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Volumn 17, Issue 2, 2009, Pages 135-166

Objective reduction in evolutionary multiobjective optimization: Theory and applications

Author keywords

Dimensionality reduction; Many objective problems; Minimum objective sets; Multiobjective optimization; Objective conflicts

Indexed keywords

ALGORITHM; ARTICLE; BIOLOGICAL MODEL; COMPUTER SIMULATION; DECISION MAKING; EVOLUTION; STATISTICAL MODEL; TELECOMMUNICATION;

EID: 66549111544     PISSN: 10636560     EISSN: 15309304     Source Type: Journal    
DOI: 10.1162/evco.2009.17.2.135     Document Type: Article
Times cited : (186)

References (47)
  • 1
    • 0031142874 scopus 로고    scopus 로고
    • On redundancy in multi criteria decision making
    • Agrell, P. J. (1997). On redundancy in multi criteria decision making. European Journal of Operational Research, 98(3):571-586.
    • (1997) European Journal of Operational Research , vol.98 , Issue.3 , pp. 571-586
    • Agrell, P.J.1
  • 3
    • 35248851504 scopus 로고    scopus 로고
    • PISA-A platform and programming language independent interface for search algorithms
    • In C. M. Fonseca, P. J. Fleming, E. Zitzler, K. Deb, and L. Thiele (Eds.), Conference on Evolutionary Multi-Criterion Optimization (EMO 2003), LNCS, Berlin: Springer
    • Bleuler, S., Laumanns, M., Thiele, L., and Zitzler, E. (2003). PISA-A platform and programming language independent interface for search algorithms. In C. M. Fonseca, P. J. Fleming, E. Zitzler, K. Deb, and L. Thiele (Eds.), Conference on Evolutionary Multi-Criterion Optimization (EMO 2003), volume 2632 of LNCS, pages 494-508. Berlin: Springer.
    • (2003) , vol.2632 , pp. 494-508
    • Bleuler, S.1    Laumanns, M.2    Thiele, L.3    Zitzler, E.4
  • 4
    • 33750250967 scopus 로고    scopus 로고
    • Are all objectives necessary? On dimensionality reduction in evolutionary multiobjective optimization
    • In T. Runarsson, H.-G. Beyer, E. Burke, J.-J. Merelo-Guervós, L. D. Whitley, and X. Yao (Eds.), Conference on Parallel Problem Solving from Nature (PPSN IX), LNCS, Berlin: Springer
    • Brockhoff, D., and Zitzler, E. (2006a). Are all objectives necessary? On dimensionality reduction in evolutionary multiobjective optimization. In T. Runarsson, H.-G. Beyer, E. Burke, J.-J. Merelo-Guervós, L. D. Whitley, and X. Yao (Eds.), Conference on Parallel Problem Solving from Nature (PPSN IX), volume 4193 of LNCS, pages 533-542. Berlin: Springer.
    • (2006) , vol.4193 , pp. 533-542
    • Brockhoff, D.1    Zitzler, E.2
  • 6
    • 79955224474 scopus 로고    scopus 로고
    • Improving hypervolume-based multiobjective evolutionary algorithms by using objective reduction methods
    • In Congress on Evolutionary Computation (CEC 2007), Piscataway, NJ: IEEE Press
    • Brockhoff, D., and Zitzler, E. (2007a). Improving hypervolume-based multiobjective evolutionary algorithms by using objective reduction methods. In Congress on Evolutionary Computation (CEC 2007), pp. 2086-2093. Piscataway, NJ: IEEE Press.
    • (2007) , pp. 2086-2093
    • Brockhoff, D.1    Zitzler, E.2
  • 12
    • 34548088235 scopus 로고    scopus 로고
    • Searching for pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems
    • In Congress on Evolutionary Computation (CEC 2006), Piscataway, NJ: IEEE Press
    • Deb, K., and Saxena, D. (2006). Searching for pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems. In Congress on Evolutionary Computation (CEC 2006), pp. 3352-3360. Piscataway, NJ: IEEE Press.
    • (2006) , pp. 3352-3360
    • Deb, K.1    Saxena, D.2
  • 13
    • 33745917564 scopus 로고    scopus 로고
    • Scalable test problems for evolutionary multi-objective optimization
    • In A. Abraham, R. Jain, and R. Goldberg (Eds.), chapter 6, Berlin: Springer
    • Deb, K., Thiele, L., Laumanns, M., and Zitzler, E. (2005). Scalable test problems for evolutionary multi-objective optimization. In A. Abraham, R. Jain, and R. Goldberg (Eds.), Evolutionary Multiobjective Optimization: Theoretical Advances and Applications, chapter 6, pp. 105-145. Berlin: Springer.
