Noisy evolutionary optimization algorithms - A comprehensive survey

Abstract Noisy optimization is currently receiving increasing popularity for its widespread applications in engineering optimization problems, where the objective functions are often found to be contaminated with noisy sensory measurements. In absence of knowledge of the noise-statistics, discriminating better trial solutions from the rest becomes difficult in the “selection” step of an evolutionary optimization algorithm with noisy objective/s. This paper provides a thorough survey of the present state-of-the-art research on noisy evolutionary algorithms for both single and multi-objective optimization problems. This is undertaken by incorporating one or more of the five strategies in traditional evolutionary algorithms. The strategies include (i) fitness sampling of individual trial solution, (ii) fitness estimation of noisy samples, (iii) dynamic population sizing over the generations, (iv) adaptation of the evolutionary search strategy, and (v) modification in the selection strategy.

[1]  Frederico G. Guimarães,et al.  Interval Robust Multi-Objective Evolutionary Algorithm , 2009, 2009 IEEE Congress on Evolutionary Computation.

[2]  Olivier Teytaud,et al.  Evolution Strategies with Additive Noise: A Convergence Rate Lower Bound , 2015, FOGA.

[3]  Martin Pelikan,et al.  Scalable Optimization via Probabilistic Modeling: From Algorithms to Applications (Studies in Computational Intelligence) , 2006 .

[4]  Hans-Georg Beyer,et al.  A general noise model and its effects on evolution strategy performance , 2006, IEEE Transactions on Evolutionary Computation.

[5]  Edward A. Silver,et al.  Tabu Search When Noise is Present: An Illustration in the Context of Cause and Effect Analysis , 1998, J. Heuristics.

[6]  Bernhard Sendhoff,et al.  A framework for evolutionary optimization with approximate fitness functions , 2002, IEEE Trans. Evol. Comput..

[7]  Kay Chen Tan,et al.  A data mining approach to evolutionary optimisation of noisy multi-objective problems , 2012, Int. J. Syst. Sci..

[8]  Junichi Suzuki,et al.  A Confidence-Based Dominance Operator in Evolutionary Algorithms for Noisy Multiobjective Optimization Problems , 2009, 2009 21st IEEE International Conference on Tools with Artificial Intelligence.

[9]  Bart Goethals,et al.  Survey on Frequent Pattern Mining , 2003 .

[10]  Benjamin W. Wah,et al.  Dynamic Control of Genetic Algorithms in a Noisy Environment , 1993, ICGA.

[11]  Kai-Yew Lum,et al.  Max-min surrogate-assisted evolutionary algorithm for robust design , 2006, IEEE Transactions on Evolutionary Computation.

[12]  Pratyusha Rakshit,et al.  Artificial Bee Colony induced multi-objective optimization in presence of noise , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[13]  Peter Stagge,et al.  Averaging Efficiently in the Presence of Noise , 1998, PPSN.

[14]  Zhuhong Zhang,et al.  Immune Algorithm with Adaptive Sampling in Noisy Environments and Its Application to Stochastic Optimization Problems , 2007, IEEE Computational Intelligence Magazine.

[15]  P. N. Suganthan,et al.  Differential Evolution: A Survey of the State-of-the-Art , 2011, IEEE Transactions on Evolutionary Computation.

[16]  Hans-Georg Beyer,et al.  Performance analysis of evolutionary optimization with cumulative step length adaptation , 2004, IEEE Transactions on Automatic Control.

[17]  Xiaodong Li,et al.  Niching Without Niching Parameters: Particle Swarm Optimization Using a Ring Topology , 2010, IEEE Transactions on Evolutionary Computation.

[18]  Helen G. Cobb,et al.  An Investigation into the Use of Hypermutation as an Adaptive Operator in Genetic Algorithms Having Continuous, Time-Dependent Nonstationary Environments , 1990 .

[19]  Kalyanmoy Deb,et al.  Dynamic Resampling for Preference-based Evolutionary Multi-Objective Optimization of Stochastic Systems , 2015, MCDM 2015.

[20]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[21]  Hussein A. Abbass,et al.  Performance analysis of evolutionary multi-objective optimization methods in noisy environments , 2004 .

[22]  Hans-Georg Beyer,et al.  A Comparison of Evolution Strategies with Other Direct Search Methods in the Presence of Noise , 2003, Comput. Optim. Appl..

