nach oben

Erschienen in:

2015 | OriginalPaper | Buchkapitel

49. Multi-Objective Evolutionary Algorithms

verfasst von : Kalyanmoy Deb

Erschienen in: Springer Handbook of Computational Intelligence

Verlag: Springer Berlin Heidelberg

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

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.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel Indicator-Based Selection

Nächstes Kapitel Parallel Multiobjective Evolutionary Algorithms

[49.1]

D.E. Goldberg: Genetic Algorithms for Search, Optimization, and Machine Learning (Addison-Wesley, Reading 1989)MATH

[49.2]

J.H. Holland: Adaptation in Natural and Artificial Systems (MIT, Ann Arbor 1975)

[49.3]

K.A. De Jong: Evolutionary Computation: A Unified Approach (MIT, Cambridge 2006)MATH

[49.4]

P.J.M. Laarhoven, E.H.L. Aarts: Simulated Annealing: Theory and Applications (Springer, Heidelberg 1987)MATHCrossRef

[49.5]

F. Glover: Tabu search - Part 1, ORSA J. Comput. 1(2), 190–206 (1989)MATHCrossRef

[49.6]

F. Glover: Tabu search - Part 2, ORSA J. Comput. 2(1), 4–32 (1990)MATHCrossRef

[49.7]

B.S.W. Schröder: Ordered Sets: An Introduction (Birkhäuser, Boston 2003)MATHCrossRef

[49.8]

K. Deb: Multi-Objective Optimization Using Evolutionary Algorithms (Wiley, Chichester 2001)MATH

[49.9]

K. Miettinen: Nonlinear Multiobjective Optimization (Kluwer, Boston 1999)MATH

[49.10]

H.T. Kung, F. Luccio, F.P. Preparata: On finding the maxima of a set of vectors, J. Assoc. Comput. Mach. 22(4), 469–476 (1975)MathSciNetMATHCrossRef

[49.11]

J. Jahn: Vector Optimization (Springer, Berlin 2004)MATHCrossRef

[49.12]

G. Rudolph: On a multi-objective evolutionary algorithm and its convergence to the Pareto set, Proc. 5th IEEE Conf. Evol. Comput. (1998) pp. 511–516

[49.13]

G. Rudolph, A. Agapie: Convergence properties of some multi-objective evolutionary algorithms, Proc. 2000 Congr. Evol. Comput. (CEC2000) (2000) pp. 1010–1016

[49.14]

O. Schütze, M. Laumanns, C.A.C. Coello, M. Dellnitz, E.-G. Talbi: Convergence of stochastic search algorithms to finite size Pareto set approximations, J. Glob. Optim. 41(4), 559–577 (2008)MathSciNetMATHCrossRef

[49.15]

O. Schütze, M. Laumanns, E. Tantar, C.A.C. Coello, E.-G. Talbi: Computing gap-free Pareto front approximations with stochastic search algorithms, Evol. Comput. J. 18(1), 65–96 (2010)CrossRef

[49.16]

K. Deb, R. Tiwari, M. Dixit, J. Dutta: Finding trade-off solutions close to KKT points using evolutionary multi-objective optimization, Proc. Congr. Evol. Comput. (CEC-2007) (2007) pp. 2109–2116

[49.17]

P. Shukla, K. Deb: On finding multiple Pareto-optimal solutions using classical and evolutionary generating methods, Eur. J. Oper. Res. (EJOR) 181(3), 1630–1652 (2007)MATHCrossRef

[49.18]

R.S. Rosenberg: Simulation of Genetic Populations with Biochemical Properties, Ph.D. Thesis (University of Michigan, Ann Arbor 1967)

[49.19]

L.J. Fogel, A.J. Owens, M.J. Walsh: Artificial Intelligence Through Simulated Evolution (Wiley, New York 1966)MATH

[49.20]

J.D. Schaffer: Some Experiments in Machine Learning Using Vector Evaluated Genetic Algorithms, Ph.D. Thesis (Vanderbilt University, Nashville 1984)

[49.21]

D.E. Goldberg, J. Richardson: Genetic algorithms with sharing for multimodal function optimization, Proc. First Int. Conf. Genet. Algorithms Their Appl. (1987) pp. 41–49

[49.22]

