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Volumn 21, Issue 3, 2011, Pages 1109-1140

Direct multisearch for multiobjective optimization

Author keywords

Data profiles; Derivative free optimization; Direct search methods; Multiobjective optimization; Nonsmooth calculus; Pareto dominance; Performance profiles; Positive spanning sets

Indexed keywords

DATA PROFILES; DERIVATIVE-FREE OPTIMIZATION; DIRECT-SEARCH METHODS; MULTI OBJECTIVE; NONSMOOTH CALCULUS; PARETO DOMINANCE; PERFORMANCE PROFILE; SPANNING SETS;

EID: 80054721921     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/10079731X     Document Type: Article
Times cited : (307)

References (49)
  • 1
    • 0043032999 scopus 로고    scopus 로고
    • Analysis of generalized pattern searches
    • DOI 10.1137/S1052623400378742, PII S1052623400378742
    • C. AUDET AND J. E. DENNIS, JR., Analysis of generalized pattern searches, SIAM J. Optim., 13 (2003), pp. 889-903. (Pubitemid 36977156)
    • (2003) SIAM Journal on Optimization , vol.13 , Issue.3 , pp. 889-903
    • Audet, C.1    Dennis Jr., J.E.2
  • 2
    • 33750265086 scopus 로고    scopus 로고
    • Mesh adaptive direct search algorithms for constrained optimization
    • C. AUDET AND J. E. DENNIS, JR., Mesh adaptive direct search algorithms for constrained optimization, SIAM J. Optim., 17 (2006), pp. 188-217.
    • (2006) SIAM J. Optim. , vol.17 , pp. 188-217
    • Audet, C.1    Dennis Jr., J.E.2
  • 3
    • 61349142526 scopus 로고    scopus 로고
    • Multiobjective optimization through a series of single-objective formulations
    • C. AUDET, G. SAVARD, AND W. ZGHAL, Multiobjective optimization through a series of single-objective formulations, SIAM J. Optim., 19 (2008), pp. 188-210.
    • (2008) SIAM J. Optim. , vol.19 , pp. 188-210
    • Audet, C.1    Savard, G.2    Zghal, W.3
  • 5
    • 55749098965 scopus 로고    scopus 로고
    • A simulated annealing-based multiobjective optimization algorithm: AMOSA
    • S. BANDYOPADHYAY, S. SAHA, U. MAULIK, AND K. DEB, A simulated annealing-based multiobjective optimization algorithm: AMOSA, IEEE Trans. Evol. Comput., 12 (2008), pp. 269-283.
    • (2008) IEEE Trans. Evol. Comput. , vol.12 , pp. 269-283
    • Bandyopadhyay, S.1    Saha, S.2    Maulik, U.3    Deb, K.4
  • 6
    • 0033341687 scopus 로고    scopus 로고
    • Generalized center method for multiobjective engineering optimization
    • F. Y. CHENG AND X. S. LI, Generalized center method for multiobjective engineering optimization, Eng. Optim., 31 (1999), pp. 641-661. (Pubitemid 30506567)
    • (1999) Engineering Optimization , vol.31 , Issue.5 , pp. 641-661
    • Cheng, F.Y.1    Li, X.S.2
  • 7
    • 0003334371 scopus 로고
    • Optimization and nonsmooth analysis
    • John Wiley & Sons, New York, reprinted as, SIAM, Philadelphia
    • F. H. CLARKE, Optimization and Nonsmooth Analysis, John Wiley & Sons, New York, 1983; reprinted as Classics Appl. Math. 5, SIAM, Philadelphia, 1990.
    • (1983) Classics Appl. Math. , vol.5 , pp. 1990
    • Clarke, F.H.1
  • 8
    • 84901438927 scopus 로고    scopus 로고
    • MOPSO: A proposal for multiple objective particle swarm optimization
    • (Los Alamitos, CA), IEEE Computer Society, New York
    • C. A. COELLO COELLO AND M. S. LECHUGA, MOPSO: A proposal for multiple objective particle swarm optimization, in Proceedings of the Congress on Evolutionary Computation (CEC 2002), vol. 2 (Los Alamitos, CA), IEEE Computer Society, New York, 2002, pp. 1051-1056.