    • (2005) Evolutionary Multiobjective Optimization: Theoretical Advances and Applications , pp. 105-145
    • Deb, K.1    Thiele, L.2    Laumanns, M.3    Zitzler, E.4
  • 14
    • 33750239892 scopus 로고    scopus 로고
    • DECA: Dimension extracting coevolutionary algorithm
    • In Genetic and Evolutionary Computation Conference (GECCO 2006), New York: ACM
    • de Jong, E. D., and Bucci, A. (2006). DECA: Dimension extracting coevolutionary algorithm. In Genetic and Evolutionary Computation Conference (GECCO 2006), pp. 313-320. New York: ACM.
    • (2006) , pp. 313-320
    • de Jong, E.D.1    Bucci, A.2
  • 15
    • 24344489452 scopus 로고    scopus 로고
    • An EMO algorithm using the hypervolume measure as selection criterion
    • In Conference on Evolutionary Multi-Criterion Optimization (EMO 2005), LNCS, Berlin: Springer
    • Emmerich, M., Beume, N., and Naujoks, B. (2005). An EMO algorithm using the hypervolume measure as selection criterion. In Conference on Evolutionary Multi-Criterion Optimization (EMO 2005), volume 3410 of LNCS, pp. 62-76. Berlin: Springer.
    • (2005) , vol.3410 , pp. 62-76
    • Emmerich, M.1    Beume, N.2    Naujoks, B.3
  • 16
    • 0032108328 scopus 로고    scopus 로고
    • A threshold of ln n for approximating set cover
    • Feige, U. (1998). A threshold of ln n for approximating set cover. J. ACM, 45(4):634-652.
    • (1998) J. ACM , vol.45 , Issue.4 , pp. 634-652
    • Feige, U.1
  • 17
    • 24344444451 scopus 로고    scopus 로고
    • Many-objective optimization: An engineering design perspective
    • In C. A. Coello Coello, A. Hernández Aguirre, and E. Zitzler (Eds.), Conference on Evolutionary Multi-Criterion Optimization (EMO 2005), LNCS, Berlin: Springer
    • Fleming, P. J., Purshouse, R. C., and Lygoe, R. J. (2005). Many-objective optimization: An engineering design perspective. In C. A. Coello Coello, A. Hernández Aguirre, and E. Zitzler (Eds.), Conference on Evolutionary Multi-Criterion Optimization (EMO 2005), volume 3410 of LNCS, pp. 14-32. Berlin: Springer.
    • (2005) , vol.3410 , pp. 14-32
    • Fleming, P.J.1    Purshouse, R.C.2    Lygoe, R.J.3
  • 18
    • 0002629429 scopus 로고
    • An overview of evolutionary algorithms in multiobjective optimization
    • Fonseca, C. M., and Fleming, P. J. (1995). An overview of evolutionary algorithms in multiobjective optimization. Evolutionary Computation, 3(1):1-16.
    • (1995) Evolutionary Computation , vol.3 , Issue.1 , pp. 1-16
    • Fonseca, C.M.1    Fleming, P.J.2
  • 19
    • 34547310269 scopus 로고    scopus 로고
    • An improved dimension-sweep algorithm for the hypervolume indicator
    • In Congress on Evolutionary Computation (CEC 2006), Piscataway, NJ: IEEE Press
    • Fonseca, C. M., Paquete, L., and López-Ibáñez, M. (2006). An improved dimension-sweep algorithm for the hypervolume indicator. In Congress on Evolutionary Computation (CEC 2006), pp. 1157-1163. Piscataway, NJ: IEEE Press.
    • (2006) , pp. 1157-1163
    • Fonseca, C.M.1    Paquete, L.2    López-Ibáñez, M.3
  • 20
    • 0017492688 scopus 로고
    • Redundant objective functions in linear vector maximum problems and their determination
    • Gal, T., and Leberling, H. (1977). Redundant objective functions in linear vector maximum problems and their determination. European Journal of Operational Research, 1(3):176-184.
    • (1977) European Journal of Operational Research , vol.1 , Issue.3 , pp. 176-184
    • Gal, T.1    Leberling, H.2
  • 22
    • 0000454216 scopus 로고    scopus 로고
    • Multicriterion decision making
    • In T. Bäck, D. B. Fogel, and Z. Michalewicz (Eds.), Bristol, UK: IOP Publishing
    • Horn, J. (1997). Multicriterion decision making. In T. Bäck, D. B. Fogel, and Z. Michalewicz (Eds.), Handbook of Evolutionary Computation. Bristol, UK: IOP Publishing.
    • (1997) Handbook of Evolutionary Computation
    • Horn, J.1
  • 23
    • 37249052832 scopus 로고    scopus 로고
    • Radar waveform optimization as a many-objective application benchmark
    • In Conference on Evolutionary Multi-Criterion Optimization (EMO 2007), LNCS, Berlin: Springer
