Multi-Objective Evolutionary Algorithms

Evolutionary algorithms (EA s) have amply shown their promise in solving various search and optimization problems for the past three decades. One of the hallmarks and niches of EAs is their ability to handle multi-objective optimization problems in their totality, which their classical counterparts lack. Suggested in the beginning of the 1990s, evolutionary multi-objective optimization (EMO ) algorithms are now routinely used in solving problems with multiple conflicting objectives in various branches of engineering, science, and commerce. In this chapter, we provide an overview of EMO methodologies by first presenting principles of EMO through an illustration of one specific algorithm and its application to an interesting real-world bi-objective optimization problem. Thereafter, we provide a list of recent research and application developments of EMO to provide a picture of some salient advancements in EMO research. The development and application of EMO to multi-objective optimization problems and their continued extensions to solve other related problems has elevated EMO research to a level which may now undoubtedly be termed as an active field of research with a wide range of theoretical and practical research and application opportunities.

[1]  Andrzej P. Wierzbicki,et al.  The Use of Reference Objectives in Multiobjective Optimization , 1979 .

[2]  Salvatore Greco,et al.  Evolutionary Multi-Criterion Optimization , 2011, Lecture Notes in Computer Science.

[3]  Kalyanmoy Deb,et al.  Integrating User Preferences into Evolutionary Multi-Objective Optimization , 2005 .

[4]  Kalyanmoy Deb,et al.  Faster Hypervolume-Based Search Using Monte Carlo Sampling , 2008, MCDM.

[5]  C. Coello TREATING CONSTRAINTS AS OBJECTIVES FOR SINGLE-OBJECTIVE EVOLUTIONARY OPTIMIZATION , 2000 .

[6]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[7]  Kalyanmoy Deb,et al.  Evolutionary multi-criterion optimization , 2010, GECCO '10.

[8]  Gary B. Lamont,et al.  Applications Of Multi-Objective Evolutionary Algorithms , 2004 .

[9]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[10]  Günter Rudolph,et al.  Convergence analysis of canonical genetic algorithms , 1994, IEEE Trans. Neural Networks.

[11]  Kaisa Miettinen,et al.  A Preference Based Interactive Evolutionary Algorithm for Multi-objective Optimization: PIE , 2011, EMO.

[12]  Kalyanmoy Deb,et al.  A Hybrid Multi-objective Evolutionary Approach to Engineering Shape Design , 2001, EMO.

[13]  David E. Goldberg,et al.  A niched Pareto genetic algorithm for multiobjective optimization , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[14]  Kalyanmoy Deb,et al.  On finding multiple Pareto-optimal solutions using classical and evolutionary generating methods , 2007, Eur. J. Oper. Res..

[15]  Kalyanmoy Deb,et al.  Interactive evolutionary multi-objective optimization and decision-making using reference direction method , 2007, GECCO '07.

[16]  Eckart Zitzler,et al.  Dimensionality Reduction in Multiobjective Optimization: The Minimum Objective Subset Problem , 2006, OR.

[17]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

[18]  B. Babu,et al.  Differential evolution for multi-objective optimization , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[19]  E. Zitzler,et al.  Offline and Online Objective Reduction in Evolutionary Multiobjective Optimization Based on Objective Conflicts , 2007 .

[20]  Kalyanmoy Deb,et al.  Distributed computing of Pareto-optimal solutions using multi-objective evolutionary algorithms , 2003 .

[21]  Patrick R. McMullen,et al.  An ant colony optimization approach to addressing a JIT sequencing problem with multiple objectives , 2001, Artif. Intell. Eng..

[22]  Kalyanmoy Deb,et al.  Multi-objective Genetic Algorithms: Problem Difficulties and Construction of Test Problems , 1999, Evolutionary Computation.

[23]  Per Kristian Lehre,et al.  On the Effect of Populations in Evolutionary Multi-Objective Optimisation , 2006, Evolutionary Computation.

[24]  Kalyanmoy Deb,et al.  Reliability-Based Optimization Using Evolutionary Algorithms , 2009, IEEE Transactions on Evolutionary Computation.

[25]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[26]  Kalyanmoy Deb,et al.  Multiobjective Problem Solving from Nature: From Concepts to Applications (Natural Computing Series) , 2008 .

[27]  Saúl Zapotecas Martínez,et al.  A Proposal to Hybridize Multi-Objective Evolutionary Algorithms with Non-gradient Mathematical Programming Techniques , 2008, PPSN.

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

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

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

[31]  Marco Laumanns,et al.  Running Time Analysis of Multi-objective Evolutionary Algorithms on a Simple Discrete Optimization Problem , 2002, PPSN.

[32]  Michael Emmerich,et al.  Metamodel Assisted Multiobjective Optimisation Strategies and their Application in Airfoil Design , 2004 .

[33]  Rajeev Kumar,et al.  Analysis of a Multiobjective Evolutionary Algorithm on the 0-1 knapsack problem , 2006, Theor. Comput. Sci..