C.M. Fonseca, P.J. Fleming: Genetic algorithms for multiobjective optimization: Formulation, discussion, and generalization, Proc. Fifth Int. Conf. Genet. Algorithms (1993) pp. 416–423

[49.23]

J. Horn, N. Nafploitis, D.E. Goldberg: A niched Pareto genetic algorithm for multi-objective optimization, Proc. First IEEE Conf. Evol. Comput. (1994) pp. 82–87

[49.24]

N. Srinivas, K. Deb: Multi-objective function optimization using non-dominated sorting genetic algorithms, Evol. Comput. J. 2(3), 221–248 (1994)CrossRef

[49.25]

C. Poloni: Hybrid GA for multi-objective aerodynamic shape optimization. In: Genetic Algorithms in Engineering and Computer Science, ed. by G. Winter, J. Periaux, M. Galan, P. Cuesta (Wiley, Chichester 1997) pp. 397–414

[49.26]

G. Rudolph: Convergence analysis of canonical genetic algorithms, IEEE Trans. Neural Netw. 5(1), 96–101 (1994)CrossRef

[49.27]

K. Deb, S. Agrawal, A. Pratap, T. Meyarivan: A fast and elitist multi-objective genetic algorithm: NSGA-II, IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)CrossRef

[49.28]

E. Zitzler, L. Thiele: Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach, IEEE Trans. Evol. Comput. 3(4), 257–271 (1999)CrossRef

[49.29]

J.D. Knowles, D.W. Corne: Approximating the non-dominated front using the Pareto archived evolution strategy, Evol. Comput. J. 8(2), 149–172 (2000)CrossRef

[49.30]

K. Deb, R.B. Agrawal: Simulated binary crossover for continuous search space, Complex Syst. 9(2), 115–148 (1995)MathSciNetMATH

[49.31]

E. Zitzler, M. Laumanns, L. Thiele: SPEA2: Improving the strength Pareto evolutionary algorithm for multiobjective optimization. In: Evolutionary Methods for Design Optimization and Control with Applications to Industrial Problems, ed. by K.C. Giannakoglou, D.T. Tsahalis, J. Périaux, K.D. Papailiou, T. Fogarty (CIMNE, Athens 2001) pp. 95–100

[49.32]

D.W. Corne, J.D. Knowles, M. Oates: The Pareto envelope-based selection algorithm for multiobjective optimization, Proc. Sixth Int. Conf. Parallel Probl. Solving Nat. VI (PPSN-VI) (2000) pp. 839–848

[49.33]

D. Van Veldhuizen, G.B. Lamont: Multiobjective evolutionary algorithms: Analyzing the state-of-the-art, Evol. Comput. J. 8(2), 125–148 (2000)CrossRef

[49.34]

C.A.C. Coello, G. Toscano: A Micro-Genetic Algorithm for Multi-Objective Optimization, Technical Report Lania-RI-2000-06 (Laboratoria Nacional de Informatica Avanzada, Xalapa 2000)

[49.35]

D.H. Loughlin, S. Ranjithan: The neighborhood constraint method: A multiobjective optimization technique, Proc. Seventh Int. Conf. Genet. Algorithms (1997) pp. 666–673

[49.36]

D. Sasaki, M. Morikawa, S. Obayashi, K. Nakahashi: Aerodynamic shape optimization of supersonic wings by adaptive range multiobjective genetic algorithms, Proc. First Int. Conf. Evol. Multi-Criterion Optim. (EMO 2001) (2001) pp. 639–652CrossRef

[49.37]

C.A.C. Coello, M.S. Lechuga: MOPSO: A proposal for multiple objective particle swarm optimization, Congr. Evol. Comput. (CEC'2002), Vol. 2 (IEEE Service Center, Piscataway 2002) pp. 1051–1056

[49.38]

S. Mostaghim, J. Teich: Strategies for finding good local guides in multi-objective particle swarm optimization (MOPSO), 2003 IEEE Swarm Intell. Symp. Proc. (IEEE Service Center, Indianapolis 2003) pp. 26–33

[49.39]

P.R. McMullen: An ant colony optimization approach to addessing a JIT sequencing problem with multiple objectives, Artifi. Intell. Eng. 15, 309–317 (2001)CrossRef

[49.40]

M. Gravel, W.L. Price, C. Gagné: Scheduling continuous casting of aluminum using a multiple objective ant colony optimization metaheuristic, Eur. J. Oper. Res. 143(1), 218–229 (2002)MATHCrossRef