[23]  Janez Brest,et al.  Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems , 2006, IEEE Transactions on Evolutionary Computation.

[24]  Jonathan E. Fieldsend,et al.  Efficiently identifying pareto solutions when objective values change , 2014, GECCO.

[25]  Jürgen Branke,et al.  Selection in the Presence of Noise , 2003, GECCO.

[26]  Kay Chen Tan,et al.  An Investigation on Noisy Environments in Evolutionary Multiobjective Optimization , 2007, IEEE Transactions on Evolutionary Computation.

[27]  John J. Grefenstette,et al.  Genetic Algorithms for Changing Environments , 1992, PPSN.

[28]  David E. Goldberg,et al.  Genetic Algorithms, Selection Schemes, and the Varying Effects of Noise , 1996, Evolutionary Computation.

[29]  Minrui Fei,et al.  Biogeography-based optimization in noisy environments , 2015 .

[30]  Thomas Bäck,et al.  Evolutionary algorithms in theory and practice - evolution strategies, evolutionary programming, genetic algorithms , 1996 .

[31]  Loo Hay Lee,et al.  Efficient Simulation Budget Allocation for Selecting an Optimal Subset , 2008, INFORMS J. Comput..

[32]  Juan Julián Merelo Guervós,et al.  A Statistical Approach to Dealing with Noisy Fitness in Evolutionary Algorithms , 2014, IJCCI.

[33]  Pratyusha Rakshit,et al.  Non-dominated Sorting Bee Colony optimization in the presence of noise , 2016, Soft Comput..

[34]  Hajime Kita,et al.  Optimization of noisy fitness functions by means of genetic algorithms using history of search with test of estimation , 2000, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[35]  Ferrante Neri,et al.  A memetic Differential Evolution approach in noisy optimization , 2010, Memetic Comput..

[36]  Kay Chen Tan,et al.  Evolutionary Multi-objective Optimization in Uncertain Environments - Issues and Algorithms , 2009, Studies in Computational Intelligence.

[37]  Kwon-Hee Lee,et al.  Robust optimization considering tolerances of design variables , 2001 .

[38]  Anthony Di Pietro Optimising evolutionary strategies for problems with varying noise strength , 2007 .

[39]  Hans-Georg Beyer,et al.  On the Benefits of Populations for Noisy Optimization , 2003, Evolutionary Computation.

[40]  Veysel Gazi,et al.  Particle swarm optimization with dynamic neighborhood topology: Three neighborhood strategies and preliminary results , 2008, 2008 IEEE Swarm Intelligence Symposium.

[41]  Olivier Teytaud,et al.  Differential evolution for strongly noisy optimization: Use 1.01n resamplings at iteration n and reach the − 1/2 slope , 2015, 2015 IEEE Congress on Evolutionary Computation (CEC).

[42]  Gerhard W. Dueck,et al.  Threshold accepting: a general purpose optimization algorithm appearing superior to simulated anneal , 1990 .

[43]  Phillip D. Stroud,et al.  Kalman-extended genetic algorithm for search in nonstationary environments with noisy fitness evaluations , 2001, IEEE Trans. Evol. Comput..

[44]  Olivier Teytaud,et al.  A mathematically derived number of resamplings for noisy optimization , 2014, GECCO.

[45]  Hussein A. Abbass,et al.  Localization for Solving Noisy Multi-Objective Optimization Problems , 2009, Evolutionary Computation.

[46]  Julia Handl,et al.  Implicit and Explicit Averaging Strategies for Simulation-Based Optimization of a Real-World Production Planning Problem , 2015, Informatica.

[47]  Jonathan E. Fieldsend,et al.  The Rolling Tide Evolutionary Algorithm: A Multiobjective Optimizer for Noisy Optimization Problems , 2015, IEEE Transactions on Evolutionary Computation.

[48]  David E. Goldberg,et al.  Nonstationary Function Optimization Using Genetic Algorithms with Dominance and Diploidy , 1987, ICGA.

[49]  Jürgen Branke,et al.  Efficient search for robust solutions by means of evolutionary algorithms and fitness approximation , 2006, IEEE Transactions on Evolutionary Computation.

