII '13.

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

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[152]  Frank Neumann,et al.  Bioinspired computation in combinatorial optimization: algorithms and their computational complexity , 2010, GECCO '12.

[153]  Martin Dostál,et al.  Evolutionary Music Composition , 2013, Handbook of Optimization.

[154]  Jakob Puchinger,et al.  Hybrid Metaheuristics for Dynamic and Stochastic Vehicle Routing , 2013, Hybrid Metaheuristics.

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[158]  Benjamin Doerr,et al.  Run-time analysis of the (1+1) evolutionary algorithm optimizing linear functions over a finite alphabet , 2012, GECCO '12.

[159]  Thomas Jansen,et al.  Fixed budget computations: a different perspective on run time analysis , 2012, GECCO '12.

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

[161]  Frank Neumann,et al.  A Parameterized Runtime Analysis of Evolutionary Algorithms for the Euclidean Traveling Salesperson Problem , 2012, AAAI.

[162]  Robert Elsässer,et al.  The impact of the power law exponent on the behavior of a dynamic epidemic type process , 2012, SPAA '12.

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

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[169]  Martin Pelikan,et al.  An introduction and survey of estimation of distribution algorithms , 2011, Swarm Evol. Comput..

[170]  Stephen R. Marsland,et al.  Convergence Properties of (μ + λ) Evolutionary Algorithms , 2011, AAAI.

[171]  Benjamin Doerr,et al.  Drift analysis , 2011, GECCO.

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

[173]  Bernd Bischl,et al.  Exploratory landscape analysis , 2011, GECCO '11.

[174]  Per Kristian Lehre,et al.  Fitness-levels for non-elitist populations , 2011, GECCO '11.

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[180]  Leslie Ann Goldberg,et al.  Adaptive Drift Analysis , 2011, Algorithmica.

[181]  Andreas Krause,et al.  Adaptive Submodularity: Theory and Applications in Active Learning and Stochastic Optimization , 2010, J. Artif. Intell. Res..

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[183]  Benjamin Doerr,et al.  Optimal Fixed and Adaptive Mutation Rates for the LeadingOnes Problem , 2010, PPSN.

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

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

[192]  Xin Yao,et al.  Analysis of Computational Time of Simple Estimation of Distribution Algorithms , 2010, IEEE Transactions on Evolutionary Computation.

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[202]  Frank Neumann,et al.  On the Effects of Adding Objectives to Plateau Functions , 2009, IEEE Transactions on Evolutionary Computation.

[203]  Per Kristian Lehre,et al.  When is an estimation of distribution algorithm better than an evolutionary algorithm? , 2009, 2009 IEEE Congress on Evolutionary Computation.

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[205]  Vahab S. Mirrokni,et al.  Non-monotone submodular maximization under matroid and knapsack constraints , 2009, STOC '09.

[206]  Dirk Sudholt,et al.  Analysis of different MMAS ACO algorithms on unimodal functions and plateaus , 2009, Swarm Intelligence.

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

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