    • Proceedings of the Congress on Evolutionary Computation (CEC 2002) , vol.2 , Issue.2002 , pp. 1051-1056
    • Coello Coello, C.A.1    Lechuga, M.S.2
  • 9
    • 79251531959 scopus 로고    scopus 로고
    • Introduction to derivative-free optimization
    • SIAM, Philadelphia
    • A. R. CONN, K. SCHEINBERG, AND L. N. VICENTE, Introduction to Derivative-Free Optimization, MOS-SIAM Ser. Optim. 8, SIAM, Philadelphia, 2009.
    • (2009) MOS-SIAM Ser. Optim. , vol.8
    • Conn, A.R.1    Scheinberg, K.2    Vicente, L.N.3
  • 10
    • 55849136587 scopus 로고    scopus 로고
    • Using simplex gradients of nonsmooth functions in direct search methods
    • A. L. CUSTÓDIO, J. E. DENNIS, JR., AND L. N. VICENTE, Using simplex gradients of nonsmooth functions in direct search methods, IMA J. Numer. Anal., 28 (2008), pp. 770-784.
    • (2008) IMA J. Numer. Anal. , vol.28 , pp. 770-784
    • Custódio, A.L.1    Jdennis Jr., J.E.2    Vicente, L.N.3
  • 11
    • 77954761405 scopus 로고    scopus 로고
    • Incorporating minimum Frobenius norm models in direct search
    • A. L. CUSTÓDIO, H. ROCHA, AND L. N. VICENTE, Incorporating minimum Frobenius norm models in direct search, Comput. Optim. Appl., 46 (2010), pp. 265-278.
    • Comput. Optim. Appl. , vol.46 , Issue.2010 , pp. 265-278
    • Custódio, A.L.1    Rocha, H.2    Vicente, L.N.3
  • 12
    • 34548504938 scopus 로고    scopus 로고
    • Using sampling and simplex derivatives in pattern search methods
    • A. L. CUSTÓDIO AND L. N. VICENTE, Using sampling and simplex derivatives in pattern search methods, SIAM J. Optim., 18 (2007), pp. 537-555.
    • (2007) SIAM J. Optim. , vol.18 , pp. 537-555
    • Custódio, A.L.1    Vicente, L.N.2
  • 13
    • 0031212567 scopus 로고    scopus 로고
    • A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems
    • I. DAS AND J. E. DENNIS, A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems, Struct. Multidiscip. Optim., 14 (1997), pp. 63-69. (Pubitemid 127676980)
    • (1997) Structural Optimization , vol.14 , Issue.1 , pp. 63-69
    • Das, I.1    Dennis, J.E.2
  • 14
    • 0032348480 scopus 로고    scopus 로고
    • Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems
    • I. DAS AND J. E. DENNIS, Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems, SIAM J. Optim., 8 (1998), pp. 631-657.
    • (1998) SIAM J. Optim. , vol.8 , pp. 631-657
    • Das, I.1    Dennis, J.E.2
  • 15
    • 0033185714 scopus 로고    scopus 로고
    • Multi-objective genetic algorithms: Problem difficulties and construction of test problems
    • K. DEB, Multi-objective genetic algorithms: Problem difficulties and construction of test problems, Evol. Comput., 7 (1999), pp. 205-230.
    • (1999) Evol. Comput. , vol.7 , pp. 205-230
    • Deb, K.1
  • 16
    • 33947670047 scopus 로고    scopus 로고
    • Towards a quick computation of well-spread Pareto-optimal solutions in Evolutionary Multi-Criterion Optimization (EMO 2003)
    • C. Fonseca et al., eds., Springer-Verlag, Berlin
    • K. DEB, M. MOHAN, AND S.MISHRA, Towards a quick computation of well-spread Pareto-optimal solutions, in Evolutionary Multi-Criterion Optimization (EMO 2003), Lecture Notes in Comput. Sci. 2632, C. Fonseca et al., eds., Springer-Verlag, Berlin, 2003, pp. 222-236.
