Handling Uncertainties in Evolutionary Multi-Objective Optimization

Evolutionary algorithms are stochastic search methods that are efficient and effective for solving sophisticated multi-objective (MO) problems. Advances made in the field of evolutionary multi-objective optimization (EMO) are the results of two decades worth of intense research, studying various topics that are unique to MO optimization. However many of these studies assume that the problem is deterministic and static, and the EMO performance generally deteriorates in the presence of uncertainties. In certain situations, the solutions found may not even be implementable in practice. In this chapter, the challenges faced in handling three different forms of uncertainties in EMO will be discussed, including 1) noisy objective functions, 2) dynamic MO fitness landscape, and 3) robust MO optimization. Specifically, the impact of these uncertainties on MO optimization will be described and the approaches/modifications to basic algorithm design for better and robust EMO performance will be presented.

[1]  Kalyanmoy Deb,et al.  Reliability-Based Multi-objective Optimization Using Evolutionary Algorithms , 2007, EMO.

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

[3]  Shigeyoshi Tsutsui,et al.  A comparative study on the effects of adding perturbations to phenotypic parameters in genetic algorithms with a robust solution searching scheme , 1999, IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.99CH37028).

[4]  Marco Farina,et al.  A fuzzy definition of "optimality" for many-criteria optimization problems , 2004, IEEE Trans. Syst. Man Cybern. Part A.

[5]  Tong Heng Lee,et al.  Design and real-time implementation of a multivariable gyro-mirror line-of-sight stabilization platform , 2002, Fuzzy Sets Syst..

[6]  Hans-Paul Schwefel,et al.  Parallel Problem Solving from Nature — PPSN IV , 1996, Lecture Notes in Computer Science.

[7]  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 .

[8]  Kay Chen Tan,et al.  Solving multiobjective vehicle routing problem with stochastic demand via evolutionary computation , 2007, Eur. J. Oper. Res..

[9]  Shapour Azarm,et al.  A multi-objective genetic algorithm for robust design optimization , 2005, GECCO '05.

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

[11]  Hugo de Garis,et al.  A Dynamic Multi-Objective Evolutionary Algorithm Based on an Orthogonal Design , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[12]  Kalyanmoy Deb,et al.  Handling constraints in robust multi-objective optimization , 2005, 2005 IEEE Congress on Evolutionary Computation.

[13]  Gary L. Haith,et al.  Comparing a coevolutionary genetic algorithm for multiobjective optimization , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[14]  Yaochu Jin,et al.  Single/Multi-objective Inverse Robust Evolutionary Design Methodology in the Presence of Uncertainty , 2007, Evolutionary Computation in Dynamic and Uncertain Environments.

[15]  Rasmus K. Ursem,et al.  Multinational GAs: Multimodal Optimization Techniques in Dynamic Environments , 2000, GECCO.

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

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

[18]  David Wallace,et al.  Dynamic multi-objective optimization with evolutionary algorithms: a forward-looking approach , 2006, GECCO.

[19]  Mark Wineberg,et al.  Enhancing the GA's Ability to Cope with Dynamic Environments , 2000, GECCO.

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

[21]  S. Tsutsui,et al.  Function optimization in nonstationary environment using steady state genetic algorithms with aging of individuals , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

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

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

[24]  Abhishek Singh,et al.  Uncertainty‐based multiobjective optimization of groundwater remediation design , 2008 .

[25]  S. Azarm,et al.  Multi-objective robust optimization using a sensitivity region concept , 2005 .

[26]  Kay Chen Tan,et al.  A Competitive-Cooperative Coevolutionary Paradigm for Dynamic Multiobjective Optimization , 2009, IEEE Transactions on Evolutionary Computation.

[27]  ZitzlerE.,et al.  Multiobjective evolutionary algorithms , 1999 .

[28]  Hartmut Schmeck,et al.  Designing evolutionary algorithms for dynamic optimization problems , 2003 .

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

[30]  Kay Chen Tan,et al.  Hybrid Multiobjective Evolutionary Design for Artificial Neural Networks , 2008, IEEE Transactions on Neural Networks.

[31]  Carlos A. Coello Coello,et al.  Design of combinational logic circuits through an evolutionary multiobjective optimization approach , 2002, Artificial Intelligence for Engineering Design, Analysis and Manufacturing.

[32]  Xiaodong Li,et al.  A Cooperative Coevolutionary Multiobjective Algorithm Using Non-dominated Sorting , 2004, GECCO.