[34]  Andrzej Osyczka,et al.  Evolutionary Algorithms for Single and Multicriteria Design Optimization , 2001 .

[35]  Qingfu Zhang,et al.  Objective Reduction in Many-Objective Optimization: Linear and Nonlinear Algorithms , 2013, IEEE Transactions on Evolutionary Computation.

[36]  Carlos A. Coello Coello,et al.  A Micro-Genetic Algorithm for Multiobjective Optimization , 2001, EMO.

[37]  Oliver Giel,et al.  Expected runtimes of a simple multi-objective evolutionary algorithm , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[38]  Kalyanmoy Deb,et al.  Finding Knees in Multi-objective Optimization , 2004, PPSN.

[39]  Bernhard Sendhoff,et al.  On Test Functions for Evolutionary Multi-objective Optimization , 2004, PPSN.

[40]  Anne Auger,et al.  Theoretically Investigating Optimal µ-Distributions for the Hypervolume Indicator: First Results for Three Objectives , 2010, PPSN.

[41]  Eckart Zitzler,et al.  Indicator-Based Selection in Multiobjective Search , 2004, PPSN.

[42]  K. Miettinen,et al.  Incorporating preference information in interactive reference point methods for multiobjective optimization , 2009 .

[43]  Kalyanmoy Deb,et al.  Non-linear Dimensionality Reduction Procedures for Certain Large-Dimensional Multi-objective Optimization Problems: Employing Correntropy and a Novel Maximum Variance Unfolding , 2007, EMO.

[44]  Aravind Srinivasan,et al.  Innovization: innovating design principles through optimization , 2006, GECCO.

[45]  Marco Laumanns,et al.  Computing Gap Free Pareto Front Approximations with Stochastic Search Algorithms , 2010, Evolutionary Computation.

[46]  Carlos A. Coello Coello,et al.  Some techniques to deal with many-objective problems , 2009, GECCO '09.

[47]  Kalyanmoy Deb,et al.  Multiobjective optimization , 1997 .

[48]  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.

[49]  Emile H. L. Aarts,et al.  Simulated Annealing: Theory and Applications , 1987, Mathematics and Its Applications.

[50]  David E. Goldberg,et al.  Genetic Algorithms with Sharing for Multimodalfunction Optimization , 1987, ICGA.

[51]  Edwin D. de Jong,et al.  Reducing bloat and promoting diversity using multi-objective methods , 2001 .

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

[53]  Günter Rudolph,et al.  Convergence properties of some multi-objective evolutionary algorithms , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[54]  Pekka Korhonen,et al.  A Visual Interactive Method for Solving the Multiple-Criteria Problem , 1986 .

[55]  Xiaoping Du,et al.  Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design , 2004, DAC 2002.

[56]  Ujjwal Maulik,et al.  A Simulated Annealing-Based Multiobjective Optimization Algorithm: AMOSA , 2008, IEEE Transactions on Evolutionary Computation.

[57]  Kalyanmoy Deb,et al.  Finding trade-off solutions close to KKT points using evolutionary multi-objective optimization , 2007, 2007 IEEE Congress on Evolutionary Computation.

[58]  Kalyanmoy Deb,et al.  An Evolutionary Multi-objective Adaptive Meta-modeling Procedure Using Artificial Neural Networks , 2007, Evolutionary Computation in Dynamic and Uncertain Environments.

[59]  C. G. Sauer OPTIMIZATION OF MULTIPLE TARGET ELECTRIC PROPULSION TRAJECTORIES , 1973 .

[60]  Marco Laumanns,et al.  Scalable Test Problems for Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

[61]  Kalyanmoy Deb,et al.  Light beam search based multi-objective optimization using evolutionary algorithms , 2007, 2007 IEEE Congress on Evolutionary Computation.

[62]  Kalyanmoy Deb,et al.  Handling many-objective problems using an improved NSGA-II procedure , 2012, 2012 IEEE Congress on Evolutionary Computation.

[63]  Kalyanmoy Deb,et al.  Automated Innovization for Simultaneous Discovery of Multiple Rules in Bi-objective Problems , 2011, EMO.

[64]  Kalyanmoy Deb,et al.  Reference point based multi-objective optimization using evolutionary algorithms , 2006, GECCO '06.

[65]  Kalyanmoy Deb,et al.  Towards automating the discovery of certain innovative design principles through a clustering-based optimization technique , 2011 .

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

[67]  Huidong Jin,et al.  Adaptive diversity maintenance and convergence guarantee in multiobjective evolutionary algorithms , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[68]  David W. Corne,et al.  Quantifying the Effects of Objective Space Dimension in Evolutionary Multiobjective Optimization , 2007, EMO.

[69]  R. Lyndon While,et al.  A Scalable Multi-objective Test Problem Toolkit , 2005, EMO.

[70]  Xin Yao,et al.  Performance Scaling of Multi-objective Evolutionary Algorithms , 2003, EMO.

[71]  Kalyanmoy Deb,et al.  A Local Search Based Evolutionary Multi-objective Optimization Approach for Fast and Accurate Convergence , 2008, PPSN.