[50]  Heike Trautmann,et al.  Pareto-dominance in noisy environments , 2009, 2009 IEEE Congress on Evolutionary Computation.

[51]  Abdullah Al Mamun,et al.  Multi-Objective Optimization with Estimation of Distribution Algorithm in a Noisy Environment , 2013, Evolutionary Computation.

[52]  R. Lyndon While,et al.  Applying evolutionary algorithms to problems with noisy, time-consuming fitness functions , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[53]  Brad L. Miller,et al.  Noise, sampling, and efficient genetic algorthms , 1997 .

[54]  Hans-Paul Schwefel,et al.  Evolution strategies – A comprehensive introduction , 2002, Natural Computing.

[55]  Hans-Georg Beyer,et al.  A New Approach for Predicting the Final Outcome of Evolution Strategy Optimization Under Noise , 2005, Genetic Programming and Evolvable Machines.

[56]  Volker Nissen,et al.  Optimization with Noisy Function Evaluations , 1998, PPSN.

[57]  Dan Simon,et al.  Markov Models for Biogeography-Based Optimization , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[58]  H. Kita,et al.  Genetic algorithms for optimization of uncertain functions and their applications , 2003, SICE 2003 Annual Conference (IEEE Cat. No.03TH8734).

[59]  Olivier Teytaud,et al.  Analysis of Different Types of Regret in Continuous Noisy Optimization , 2016, GECCO.

[60]  Jonathan E. Fieldsend,et al.  Multi-objective optimisation in the presence of uncertainty , 2005, 2005 IEEE Congress on Evolutionary Computation.

[61]  Jonathan E. Fieldsend,et al.  On the efficient maintenance and updating of Pareto solutions when assigned objectives values may change , 2013 .

[62]  Olivier Teytaud,et al.  On the adaptation of noise level for stochastic optimization , 2007, 2007 IEEE Congress on Evolutionary Computation.

[63]  Jerry M. Mendel,et al.  Interval Type-2 Fuzzy Logic Systems Made Simple , 2006, IEEE Transactions on Fuzzy Systems.

[64]  Craig W. Reynolds Evolution of corridor following behavior in a noisy world , 1994 .

[65]  Giovanni Iacca,et al.  Noise analysis compact differential evolution , 2012, Int. J. Syst. Sci..

[66]  Günter Rudolph,et al.  A partial order approach to noisy fitness functions , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[67]  Philipp Limbourg,et al.  An optimization algorithm for imprecise multi-objective problem functions , 2005, 2005 IEEE Congress on Evolutionary Computation.

[68]  Kay Chen Tan,et al.  An investigation on noise-induced features in robust evolutionary multi-objective optimization , 2010, Expert Syst. Appl..

[69]  A. Tsoularis,et al.  Analysis of logistic growth models. , 2002, Mathematical biosciences.

[70]  Ingo Rechenberg,et al.  Evolutionsstrategie : Optimierung technischer Systeme nach Prinzipien der biologischen Evolution , 1973 .

[71]  Volker Nissen,et al.  On the robustness of population-based versus point-based optimization in the presence of noise , 1998, IEEE Trans. Evol. Comput..

[72]  Pratyusha Rakshit,et al.  Uncertainty Management in Differential Evolution Induced Multiobjective Optimization in Presence of Measurement Noise , 2014, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[73]  Céline Villa,et al.  Multi-objective Optimization under Uncertain Objectives: Application to Engineering Design Problem , 2013, EMO.

[74]  Kalyanmoy Deb,et al.  Hybrid Dynamic Resampling Algorithms for Evolutionary Multi-objective Optimization of Invariant-Noise Problems , 2016, EvoApplications.

[75]  Hans-Georg Beyer,et al.  Local performance of the (1 + 1)-ES in a noisy environment , 2002, IEEE Trans. Evol. Comput..

[76]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[77]  Pierre Legendre,et al.  Statistical comparison of univariate tests of homogeneity of variances , 2001 .

[78]  Paul J. Darwen,et al.  Co-evolutionary learning on noisy tasks , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[79]  Kalyanmoy Deb,et al.  Introducing Robustness in Multi-Objective Optimization , 2006, Evolutionary Computation.

[80]  Amit Konar,et al.  Improved differential evolution algorithms for handling noisy optimization problems , 2005, 2005 IEEE Congress on Evolutionary Computation.