    • Lecture Notes in Comput. Sci. , vol.2632 , Issue.2003 , pp. 222-236
    • Deb, K.1    Mohan, M.2    Mishra, S.3
  • 17
  • 20
    • 28244496090 scopus 로고    scopus 로고
    • Benchmarking optimization software with performance profiles
    • DOI 10.1007/s101070100263
    • E. D. DOLAN AND J. J. MORÉ, Benchmarking optimization software with performance profiles, Math. Program., 91 (2002), pp. 201-213. (Pubitemid 44744777)
    • (2002) Mathematical Programming, Series B , vol.91 , Issue.2 , pp. 201-213
    • Dolan, E.D.1    More, J.J.2
  • 21
    • 0031701082 scopus 로고    scopus 로고
    • Multiobjective optimization and multiple constraint handling with evolutionary algorithms - Part I: A unified formulation
    • PII S1083442798001337
    • C. M. FONSECA AND P. J. FLEMING, Multiobjective optimization and multiple constraint handling with evolutionary algorithms-Part I: A unified formulation, IEEE Trans. Syst. Man Cybern. A Syst. Hum., 28 (1998), pp. 26-37. (Pubitemid 128748052)
    • (1998) IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans. , vol.28 , Issue.1 , pp. 26-37
    • Fonseca, C.M.1    Fleming, P.J.2
  • 22
    • 0001415052 scopus 로고
    • A modeling language for mathematical programming
    • R. FOURER, D. M. GAY, AND B. W. KERNIGHAN, A modeling language for mathematical programming, Manage. Sci., 36 (1990), pp. 519-554.
    • (1990) Manage. Sci. , vol.36 , pp. 519-554
    • Fourer, R.1    Gay, D.M.2    Kernighan, B.W.3
  • 23
    • 33846886525 scopus 로고    scopus 로고
    • Derivative-free generation and interpolation of convex Pareto optimal IMRT plans
    • DOI 10.1088/0031-9155/51/24/005, PII S0031915506289152, 005
    • A. L. HOFFMANN, A. Y.D. SIEM, D. DEN HERTOG, J. H. A. M.KAANDERS, AND H. HUIZENGA, Derivative-free generation and interpolation of convex Pareto optimal IMRT plans, Phys. Med. Biol., 51 (2006), pp. 6349-6369. (Pubitemid 46217626)
    • (2006) Physics in Medicine and Biology , vol.51 , Issue.24 , pp. 6349-6369
    • Hoffmann, A.L.1    Siem, A.Y.D.2    Den Hertog, D.3    Kaanders, J.H.A.M.4    Huizenga, H.5
  • 24
    • 24344435210 scopus 로고    scopus 로고
    • A scalable multi-objective test problem toolkit in Evolutionary Multi-Criterion Optimization (EMO 2005)
    • C. A. Coello Coello et al., eds., Springer-Verlag, Berlin
    • S. HUBAND, L. BARONE, L. WHILE, AND P. HINGSTON, A scalable multi-objective test problem toolkit, in Evolutionary Multi-Criterion Optimization (EMO 2005), Lecture Notes in Comput. Sci. 3410, C. A. Coello Coello et al., eds., Springer-Verlag, Berlin, 2005, pp. 280-295.
    • Lecture Notes in Comput. Sci. , vol.3410 , Issue.2005 , pp. 280-295
    • Huband, S.1    Barone, L.2    While, L.3    Hingston, P.4
  • 25
    • 33749860403 scopus 로고    scopus 로고
    • A review of multiobjective test problems and a scalable test problem toolkit
    • DOI 10.1109/TEVC.2005.861417
    • S. HUBAND, P. HINGSTON, L. BARONE, AND L.WHILE, A review of multiobjective test problems and a scalable test problem toolkit, IEEE Trans. Evol. Comput., 10 (2006), pp. 477-506. (Pubitemid 44560739)
    • (2006) IEEE Transactions on Evolutionary Computation , vol.10 , Issue.5 , pp. 477-506
    • Huband, S.1    Hingston, P.2    Barone, L.3    While, L.4
  • 26
    • 0003770178 scopus 로고
    • Multiple objective decision making-methods and applications: A state-of-the-art survey
    • Springer-Verlag, Berlin
    • C.-L. HWANG AND A. S. MD. MASUD, Multiple Objective Decision Making-Methods and Applications: A State-of-the-Art Survey, Lecture Notes in Econom. Math. Systems 164, Springer-Verlag, Berlin, 1979.