[72]  Kenneth de Jong,et al.  Evolutionary computation: a unified approach , 2007, GECCO.

[73]  Thomas A. Cruse,et al.  Reliability-Based Mechanical Design , 1997 .

[74]  Marco Laumanns,et al.  Running time analysis of multiobjective evolutionary algorithms on pseudo-Boolean functions , 2004, IEEE Transactions on Evolutionary Computation.

[75]  M. Fleischer,et al.  The Measure of Pareto Optima , 2003, EMO.

[76]  Kazuhiro Nakahashi,et al.  Aerodynamic Shape Optimization of Supersonic Wings by Adaptive Range Multiobjective Genetic Algorithms , 2001, EMO.

[77]  Kalyanmoy Deb,et al.  MULTI-OBJECTIVE FUNCTION OPTIMIZATION USING NON-DOMINATED SORTING GENETIC ALGORITHMS , 1994 .

[78]  Andy J. Keane,et al.  Metamodeling Techniques For Evolutionary Optimization of Computationally Expensive Problems: Promises and Limitations , 1999, GECCO.

[79]  Kalyanmoy Deb,et al.  Simulated Binary Crossover for Continuous Search Space , 1995, Complex Syst..

[80]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[81]  Kalyanmoy Deb,et al.  Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms , 1994, Evolutionary Computation.

[82]  R. Lyndon While,et al.  A faster algorithm for calculating hypervolume , 2006, IEEE Transactions on Evolutionary Computation.

[83]  Kalyanmoy Deb,et al.  Computationally effective search and optimization procedure using coarse to fine approximations , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[84]  Michael T. M. Emmerich,et al.  Single- and multiobjective evolutionary optimization assisted by Gaussian random field metamodels , 2006, IEEE Transactions on Evolutionary Computation.

[85]  Joshua D. Knowles,et al.  An Evolutionary Approach to Multiobjective Clustering , 2007, IEEE Transactions on Evolutionary Computation.

[86]  Marc Gravel,et al.  Scheduling continuous casting of aluminum using a multiple objective ant colony optimization metaheuristic , 2002, Eur. J. Oper. Res..

[87]  Martin J. Oates,et al.  The Pareto Envelope-Based Selection Algorithm for Multi-objective Optimisation , 2000, PPSN.

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

[89]  C.A. Coello Coello,et al.  MOPSO: a proposal for multiple objective particle swarm optimization , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[90]  Lucas Bradstreet,et al.  A Fast Incremental Hypervolume Algorithm , 2008, IEEE Transactions on Evolutionary Computation.

[91]  Tong Heng Lee,et al.  Multiobjective Evolutionary Algorithms and Applications , 2005, Advanced Information and Knowledge Processing.

[92]  Lothar Thiele,et al.  Multiobjective genetic programming: reducing bloat using SPEA2 , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[93]  Kyriakos C. Giannakoglou,et al.  Design of optimal aerodynamic shapes using stochastic optimization methods and computational intelligence , 2002 .

[94]  Jürgen Teich,et al.  Strategies for finding good local guides in multi-objective particle swarm optimization (MOPSO) , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

[95]  G. Rudolph On a multi-objective evolutionary algorithm and its convergence to the Pareto set , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[96]  Marco Laumanns,et al.  Convergence of stochastic search algorithms to finite size pareto set approximations , 2008, J. Glob. Optim..

[97]  S. Ranji Ranjithan,et al.  The Neighborhood Constraint Method: A Genetic Algorithm-Based Multiobjective Optimization Technique , 1997, ICGA.

[98]  Gary B. Lamont,et al.  Multiobjective Evolutionary Algorithms: Analyzing the State-of-the-Art , 2000, Evolutionary Computation.

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

[100]  Joshua D. Knowles,et al.  On metrics for comparing nondominated sets , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[101]  Marco Laumanns,et al.  Combining Convergence and Diversity in Evolutionary Multiobjective Optimization , 2002, Evolutionary Computation.

[102]  Carlos M. Fonseca,et al.  Exploring the Performance of Stochastic Multiobjective Optimisers with the Second-Order Attainment Function , 2005, EMO.

[103]  David W. Corne,et al.  Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy , 2000, Evolutionary Computation.

[104]  Frank Neumann,et al.  Minimum spanning trees made easier via multi-objective optimization , 2005, GECCO '05.

[105]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[106]  Lawrence J. Fogel,et al.  Artificial Intelligence through Simulated Evolution , 1966 .

[107]  Evan J. Hughes,et al.  Evolutionary many-objective optimisation: many once or one many? , 2005, 2005 IEEE Congress on Evolutionary Computation.

[108]  John W. Hartmann,et al.  Optimal multi-objective low-thrust spacecraft trajectories , 2000 .

[109]  Peter J. Fleming,et al.  Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization , 1993, ICGA.

[110]  Kalyanmoy Deb,et al.  Multiobjective Problem Solving from Nature: From Concepts to Applications , 2008, Natural Computing Series.