[81]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[82]  T. Back,et al.  Thresholding-a selection operator for noisy ES , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[83]  Hussein A. Abbass,et al.  Fitness inheritance for noisy evolutionary multi-objective optimization , 2005, GECCO '05.

[84]  Juan Rada-Vilela,et al.  Population Statistics for Particle Swarm Optimization on Problems Subject to Noise , 2014 .

[85]  Chun-an Liu,et al.  New Dynamic Constrained Optimization PSO Algorithm , 2008, 2008 Fourth International Conference on Natural Computation.

[86]  Bernhard Sendhoff,et al.  Fitness Approximation In Evolutionary Computation - a Survey , 2002, GECCO.

[87]  Jean-Louis Coulomb,et al.  A Surrogate Genetic Programming Based Model to Facilitate Robust Multi-Objective Optimization: A Case Study in Magnetostatics , 2013, IEEE Transactions on Magnetics.

[88]  Kalyanmoy Deb,et al.  Reference point based multi-objective optimization using evolutionary algorithms , 2006, GECCO.

[89]  Kumpati S. Narendra,et al.  Learning Automata - A Survey , 1974, IEEE Trans. Syst. Man Cybern..

[90]  Anne Auger,et al.  On the convergence of the $(1+1)$-ES in noisy spherical environments , 2007 .

[91]  James Kennedy,et al.  Bare bones particle swarms , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

[92]  Hans-Georg Beyer,et al.  Actuator Noise in Recombinant Evolution Strategies on General Quadratic Fitness Models , 2004, GECCO.

[93]  Pratyusha Rakshit,et al.  Type-2 fuzzy induced non-dominated sorting bee colony for noisy optimization , 2015, 2015 IEEE Congress on Evolutionary Computation (CEC).

[94]  David E. Goldberg,et al.  Optimal sampling in a noisy genetic algorithm for risk-based remediation design , 2001 .

[95]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1992, Artificial Intelligence.

[96]  Hans-Georg Beyer,et al.  The Steady State Behavior of ( μ / μ I , λ )-ES on Ellipsoidal Fitness Models Disturbed by Noise , 2003 .

[97]  Hans-Georg Beyer,et al.  Efficiency and Mutation Strength Adaptation of the (mu, muI, lambda)-ES in a Noisy Environment , 2000, PPSN.

[98]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[99]  Hans-Georg Beyer,et al.  Performance analysis of evolution strategies with multi-recombination in high-dimensional RN-search spaces disturbed by noise , 2002, Theor. Comput. Sci..

[100]  T. Ray Constrained robust optimal design using a multiobjective evolutionary algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[101]  Qingfu Zhang,et al.  Multiobjective optimization Test Instances for the CEC 2009 Special Session and Competition , 2009 .

[102]  Bernhard Sendhoff,et al.  Functions with noise-induced multimodality: a test for evolutionary robust Optimization-properties and performance analysis , 2006, IEEE Transactions on Evolutionary Computation.

[103]  M. E. Muller,et al.  A Note on the Generation of Random Normal Deviates , 1958 .

[104]  Olivier Teytaud,et al.  Analysis of runtime of optimization algorithms for noisy functions over discrete codomains , 2015, Theor. Comput. Sci..

[105]  Jürgen Branke,et al.  Sequential Sampling in Noisy Environments , 2004, PPSN.

[106]  Thomas Bäck,et al.  Robust design of multilayer optical coatings by means of evolutionary algorithms , 1998, IEEE Trans. Evol. Comput..

[107]  Dan Simon,et al.  Biogeography-Based Optimization , 2022 .

[108]  Robert Hooke,et al.  `` Direct Search'' Solution of Numerical and Statistical Problems , 1961, JACM.

[109]  Dirk Thierens,et al.  Benchmarking Parameter-Free AMaLGaM on Functions With and Without Noise , 2013, Evolutionary Computation.

[110]  Kay Chen Tan,et al.  Noise Handling in Evolutionary Multi-Objective Optimization , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[111]  Hajime Kita,et al.  Optimization of Noisy Fitness Functions by Means of Genetic Algorithms Using History of Search , 2000, PPSN.