[49.41]

B.V. Babu, M.L. Jehan: Differential evolution for multi-objective optimization, Proc. 2003 Congr. Evol. Comput. (CEC'2003), Vol. 4 (IEEE, Canberra 2003) pp. 2696–2703CrossRef

[49.42]

S. Bandyopadhyay, S. Saha, U. Maulik, K. Deb: A simulated annealing-based multiobjective optimization algorithm: Amosa, IEEE Trans. Evol. Comput. 12(3), 269–283 (2008)CrossRef

[49.43]

M.P. Hansen: Tabu search in multiobjective optimization: MOTS, Thirteenth Int. Conf. Multi-Criterion Decis. Mak. (MCDM'97) (University of Cape Town, Cape Town 1997)

[49.44]

C.A.C. Coello, D.A. VanVeldhuizen, G. Lamont: Evolutionary Algorithms for Solving Multi-Objective Problems (Kluwer, Boston 2002)MATHCrossRef

[49.45]

C.A.C. Coello, G.B. Lamont: Applications of Multi-Objective Evolutionary Algorithms (World Scientific, Singapore 2004)MATHCrossRef

[49.46]

A. Osyczka: Evolutionary Algorithms for Single and Multicriteria Design Optimization (Physica, Heidelberg 2002)MATH

[49.47]

K.C. Tan, E.F. Khor, T.H. Lee: Multiobjective Evolutionary Algorithms and Applications (Springer, London 2005)MATH

[49.48]

E. Zitzler, K. Deb, L. Thiele, C.A.C. Coello, D.W. Corne: Evolutionary Multi-Criterion Optimization, 1st International Conference (EMO-2001), Lecture Notes in Computer Science, Vol. 1993 (Springer, Heidelberg 2001)CrossRef

[49.49]

C.M. Fonseca, P. Fleming, E. Zitzler, K. Deb, L. Thiele: Evolutionary Multi-Criterion Optimization, 2nd International Conference, (EMO-2003), Lecture Notes in Computer Science, Vol. 2632 (Springer, Heidelberg 2003)MATHCrossRef

[49.50]

C.A.C. Coello, A.H. Aguirre, E. Zitzler: Evolutionary Multi-Criterion Optimization, 3rd International Conference (EMO-2005), Lecture Notes in Computer Science, Vol. 3410 (Springer, Heidelberg 2005)MATHCrossRef

[49.51]

S. Obayashi, K. Deb, C. Poloni, T. Hiroyasu, T. Murata: Evolutionary Multi-Criterion Optimization, 4th International Conference (EMO-2007), Lecture Notes in Computer Science, Vol. 4403 (Springer, Heidelberg 2007)MATHCrossRef

[49.52]

M. Ehrgott, C.M. Fonseca, X. Gandibleux, J.-K. Hao, M. Sevaux: Evolutionary Multi-Criterion Optimization, 5th International Conference (EMO-2009), Lecture Notes in Computer Science, Vol. 5467 (Springer, Heidelberg 2009)MATHCrossRef

[49.53]

R.H.C. Takahashi, K. Deb, E.F. Wanner, S. Greco: Evolutionary Multi-Criterion Optimization, 6th International Conference (EMO-2011), Lecture Notes in Computer Science, Vol. 6576 (Springer, Heidelberg 2011)MATHCrossRef

[49.54]

C. A. Coello: List of references on evolutionary multiobjective optimization (emo), http://www.lania.mx/~ccoello/EMOO/EMOObib.html

[49.55]

V. Coverstone-Carroll, J.W. Hartmann, W.J. Mason: Optimal multi-objective low-thurst spacecraft trajectories, Comput. Meth. Appl. Mech. Eng. 186(2–4), 387–402 (2000)MATHCrossRef

[49.56]

C.G. Sauer: Optimization of multiple target electric propulsion trajectories, AIAA 11th Aerosp. Sci. Meet. (1973), Paper Number 73–205

[49.57]

K. Deb, T. Goel: A hybrid multi-objective evolutionary approach to engineering shape design, Proc. First Int. Conf. Evol. Multi-Criterion Optim. (EMO-01) (2001) pp. 385–399CrossRef

[49.58]