    • (1979) Lecture Notes in Econom. Math. Systems 164
    • Hwang, C.-L.1    Md. Masud, A.S.2
  • 28
    • 0142172455 scopus 로고    scopus 로고
    • Dynamic weighted aggregation for evolutionary multi-objective optimization: Why does it work and how?
    • GECCO'01 L. Spector et al., eds., Morgan Kaufmann, San Francisco
    • Y. JIN, M. OLHOFER, AND B. SENDHOFF, Dynamic weighted aggregation for evolutionary multi-objective optimization: Why does it work and how?, in Proceedings of Genetic and Evolutionary Computation Conference, GECCO'01, L. Spector et al., eds., Morgan Kaufmann, San Francisco, 2001, pp. 1042- 1049.
    • (2001) Proceedings of Genetic and Evolutionary Computation Conference , pp. 1042-1049
    • Jin, Y.1    Olhofer, M.2    Sendhoff, B.3
  • 30
    • 0034199912 scopus 로고    scopus 로고
    • Approximating the nondominated front using the Pareto archived evolution strategy
    • J. D. KNOWLES AND D. W. CORNE, Approximating the nondominated front using the Pareto archived evolution strategy, Evol. Comput., 8 (2000), pp. 149-172.
    • (2000) Evol. Comput. , vol.8 , pp. 149-172
    • Knowles, J.D.1    Corne, D.W.2
  • 31
    • 0242667172 scopus 로고    scopus 로고
    • Optimization by direct search: New perspectives on some classical and modern methods
    • T. G. KOLDA, R. M. LEWIS, AND V. TORCZON, Optimization by direct search: New perspectives on some classical and modern methods, SIAM Rev., 45 (2003), pp. 385-482.
    • (2003) SIAM Rev. , vol.45 , pp. 385-482
    • Kolda, T.G.1    Lewis, R.M.2    Torczon, V.3
  • 32
    • 84904913154 scopus 로고
    • A variant of evolution strategies for vector optimization, in Parallel Problem Solving from Nature-PPSN I
    • H. P. Schwefel and R. Männer, eds., Springer-Verlag, Berlin
    • F. KURSAWE, A variant of evolution strategies for vector optimization, in Parallel Problem Solving from Nature-PPSN I, Lecture Notes in Comput. Sci. 496, H. P. Schwefel and R. Männer, eds., Springer- Verlag, Berlin, 1991, pp. 193-197.
    • (1991) Lecture Notes in Comput. Sci. , vol.496 , pp. 193-197
    • Kursawe, F.1
  • 33
    • 0038182259 scopus 로고    scopus 로고
    • Multiobjective optimization techniques for the design of induction motors
    • G. LIUZZI, S.LUCIDI, F.PARASILITI, AND M. VILLANI, Multiobjective optimization techniques for the design of induction motors, IEEE Trans. Magn., 39 (2003), pp. 1261-1264.
    • (2003) IEEE Trans. Magn. , vol.39 , pp. 1261-1264
    • Liuzzi, G.1    Lucidi, S.2    Parasiliti, F.3    Villani, M.4
  • 34
    • 80054722378 scopus 로고    scopus 로고
    • A synthetic approach to multiobjective optimization
    • to appear
    • A. LOVISON, A synthetic approach to multiobjective optimization, SIAM J. Optim., to appear.
    • SIAM J. Optim.
    • Lovison, A.1
  • 35
    • 2442535151 scopus 로고    scopus 로고
    • Survey of multi-objective optimization methods for engineering
    • R. T. MARLER AND J. S. ARORA, Survey of multi-objective optimization methods for engineering, Struct. Multidiscip. Optim., 26 (2004), pp. 369-395.