[112]  E. J. Hughes,et al.  Constraint handling with uncertain and noisy multi-objective evolution , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[113]  Kalyanmoy Deb,et al.  Hybrid Dynamic Resampling for Guided Evolutionary Multi-Objective Optimization , 2015, EMO.

[114]  Hans-Georg Beyer,et al.  The Steady State Behavior of (µ/µI, lambda)-ES on Ellipsoidal Fitness Models Disturbed by Noise , 2003, GECCO.

[115]  Ling Wang,et al.  Particle swarm optimization for function optimization in noisy environment , 2006, Appl. Math. Comput..

[116]  Thomas Bäck,et al.  Using the uncertainty handling CMA-ES for finding robust optima , 2011, GECCO '11.

[117]  Martin Middendorf,et al.  A hierarchical particle swarm optimizer for noisy and dynamic environments , 2006, Genetic Programming and Evolvable Machines.

[118]  Junichi Suzuki,et al.  A Non-parametric Statistical Dominance Operator for Noisy Multiobjective Optimization , 2012, SEAL.

[119]  J. Proudfoot,et al.  Noise , 1931, The Indian medical gazette.

[120]  Thomas Bäck,et al.  Evolution strategies applied to perturbed objective functions , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[121]  Robert Ivor John,et al.  Evolutionary optimisation of noisy multi-objective problems using confidence-based dynamic resampling , 2010, Eur. J. Oper. Res..

[122]  Eckart Zitzler,et al.  A Preliminary Study on Handling Uncertainty in Indicator-Based Multiobjective Optimization , 2006, EvoWorkshops.

[123]  Gary B. Fogel,et al.  Noisy optimization problems - a particular challenge for differential evolution? , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[124]  Bernhard Sendhoff,et al.  On Evolutionary Optimization with Approximate Fitness Functions , 2000, GECCO.

[125]  Dan Boneh,et al.  On genetic algorithms , 1995, COLT '95.

[126]  Hans-Georg Beyer,et al.  Investigation of the (/spl mu/, /spl lambda/)-ES in the presence of noise , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[127]  B. S Simulated Annealing with Noisy or Imprecise Energy Measurements , 2004 .

[128]  L. Darrell Whitley,et al.  Searching in the Presence of Noise , 1996, PPSN.

[129]  Kwang Ryel Ryu,et al.  Deriving a robust policy for container stacking using a noise-tolerant genetic algorithm , 2012, RACS.

[130]  Thomas Bäck,et al.  Evolution Strategies on Noisy Functions: How to Improve Convergence Properties , 1994, PPSN.

[131]  Jürgen Branke,et al.  Simulated annealing in the presence of noise , 2008, J. Heuristics.

[132]  H. Beyer Evolutionary algorithms in noisy environments : theoretical issues and guidelines for practice , 2000 .

[133]  M. Feigenbaum Quantitative universality for a class of nonlinear transformations , 1978 .

[134]  Shigeyoshi Tsutsui,et al.  A Robust Solution Searching Scheme in Genetic Search , 1996, PPSN.

[135]  Kalyanmoy Deb,et al.  A comparative study of dynamic resampling strategies for guided Evolutionary Multi-objective Optimization , 2013, 2013 IEEE Congress on Evolutionary Computation.

[136]  Chun-Hung Chen,et al.  Simulation Budget Allocation for Further Enhancing the Efficiency of Ordinal Optimization , 2000, Discret. Event Dyn. Syst..

[137]  Bernhard Sendhoff,et al.  On the Impact of Systematic Noise on the Evolutionary Optimization Performance—A Sphere Model Analysis , 2004, Genetic Programming and Evolvable Machines.

[138]  Stuart Kauffman,et al.  Adaptive walks with noisy fitness measurements , 1995, Molecular Diversity.

[139]  MengChu Zhou,et al.  A learning automata-based particle swarm optimization algorithm for noisy environment , 2015, 2015 IEEE Congress on Evolutionary Computation (CEC).

[140]  Florian Siegmund,et al.  Sequential Sampling in Noisy Multi-Objective Evolutionary Optimization , 2009 .

[141]  Eckart Zitzler,et al.  Handling Uncertainty in Indicator-Based Multiobjective Optimization , 2006 .

[142]  U. Diwekar,et al.  Stochastic annealing for synthesis under uncertainty , 1995 .