K. Sindhya, K. Deb, K. Miettinen: A local search based evolutionary multi-objective optimization technique for fast and accurate convergence, Proc. Parallel Probl. Solving Nat. (PPSN-2008) (Springer, Berlin 2008)

[49.59]

H. Jin, M.-L. Wong: Adaptive diversity maintenance and convergence guarantee in multiobjective evolutionary algorithms, Proc. Congr. Evol. Comput. (CEC-2003) (2003) pp. 2498–2505

[49.60]

Z.M. Saul, C.A.C. Coello: A proposal to hybridize multi-objective evolutionary algorithms with non-gradient mathematical programming techniques, Proc. Parallel Probl. Solving Nat. (PPSN-2008) (2008) pp. 837–846

[49.61]

M. Fleischer: The measure of Pareto optima: Applications to multi-objective optimization, Proc. Second Int. Conf. Evol. Multi-Criterion Optim. (EMO-2003) (Springer, Berlin 2003) pp. 519–533CrossRef

[49.62]

L. While, P. Hingston, L. Barone, S. Huband: Afaster algorithm for calculating hypervolume, IEEE Trans. Evol. Comput. 10(1), 29–38 (2006)CrossRef

[49.63]

L. Bradstreet, L. While, L. Barone: A fast incremental hypervolume algorithm, IEEE Trans. Evol. Comput. 12(6), 714–723 (2008)CrossRef

[49.64]

M. Laumanns, L. Thiele, K. Deb, E. Zitzler: Combining convergence and diversity in evolutionary multi-objective optimization, Evol. Comput. 10(3), 263–282 (2002)CrossRef

[49.65]

P.A.N. Bosman, D. Thierens: The balance between proximity and diversity in multiobjective evolutionary algorithms, IEEE Trans. Evol. Comput. 7(2), 174–188 (2003)CrossRef

[49.66]

C.A.C. Coello: Treating objectives as constraints for single objective optimization, Eng. Optim. 32(3), 275–308 (2000)CrossRef

[49.67]

S. Bleuler, M. Brack, E. Zitzler: Multiobjective genetic programming: Reducing bloat using SPEA2, Proc. 2001 Congr. Evol. Comput. (2001) pp. 536–543

[49.68]

E.D. De Jong, R.A. Watson, J.B. Pollack: Reducing bloat and promoting diversity using multi-objective methods, Proc. Genet. Evol. Comput. Conf. (GECCO-2001) (2001) pp. 11–18

[49.69]

J. Handl, J.D. Knowles: An evolutionary approach to multiobjective clustering, IEEE Trans. Evol. Comput. 11(1), 56–76 (2007)CrossRef

[49.70]

F. Neumann, I. Wegener: Minimum spanning trees made easier via multi-objective optimization, GECCO'05: Proc. 2005 Conf. Genetic Evol. Comput. (ACM, New York 2005) pp. 763–769CrossRef

[49.71]

J.D. Knowles, D.W. Corne, K. Deb: Multiobjective Problem Solving from Nature, Springer Natural Computing Series (Springer, Heidelberg 2008)MATHCrossRef

[49.72]

K. Deb, S. Gupta, D. Daum, J. Branke, A. Mall, D. Padmanabhan: Reliability-based optimization using evolutionary algorithms, IEEE Trans. Evol. Comput. 13(5), 1054–1074 (2009)CrossRef

[49.73]

K. Deb, H. Gupta: Introducing robustness in multi-objective optimization, Evol. Comput. J. 14(4), 463–494 (2006)CrossRef

[49.74]

M. Basseur, E. Zitzler: Handling uncertainty in indicator-based multiobjective optimization, Int. J. Comput. Intell. Res. 2(3), 255–272 (2006)MathSciNet

[49.75]

T.R. Cruse: Reliability-Based Mechanical Design (Marcel Dekker, New York 1997)

[49.76]

X. Du, W. Chen: Sequential optimization and reliability assessment method for efficient probabilistic design, ASME Trans. J. Mech. Des. 126(2), 225–233 (2004)CrossRef

[49.77]

J. Branke, K. Deb, H. Dierolf, M. Osswald: Finding knees in multi-objective optimization, Lect. Notes Comput. Sci. 3242, 722–731 (2004)CrossRef

[49.78]

A.P. Wierzbicki: The use of reference objectives in multiobjective optimization. In: Multiple Criteria Decision Making Theory and Applications, ed. by G. Fandel, T. Gal (Springer, Berlin 1980) pp. 468–486CrossRef