    • (2004) Struct. Multidiscip. Optim. , vol.26 , pp. 369-395
    • Marler, R.T.1    Arora, J.S.2
  • 36
    • 0033895382 scopus 로고    scopus 로고
    • Comparison of three methods for selecting values of input variables in the analysis of output from a computer code
    • M. D. MCKAY, R. J. BECKMAN, AND W. J. CONOVER, A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, 42 (2000), pp. 55-61. (Pubitemid 30553341)
    • (2000) Technometrics , vol.42 , Issue.1 , pp. 55-61
    • Mckay, M.D.1    Beckman, R.J.2    Conover, W.J.3
  • 38
    • 68949099095 scopus 로고    scopus 로고
    • Benchmarking derivative-free optimization algorithms
    • also available at
    • J. J. MORÉ AND S. M. WILD, Benchmarking derivative-free optimization algorithms, SIAM J. Optim., 20 (2009), pp. 172-191; also available at http://www.mcs.anl.gov/~more/dfo.
    • (2009) SIAM J. Optim. , vol.20 , pp. 172-191
    • Moré, J.J.1    Wild, S.M.2
  • 42
    • 0000599395 scopus 로고
    • Multiple objective optimization with vector evaluated genetic algorithms
    • Lawrence Erlbaum Associates, Hillsdale, NJ
    • J. D. SCHAFFER, Multiple objective optimization with vector evaluated genetic algorithms, in Proceedings of the 1st International Conference on Genetic Algorithms, Lawrence Erlbaum Associates, Hillsdale, NJ, 1985, pp. 93-100.
    • (1985) Proceedings of the 1st International Conference on Genetic Algorithms , pp. 93-100
    • Schaffer, J.D.1
  • 43
    • 0343440745 scopus 로고
    • Multiple criteria optimization: Theory
    • John Wiley & Sons, New York
    • R. STEUER, Multiple Criteria Optimization: Theory, Computation and Application, John Wiley & Sons, New York, 1986.
    • (1986) Computation and Application
    • Steuer, R.1
  • 45
    • 0031540855 scopus 로고    scopus 로고
    • On the convergence of pattern search algorithms
    • V. TORCZON, On the convergence of pattern search algorithms, SIAM J. Optim., 7 (1997), pp. 1-25.
    • (1997) SIAM J. Optim. , vol.7 , pp. 1-25
    • Torczon, V.1
  • 46
    • 34548479280 scopus 로고    scopus 로고
    • A particle swarm pattern search method for bound constrained global optimization
    • DOI 10.1007/s10898-007-9133-5
    • A. I. F. VAZ AND L. N. VICENTE, A particle swarm pattern search method for bound constrained global optimization, J. Global Optim., 39 (2007), pp. 197-219. (Pubitemid 47373392)
    • (2007) Journal of Global Optimization , vol.39 , Issue.2 , pp. 197-219
    • Vaz, A.I.F.1    Vicente, L.N.2
  • 47
    • 68949135173 scopus 로고    scopus 로고
    • PSwarm: A hybrid solver for linearly constrained global derivative-free optimization
    • A. I. F. VAZ AND L. N. VICENTE, PSwarm: A hybrid solver for linearly constrained global derivative-free optimization, Optim. Methods Softw., 24 (2009), pp. 669-685.
    • (2009) Optim. Methods Softw. , vol.24 , pp. 669-685
    • Vaz, A.I.F.1    Vicente, L.N.2
  • 48
    • 80054772896 scopus 로고    scopus 로고
    • Analysis of direct searches for discontinuous functions
    • to appear
    • L. N. VICENTE AND A. L. CUSTÓDIO, Analysis of direct searches for discontinuous functions, Math. Program., to appear.
    • Math. Program.
    • Vicente, L.N.1    Custódio, A.L.2
  • 49
    • 0034199979 scopus 로고    scopus 로고
    • Comparison of multiobjective evolutionary algorithms: Empirical results
    • E. ZITZLER, K. DEB, AND L. THIELE, Comparison of multiobjective evolutionary algorithms: Empirical results, Evol. Comput., 8 (2000), pp. 173-195.
    • (2000) Evol. Comput. , vol.8 , pp. 173-195
    • Zitzler, E.1    Deb, K.2    Thiele, L.3


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