[143]  Kalyanmoy Deb,et al.  Standard Error Dynamic Resampling for Preference-based Evolutionary Multi-objective Optimization , 2015 .

[144]  Joshua D. Knowles,et al.  Multiobjective Optimization on a Budget of 250 Evaluations , 2005, EMO.

[145]  Abhishek Singh,et al.  Uncertainty‐based multiobjective optimization of groundwater remediation design , 2003 .

[146]  Ronald W. Morrison,et al.  Designing Evolutionary Algorithms for Dynamic Environments , 2004, Natural Computing Series.

[147]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

[148]  Magnus Rattray,et al.  Noisy Fitness Evaluation in Genetic Algorithms and the Dynamics of Learning , 1996, FOGA.

[149]  Shahryar Rahnamayan,et al.  Opposition-Based Differential Evolution for Optimization of Noisy Problems , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[150]  Kwang Ryel Ryu,et al.  Accumulative sampling for noisy evolutionary multi-objective optimization , 2011, GECCO '11.

[151]  Alcherio Martinoli,et al.  Analysis of fitness noise in particle swarm optimization: From robotic learning to benchmark functions , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[152]  David J. Sheskin,et al.  Handbook of Parametric and Nonparametric Statistical Procedures , 1997 .

[153]  Hajime Kita,et al.  Online optimization of an engine controller by means of a genetic algorithm using history of search , 2000, 2000 26th Annual Conference of the IEEE Industrial Electronics Society. IECON 2000. 2000 IEEE International Conference on Industrial Electronics, Control and Instrumentation. 21st Century Technologies.

[154]  Benjamin W. Wah,et al.  Scheduling of Genetic Algorithms in a Noisy Environment , 1994, Evolutionary Computation.

[155]  Russell C. Eberhart,et al.  Adaptive particle swarm optimization: detection and response to dynamic systems , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[156]  Tong Heng Lee,et al.  Evolutionary algorithms with dynamic population size and local exploration for multiobjective optimization , 2001, IEEE Trans. Evol. Comput..

[157]  X. Yao,et al.  Combining landscape approximation and local search in global optimization , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[158]  Pratyusha Rakshit,et al.  Differential evolution for noisy multiobjective optimization , 2015, Artif. Intell..

[159]  Olivier Teytaud,et al.  Simple and cumulative regret for continuous noisy optimization , 2016, Theor. Comput. Sci..

[160]  Hans-Georg Beyer,et al.  Efficiency and Mutation Strength Adaptation of the in a Noisy Environment , 2000 .

[161]  Jonathan E. Fieldsend Elite Accumulative Sampling Strategies for Noisy Multi-objective Optimisation , 2015, EMO.

[162]  Benjamin M. Adams,et al.  Advanced Topics in Statistical Process Control : The Power of Shewhart's Charts , 1995 .

[163]  J. Fitzpatrick,et al.  Genetic Algorithms in Noisy Environments , 2005, Machine Learning.

[164]  P. Koumoutsakos,et al.  Multiobjective evolutionary algorithm for the optimization of noisy combustion processes , 2002 .

[165]  Jürgen Teich,et al.  Pareto-Front Exploration with Uncertain Objectives , 2001, EMO.

[166]  Bo Liu,et al.  Hybrid differential evolution for noisy optimization , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[167]  Leszek Siwik,et al.  Elitist Evolutionary Multi-Agent System in solving noisy multi-objective optimization problems , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[168]  Bernhard Sendhoff,et al.  Evolution Strategies for Robust Optimization , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[169]  J. Kiefer,et al.  Sequential minimax search for a maximum , 1953 .

[170]  Ek Peng Chew,et al.  A simulation study on sampling and selecting under fixed computing budget , 2003, Proceedings of the 2003 Winter Simulation Conference, 2003..

[171]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[172]  Pratyusha Rakshit,et al.  Realization of an Adaptive Memetic Algorithm Using Differential Evolution and Q-Learning: A Case Study in Multirobot Path Planning , 2013, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[173]  Juan Julián Merelo Guervós,et al.  There is noisy lunch: A study of noise in evolutionary optimization problems , 2015, 2015 7th International Joint Conference on Computational Intelligence (IJCCI).

[174]  Jason Brownlee,et al.  Clever Algorithms: Nature-Inspired Programming Recipes , 2012 .