[49.79]

P. Korhonen, J. Laakso: A visual interactive method for solving the multiple criteria problem, Eur. J. Oper. Res. 24, 277–287 (1986)MathSciNetMATHCrossRef

[49.80]

J. Branke, K. Deb, K. Miettinen, R. Slowinski: Multiobjective Optimization: Interactive and Evolutionary Approaches (Springer, Berlin 2008)MATHCrossRef

[49.81]

K. Deb, J. Sundar, N. Uday, S. Chaudhuri: Reference point based multi-objective optimization using evolutionary algorithms, Int. J. Comput. Intell. Res. (IJCIR) 2(6), 273–286 (2006)MathSciNet

[49.82]

K. Deb, A. Kumar: Light beam search based multi-objective optimization using evolutionary algorithms, Proc. Congr. Evol. Comput. (CEC-07) (2007) pp. 2125–2132

[49.83]

K. Deb, A. Kumar: Interactive evolutionary multi-objective optimization and decision-making using reference direction method, Proc. Genet. Evol. Comput. Conf. (GECCO-2007) (ACM, New York 2007) pp. 781–788

[49.84]

L. Thiele, K. Miettinen, P. Korhonen, J. Molina: A Preference-Based Interactive Evolutionary Algorithm for Multiobjective Optimization, Technical Report Working Paper W-412 (Helsingin School of Economics, Helsingin Kauppakorkeakoulu 2007)

[49.85]

M. Luque, K. Miettinen, P. Eskelinen, F. Ruiz: Incorporating preference information in interactive reference point based methods for multiobjective optimization, Omega 37(2), 450–462 (2009)CrossRef

[49.86]

V. Khare, X. Yao, K. Deb: Performance scaling of multi-objective evolutionary algorithms, Lect. Notes Comput. Sci. 2632, 376–390 (2003)MATHCrossRef

[49.87]

J. Knowles, D. Corne: Quantifying the effects of objective space dimension in evolutionary multiobjective optimization, Lect. Notes Comput. Sci. 4403, 757–771 (2007)CrossRef

[49.88]

J.A. López, C.A.C. Coello: Some techniques to deal with many-objective problems, Proc. 11th Annu. Conf. Companion Genet. Evol. Comput. Conf. (ACM, New York 2009) pp. 2693–2696

[49.89]

E.J. Hughes: Evolutionary many-objective optimisation: Many once or one many?, IEEE Congr. Evol. Comput. (CEC-2005) (2005) pp. 222–227CrossRef

[49.90]

D.K. Saxena, J.A. Duro, A. Tiwari, K. Deb, Q. Zhang: Objective reduction in many-objective optimization: Linear and nonlinear algorithms, IEEE Trans. Evol. Comput. 17(1), 77–99 (2013)CrossRef

[49.91]

K. Deb, H. Jain: An Improved NSGA-II Procedure for Many-Objective Optimization, Part I: Problems with Box Constraints, Tech. Rep. KanGAL Report, Vol. 2012009 (Indian Institute of Technology, Kanpur 2012)

[49.92]

K. Deb, H. Jain: An Improved NSGA-II Procedure for Many-Objective Optimization, Part II: Handling Constraints and Extending to an Adaptive Approach, Tech. Rep. KanGAL Report, Vol. 2012010 (Indian Institute of Technology, Kanpur 2012)

[49.93]

K. Deb, H. Jain: Handling many-objective problems using an improved NSGA-II procedure, Proc. World Congr. Comput. Intell. (WCCI-2012) (2012)

[49.94]

Q. Zhang, H. Li: MOEA/D: A multiobjective evolutionary algorithm based on decomposition, Evol. Comput. IEEE Trans. 11(6), 712–731 (2007)CrossRef

[49.95]

J. Branke, K. Deb: Integrating user preferences into evolutionary multi-objective optimization. In: Knowledge Incorporation in Evolutionary Computation, ed. by Y. Jin (Springer, Heidelberg 2004) pp. 461–477

[49.96]

K. Deb, P. Zope, A. Jain: Distributed computing of pareto-optimal solutions using multi-objective evolutionary algorithms, Lect. Notes Comput. Sci. 2632, 535–549 (2003)MATH

[49.97]