[33]  Hajime Kita,et al.  Adaptation to a Changing Environment by Means of the Feedback Thermodynamical Genetic Algorithm , 1996, PPSN.

[34]  Marco Laumanns,et al.  SPEA2: Improving the strength pareto evolutionary algorithm , 2001 .

[35]  Kay Chen Tan,et al.  Noise-induced features in robust multi-objective optimization problems , 2007, 2007 IEEE Congress on Evolutionary Computation.

[36]  Terence C. Fogarty,et al.  Adaptive Combustion Balancing in Multiple Burner Boiler Using a Genetic Algorithm with Variable Range of Local Search , 1997, ICGA.

[37]  Zhuhong Zhang,et al.  Multiobjective optimization immune algorithm in dynamic environments and its application to greenhouse control , 2008, Appl. Soft Comput..

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

[39]  Dirk Thierens,et al.  The balance between proximity and diversity in multiobjective evolutionary algorithms , 2003, IEEE Trans. Evol. Comput..

[40]  Jürgen Branke,et al.  Evolutionary Optimization in Dynamic Environments , 2001, Genetic Algorithms and Evolutionary Computation.

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

[42]  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).

[43]  Kalyanmoy Deb,et al.  Dynamic multiobjective optimization problems: test cases, approximations, and applications , 2004, IEEE Transactions on Evolutionary Computation.

[44]  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).

[45]  Marco Laumanns,et al.  A unified model for multi-objective evolutionary algorithms with elitism , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

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

[47]  Carlos A. Coello Coello,et al.  A coevolutionary multi-objective evolutionary algorithm , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[48]  Gary G. Yen,et al.  Rank-density-based multiobjective genetic algorithm and benchmark test function study , 2003, IEEE Trans. Evol. Comput..

[49]  Hajime Kita,et al.  Adaptation to a Changing Environment by Means of the Thermodynamical Genetic Algorithm , 1999 .

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

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

[52]  Philipp Limbourg,et al.  Multi-objective Optimization of Problems with Epistemic Uncertainty , 2005, EMO.

[53]  J. Branke.  Reducing the sampling variance when searching for robust solutions , 2001 .

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

[55]  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).

[56]  Nachol Chaiyaratana,et al.  Multi-objective Co-operative Co-evolutionary Genetic Algorithm , 2002, PPSN.

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

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

[59]  Bernhard Sendhoff,et al.  Constructing Dynamic Optimization Test Problems Using the Multi-objective Optimization Concept , 2004, EvoWorkshops.

[60]  Kenneth A. De Jong,et al.  Cooperative Coevolution: An Architecture for Evolving Coadapted Subcomponents , 2000, Evolutionary Computation.

[61]  Tong Heng Lee,et al.  A Study on Distribution Preservation Mechanism in Evolutionary Multi-Objective Optimization , 2005, Artificial Intelligence Review.

[62]  Shigeyoshi Tsutsui,et al.  Genetic algorithms with a robust solution searching scheme , 1997, IEEE Trans. Evol. Comput..

[63]  Kittipong Boonlong,et al.  Multi-objective Optimisation by Co-operative Co-evolution , 2004, PPSN.

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

[65]  Kalyanmoy Deb,et al.  Dynamic Multi-objective Optimization and Decision-Making Using Modified NSGA-II: A Case Study on Hydro-thermal Power Scheduling , 2007, EMO.

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

[67]  Kay Chen Tan,et al.  A distributed Cooperative coevolutionary algorithm for multiobjective optimization , 2006, IEEE Transactions on Evolutionary Computation.

[68]  Sandor Markon,et al.  Threshold selection, hypothesis tests, and DOE methods , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[69]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[70]  John J. Grefenstette,et al.  An Approach to Anytime Learning , 1992, ML.

[71]  Bernhard Sendhoff,et al.  Trade-Off between Performance and Robustness: An Evolutionary Multiobjective Approach , 2003, EMO.

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

[73]  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).

[74]  Kay Chen Tan,et al.  Evolving the Tradeoffs between Pareto-Optimality and Robustness in Multi-Objective Evolutionary Algorithms , 2007, Evolutionary Computation in Dynamic and Uncertain Environments.

[75]  Richard K. Belew,et al.  New Methods for Competitive Coevolution , 1997, Evolutionary Computation.

[76]  David E. Goldberg,et al.  The Design of Innovation: Lessons from and for Competent Genetic Algorithms , 2002 .

[77]  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.

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

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