[175]  Petros Koumoutsakos,et al.  A Method for Handling Uncertainty in Evolutionary Optimization With an Application to Feedback Control of Combustion , 2009, IEEE Transactions on Evolutionary Computation.

[176]  Jürgen Branke,et al.  Creating Robust Solutions by Means of Evolutionary Algorithms , 1998, PPSN.

[177]  Averill M. Law,et al.  Simulation Modeling and Analysis , 1982 .

[178]  Liang Shi,et al.  ASAGA: an adaptive surrogate-assisted genetic algorithm , 2008, GECCO '08.

[179]  H. Beyer An alternative explanation for the manner in which genetic algorithms operate. , 1997, Bio Systems.

[180]  Jürgen Branke,et al.  Efficient fitness estimation in noisy environments , 2001 .

[181]  Renato A. Krohling,et al.  Swarm algorithms with chaotic jumps applied to noisy optimization problems , 2011, Inf. Sci..

[182]  Yaochu Jin,et al.  A comprehensive survey of fitness approximation in evolutionary computation , 2005, Soft Comput..

[183]  Swagatam Das,et al.  Dynamic Constrained Optimization with offspring repair based Gravitational Search Algorithm , 2013, 2013 IEEE Congress on Evolutionary Computation.

[184]  Shengxiang Yang,et al.  Evolutionary Computation in Dynamic and Uncertain Environments , 2007, Studies in Computational Intelligence.

[185]  Evan J. Hughes Evolutionary algorithm with a novel insertion operator for optimising noisy functions , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[186]  Ferrante Neri,et al.  Differential Evolution with Noise Analyzer , 2009, EvoWorkshops.

[187]  Mauro Valorani,et al.  Optimization methods for non-smooth or noisy objective functions in fluid design problems , 1995 .

[188]  Hamidreza Eskandari,et al.  Handling uncertainty in evolutionary multiobjective optimization: SPGA , 2007, 2007 IEEE Congress on Evolutionary Computation.

[189]  Olivier Teytaud,et al.  Algorithm portfolios for noisy optimization , 2015, Annals of Mathematics and Artificial Intelligence.

[190]  Hamidreza Eskandari,et al.  Evolutionary multiobjective optimization in noisy problem environments , 2009, J. Heuristics.

[191]  Tim Blackwell,et al.  Particle Swarm Optimization in Dynamic Environments , 2007, Evolutionary Computation in Dynamic and Uncertain Environments.

[192]  Evan J. Hughes,et al.  Evolutionary Multi-objective Ranking with Uncertainty and Noise , 2001, EMO.

[193]  Paul J. Darwen,et al.  Computationally intensive and noisy tasks: co-evolutionary learning and temporal difference learning on Backgammon , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[194]  Jürgen Branke,et al.  Evolutionary optimization in uncertain environments-a survey , 2005, IEEE Transactions on Evolutionary Computation.

[195]  Shu Tezuka Linear Congruential Generators , 1995 .

[196]  David W. Corne,et al.  Noisy Multiobjective Optimization on a Budget of 250 Evaluations , 2009, EMO.

[197]  G.L. Soares,et al.  Robust Multi-Objective TEAM 22 Problem: A Case Study of Uncertainties in Design Optimization , 2009, IEEE Transactions on Magnetics.

[198]  Kalyanmoy Deb,et al.  Genetic Algorithms, Noise, and the Sizing of Populations , 1992, Complex Syst..

[199]  Hussein A. Abbass,et al.  Robustness Against the Decision-Maker's Attitude to Risk in Problems With Conflicting Objectives , 2012, IEEE Transactions on Evolutionary Computation.

[200]  H.-G. Beyer,et al.  Mutate large, but inherit small ! On the analysis of rescaled mutations in (1, λ)-ES with noisy fitness data , 1998 .

[201]  Shengxiang Yang,et al.  Associative Memory Scheme for Genetic Algorithms in Dynamic Environments , 2006, EvoWorkshops.

[202]  Pratyusha Rakshit,et al.  Extending multi-objective differential evolution for optimization in presence of noise , 2015, Inf. Sci..

[203]  Chen-Khong Tham,et al.  Uncertainties reducing Techniques in evolutionary computation , 2007, 2007 IEEE Congress on Evolutionary Computation.