K. Deb, D. Saxena: Searching for Pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems, Proc. World Congr. Comput. Intell. (WCCI-2006) (2006) pp. 3352–3360

[49.98]

D.K. Saxena, K. Deb: Non-linear dimensionality reduction procedures for certain large-dimensional multi-objective optimization problems: Employing correntropy and a novel maximum variance unfolding, Proc. Fourth Int. Conf. Evol. Multi-Criterion Optim. (EMO-2007) (2007) pp. 772–787CrossRef

[49.99]

D. Brockhoff, E. Zitzler: Dimensionality reduction in multiobjective optimization: The minimum objective subset problem. In: Operations Research Proceedings 2006, ed. by K.H. Waldmann, U.M. Stocker (Springer, Heidelberg 2007) pp. 423–429CrossRef

[49.100]

D. Brockhoff, E. Zitzler: Offline and Online Objective Reduction in Evolutionary Multiobjective Optimization Based on Objective Conflicts, TIK Report, Vol. 269 (Institut für Technische Informatik und Kommunikationsnetze, ETH Zürich 2007)MATH

[49.101]

M. Farina, P. Amato: A fuzzy definition of optimality for many criteria optimization problems, IEEE Trans. Syst., Man Cybern. Part A: Syst, Hum. 34(3), 315–326 (2004)

[49.102]

K. Deb, A. Srinivasan: Innovization: Innovating design principles through optimization, Proc. Genet. Evol. Comput. Conf. (GECCO-2006) (ACM, New York 2006) pp. 1629–1636

[49.103]

S. Bandaru, K. Deb: Towards automating the discovery of certain innovative design principles through a clustering based optimization technique, Eng. Optim. 43(9), 1–941 (2011)MathSciNetCrossRef

[49.104]

S. Bandaru, K. Deb: Automated innovization for simultaneous discovery of multiple rules in bi-objective problems, Proc. Sixth Int. Conf. Evol. Multi-Criterion Optim. (EMO-2011) (Springer, Heidelberg 2011) pp. 1–15CrossRef

[49.105]

J. Branke: Evolutionary Optimization in Dynamic Environments (Springer, Heidelberg 2001)MATH

[49.106]

K. Deb, U.B. Rao, S. Karthik: Dynamic multi-objective optimization and decision-making using modified NSGA-II: A case study on hydro-thermal power scheduling bi-objective optimization problems, Proc. Fourth Int. Conf. Evol. Multi-Criterion Optim. (EMO-2007) (2007)

[49.107]

K. Deb: Multi-objective genetic algorithms: Problem difficulties and construction of test problems, Evol. Comput. J. 7(3), 205–230 (1999)CrossRef

[49.108]

K. Deb, L. Thiele, M. Laumanns, E. Zitzler: Scalable test problems for evolutionary multi-objective optimization. In: Evolutionary Multiobjective Optimization, ed. by A. Abraham, L. Jain, R. Goldberg (Springer, London 2005) pp. 105–145CrossRef

[49.109]

S. Huband, L. Barone, L. While, P. Hingston: A scalable multi-objective test problem toolkit, Proc. Evol. Multi-Criterion Optim. (EMO-2005) (Springer, Berlin 2005)

[49.110]

T. Okabe, Y. Jin, M. Olhofer, B. Sendhoff: On test functions for evolutionary multi-objective optimization, Parallel Problem Solving from Nature (PPSN VIII) (2004) pp. 792–802

[49.111]

J.D. Knowles, D.W. Corne: On metrics for comparing nondominated sets, Congr. Evol. Comput. (CEC-2002) (IEEE, Piscataway 2002) pp. 711–716

[49.112]

M. P. Hansen, A. Jaskiewicz: Evaluating the Quality of Aapproximations to the Non-Dominated Set, Technical Report IMM-REP-1998-7 (Institute of Mathematical Modelling, Technical University of Denmark, Lyngby 1998)

[49.113]

E. Zitzler, L. Thiele, M. Laumanns, C.M. Fonseca, V.G. Fonseca: Performance assessment of multiobjective optimizers: An analysis and review, IEEE Trans. Evol. Comput. 7(2), 117–132 (2003)CrossRef

[49.114]

E. Zitzler, S. Künzli: Indicator-based selection in multiobjective search, Lect. Notes Comput. Sci. 3242, 832–842 (2004)CrossRef

