Introduction to Evolutionary Multiobjective Optimization

In its current state, evolutionary multiobjective optimization (EMO) is an established field of research and application with more than 150 PhD theses, more than ten dedicated texts and edited books, commercial softwares and numerous freely downloadable codes, a biannual conference series running successfully since 2001, special sessions and workshops held at all major evolutionary computing conferences, and full-time researchers from universities and industries from all around the globe. In this chapter, we provide a brief introduction to EMO principles, illustrate some EMO algorithms with simulated results, and outline the current research and application potential of EMO. For solving multiobjective optimization problems, EMO procedures attempt to find a set of well-distributed Pareto-optimal points, so that an idea of the extent and shape of the Pareto-optimal front can be obtained. Although this task was the early motivation of EMO research, EMO principles are now being found to be useful in various other problem solving tasks, enabling one to treat problems naturally as they are. One of the major current research thrusts is to combine EMO procedures with other multiple criterion decision making (MCDM) () tools so as to develop hybrid and interactive multiobjective optimization algorithms for finding a set of trade-off optimal solutions and then choose a preferred solution for implementation. This chapter provides the background of EMO principles and their potential to launch such collaborative studies with MCDM researchers in the coming years.

[1]  Alden H. Wright,et al.  Implicit Parallelism , 2003, GECCO.

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

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

[4]  Marco Laumanns,et al.  SPEA2: Improving the Strength Pareto Evolutionary Algorithm For Multiobjective Optimization , 2002 .

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

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

[7]  Francisco Herrera,et al.  Tackling Real-Coded Genetic Algorithms: Operators and Tools for Behavioural Analysis , 1998, Artificial Intelligence Review.

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

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

[10]  Kaisa Miettinen,et al.  Nonlinear multiobjective optimization , 1998, International series in operations research and management science.

[11]  Mitsuo Gen,et al.  Genetic algorithms and engineering design , 1997 .

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

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

[14]  Christos Dimopoulos,et al.  A review of evolutionary multiobjective optimization applications in the area of production research , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

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

[16]  Zbigniew Michalewicz,et al.  Genetic Algorithms Plus Data Structures Equals Evolution Programs , 1994 .

[17]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

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

[19]  Kalyanmoy Deb,et al.  Constrained Test Problems for Multi-objective Evolutionary Optimization , 2001, EMO.

[20]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[21]  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).

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

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

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

[25]  Dirk Thierens,et al.  Toward a Better Understanding of Mixing in Genetic Algorithms , 1993 .

[26]  W. Vent,et al.  Rechenberg, Ingo, Evolutionsstrategie — Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. 170 S. mit 36 Abb. Frommann‐Holzboog‐Verlag. Stuttgart 1973. Broschiert , 1975 .

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

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

[29]  Donald O. Walter,et al.  Self-Organizing Systems , 1987, Life Science Monographs.

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

[31]  Julian F. Miller,et al.  Genetic and Evolutionary Computation — GECCO 2003 , 2003, Lecture Notes in Computer Science.

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

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

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

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

[36]  Karl-Heinz Waldmann,et al.  Operations Research Proceedings 2006 , 2007 .

[37]  Carlos A. Coello Coello,et al.  Evolutionary Multi-Objective Optimization: A Critical Review , 2003 .

[38]  Stefan Roth,et al.  Covariance Matrix Adaptation for Multi-objective Optimization , 2007, Evolutionary Computation.

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

[40]  Thomas Jansen.  On the utility of populations , 2004 .

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

[42]  Kalyanmoy Deb,et al.  Towards a Quick Computation of Well-Spread Pareto-Optimal Solutions , 2003, EMO.

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

[44]  Kalyanmoy Deb,et al.  A Computationally Efficient Evolutionary Algorithm for Real-Parameter Optimization , 2002, Evolutionary Computation.

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

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

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

[48]  Martin J. Oates,et al.  PESA-II: region-based selection in evolutionary multiobjective optimization , 2001 .

[49]  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).

[50]  R. Lyndon While,et al.  A review of multiobjective test problems and a scalable test problem toolkit , 2006, IEEE Transactions on Evolutionary Computation.

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

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

[53]  Kalyanmoy Deb,et al.  A Niched-Penalty Approach for Constraint Handling in Genetic Algorithms , 1999, ICANNGA.

[54]  K. Deb,et al.  Optimal Scheduling of Casting Sequence Using Genetic Algorithms , 2003 .

[55]  Thomas Bäck,et al.  Parallel Problem Solving from Nature — PPSN V , 1998, Lecture Notes in Computer Science.

[56]  Kalyanmoy Deb,et al.  Multi-objective test problems, linkages, and evolutionary methodologies , 2006, GECCO.

[57]  Lakhmi C. Jain,et al.  Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

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

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

[60]  Peter J. Fleming,et al.  On the Performance Assessment and Comparison of Stochastic Multiobjective Optimizers , 1996, PPSN.

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

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

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

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

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

[66]  M. Hansen,et al.  Evaluating the quality of approximations to the non-dominated set , 1998 .

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

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

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

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

[71]  Zbigniew Michalewicz,et al.  Handbook of Evolutionary Computation , 1997 .

[72]  Marco Laumanns,et al.  Scalable multi-objective optimization test problems , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

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

[74]  Bogdan Filipic,et al.  DEMO: Differential Evolution for Multiobjective Optimization , 2005, EMO.

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

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

[77]  David W. Corne,et al.  Techniques for highly multiobjective optimisation: some nondominated points are better than others , 2007, GECCO '07.

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

[79]  L. Jain,et al.  Evolutionary multiobjective optimization : theoretical advances and applications , 2005 .

[80]  Marco Laumanns,et al.  A Tutorial on Evolutionary Multiobjective Optimization , 2004, Metaheuristics for Multiobjective Optimisation.

[81]  Xin Yao,et al.  Parallel Problem Solving from Nature PPSN VI , 2000, Lecture Notes in Computer Science.

[82]  Lothar Thiele,et al.  Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study , 1998, PPSN.

[83]  Yaochu Jin,et al.  Knowledge incorporation in evolutionary computation , 2005 .

[84]  Kalyanmoy Deb,et al.  Omni-optimizer: A generic evolutionary algorithm for single and multi-objective optimization , 2008, Eur. J. Oper. Res..

[85]  J. D. Schaffer,et al.  Some experiments in machine learning using vector evaluated genetic algorithms (artificial intelligence, optimization, adaptation, pattern recognition) , 1984 .

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

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

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

[89]  Nicholas J. Radcliffe,et al.  Forma Analysis and Random Respectful Recombination , 1991, ICGA.

[90]  Hans-Paul Schwefel,et al.  Evolution and optimum seeking , 1995, Sixth-generation computer technology series.

[91]  Kalyanmoy Deb,et al.  Searching for Robust Pareto-Optimal Solutions in Multi-objective Optimization , 2005, EMO.

[92]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

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

[94]  Kalyanmoy Deb,et al.  An introduction to genetic algorithms , 1999 .

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

[96]  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.

[97]  Hans-Paul Schwefel,et al.  Evolution and Optimum Seeking: The Sixth Generation , 1993 .

[98]  Lawrence J. Fogel,et al.  Intelligence Through Simulated Evolution: Forty Years of Evolutionary Programming , 1999 .

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

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

[101]  Simon French,et al.  Multiple Criteria Decision Making: Theory and Application , 1981 .

[102]  Mitsuo Gen,et al.  Genetic Algorithms and Manufacturing Systems Design , 1996 .

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

[104]  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).

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

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

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