[49.115]

C.M. Fonseca, P.J. Fleming: On the performance assessment and comparison of stochastic multiobjective optimizers. In: Parallel Problem Solving from Nature (PPSN IV), ed. by H.-M. Voigt, W. Ebeling, I. Rechenberg, H.-P. Schwefel (Springer, Berlin 1996), pp. 584–593, Also available as Lecture Notes in Computer Science Vol. 1141

[49.116]

C.M. Fonseca, V. da Grunert Fonseca, L. Paquete: Exploring the performance of stochastic multiobjective optimisers with the second-order attainment function, Third Int. Conf. Evol. Multi-Criterion Optim. (EMO-2005) (Springer, Berlin 2005) pp. 250–264CrossRef

[49.117]

A. Auger, J. Bader, D. Brockhoff: Theoretically investigating optimal μ-distributions for the hypervolume indicator: First results for three objectives, Lect. Notes Comput. Sci. 6238, 586–596 (2010)

[49.118]

J. Bader, K. Deb, E. Zitzler: Faster hypervolume-based search using monte carlo sampling, Lect. Notes Econ. Math. Syst. 634, 313–326 (2010)MATHCrossRef

[49.119]

M. Laumanns, L. Thiele, E. Zitzler, E. Welzl, K. Deb: Running time analysis of multi-objective evolutionary algorithms on a simple discrete optimization problem, Proc. Seventh Conf. Parallel Probl. Solving Nat. (PPSN-VII) (2002) pp. 44–53

[49.120]

O. Giel: Expected runtimes of a simple multi-objective evolutionary algorithm, Proc. Congr. Evol. Comput. (CEC-2003) (IEEE, Piscatway 2003) pp. 1918–1925

[49.121]

M. Laumanns, L. Thiele, E. Zitzler: Running time analysis of multiobjective evolutionary algorithms on pseudo-Boolean functions, IEEE Trans. Evol. Comput. 8(2), 170–182 (2004)MATHCrossRef

[49.122]

O. Giel, P.K. Lehre: On the effect of populations in evolutionary multi-objective optimization, Proc. 8th Annu. Genet. Evol. Comput. Conf. (GECCO 2006) (ACM, New York 2006) pp. 651–658

[49.123]

R. Kumar, N. Banerjee: Analysis of a multiobjective evolutionary algorithm on the 0-1 knapsack problem, Theor. Comput. Sci. 358(1), 104–120 (2006)MathSciNetMATHCrossRef

[49.124]

M.A. El-Beltagy, P.B. Nair, A.J. Keane: Metamodelling techniques for evolutionary optimization of computationally expensive problems: Promises and limitations, Proc. Genet. Evol. Comput. Conf. (GECCO-1999) (Morgan Kaufman, San Mateo 1999) pp. 196–203

[49.125]

K.C. Giannakoglou: Design of optimal aerodynamic shapes using stochastic optimization methods and computational intelligence, Prog. Aerosp. Sci. 38(1), 43–76 (2002)CrossRef

[49.126]

P.K.S. Nain, K. Deb: Computationally effective search and optimization procedure using coarse to fine approximations, Proc. Congr. Evol. Comput. (CEC-2003) (2003) pp. 2081–2088

[49.127]

K. Deb, P.K.S. Nain: An Evolutionary Multi-Objective Adaptive Meta-Modeling Procedure Using Artificial Neural Networks (Springer, Berlin 2007) pp. 297–322

[49.128]

M. Emmerich, K.C. Giannakoglou, B. Naujoks: Single and multiobjective evolutionary optimization assisted by gaussian random field metamodels, IEEE Trans. Evol. Comput. 10(4), 421–439 (2006)CrossRef

[49.129]

M. Emmerich, B. Naujoks: Metamodel-assisted multiobjective optimisation strategies and their application in airfoil design, Adaptive Computing in Design and Manufacture VI (Springer, London 2004) pp. 249–260

Titel: Multi-Objective Evolutionary Algorithms
verfasst von: Kalyanmoy Deb
Verlag: Springer Berlin Heidelberg
Buch: Springer Handbook of Computational Intelligence
Print ISBN: 978-3-662-43504-5

Electronic ISBN: 978-3-662-43505-2

Copyright-Jahr: 2015
DOI: https://doi.org/10.1007/978-3-662-43505-2_49

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Premium Partner