    • Hughes, E. J. (2007). Radar waveform optimization as a many-objective application benchmark. In Conference on Evolutionary Multi-Criterion Optimization (EMO 2007), volume 4403 of LNCS, pp. 700-714. Berlin: Springer.
    • (2007) , vol.4403 , pp. 700-714
    • Hughes, E.J.1
  • 24
    • 20944439075 scopus 로고    scopus 로고
    • Helper-objectives: Using multi-objective evolutionary algorithms for single objective optimisation
    • Jensen, M. T. (2004). Helper-objectives: Using multi-objective evolutionary algorithms for singleobjective optimisation. Journal of Mathematical Modelling and Algorithms, 3(4):323-347.
    • (2004) Journal of Mathematical Modelling and Algorithms , vol.3 , Issue.4 , pp. 323-347
    • Jensen, M.T.1
  • 25
    • 35248887077 scopus 로고    scopus 로고
    • Performance scaling of multi-objective evolutionary algorithms
    • In Conference on Evolutionary Multi-Criterion Optimization (EMO 2003), LNCS, Berlin: Springer
    • Khare, V. R., Yao, X., and Deb, K. (2003). Performance scaling of multi-objective evolutionary algorithms. In Conference on Evolutionary Multi-Criterion Optimization (EMO 2003), volume 2632 of LNCS, pp. 376-390. Berlin: Springer.
    • (2003) , vol.2632 , pp. 376-390
    • Khare, V.R.1    Yao, X.2    Deb, K.3
  • 27
    • 84931320658 scopus 로고    scopus 로고
    • Reducing local optima in single-objective problems by multi-objectivization
    • In E. Zitzler, K. Deb, L. Thiele, C. A. Coello Coello, and D. Corne (Eds.), Conference on Evolutionary Multi-Criterion Optimization (EMO 2001), LNCS, Berlin: Springer
    • Knowles, J. D., Watson, R. A., and Corne, D. W. (2001). Reducing local optima in single-objective problems by multi-objectivization. In E. Zitzler, K. Deb, L. Thiele, C. A. Coello Coello, and D. Corne (Eds.), Conference on Evolutionary Multi-Criterion Optimization (EMO 2001), volume 1993 of LNCS, pp. 269-283. Berlin: Springer.
    • (2001) , vol.1993 , pp. 269-283
    • Knowles, J.D.1    Watson, R.A.2    Corne, D.W.3
  • 28
    • 4344673791 scopus 로고    scopus 로고
    • Running time analysis of evolutionary algorithms on a simplified multiobjective knapsack problem
    • Laumanns, M., Thiele, L., and Zitzler, E. (2004). Running time analysis of evolutionary algorithms on a simplified multiobjective knapsack problem. Natural Computing, 3(1):37-51.
    • (2004) Natural Computing , vol.3 , Issue.1 , pp. 37-51
    • Laumanns, M.1    Thiele, L.2    Zitzler, E.3
  • 29
    • 33748121602 scopus 로고    scopus 로고
    • Minimum spanning trees made easier via multi-objective optimization
    • Neumann, F., and Wegener, I. (2006). Minimum spanning trees made easier via multi-objective optimization. Natural Computing, 5(3):305-319.
    • (2006) Natural Computing , vol.5 , Issue.3 , pp. 305-319
    • Neumann, F.1    Wegener, I.2
  • 30
    • 66549103002 scopus 로고    scopus 로고
    • Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., and Murata, T. (Eds.). (2007). Conference on Evolutionary Multi-Criterion Optimization (EMO 2007), volume 4403 of LNCS. Berlin: Springer
    • Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., and Murata, T. (Eds.). (2007). Conference on Evolutionary Multi-Criterion Optimization (EMO 2007), volume 4403 of LNCS. Berlin: Springer.
  • 31
    • 84878586194 scopus 로고    scopus 로고
    • Timetabling the classes of an entire university with an evolutionary algorithm
    • In Conference on Parallel Problem Solving From Nature (PPSN V), Berlin: Springer
    • Paechter, B., Rankin, R. C., Cumming, A., and Fogarty, T. C. (1998). Timetabling the classes of an entire university with an evolutionary algorithm. In Conference on Parallel Problem Solving From Nature (PPSN V), pp. 865-874. Berlin: Springer.
    • (1998) , pp. 865-874
    • Paechter, B.1    Rankin, R.C.2    Cumming, A.3    Fogarty, T.C.4
  • 32
    • 35248871555 scopus 로고    scopus 로고
    • Conflict, harmony, and independence: Relationships in evolutionary multi-criterion optimisation
    • In Conference on Evolutionary Multi-Criterion Optimization (EMO 2003), volume 2632 of LNCS, Berlin: Springer
    • Purshouse, R. C., and Fleming, P. J. (2003a). Conflict, harmony, and independence: Relationships in evolutionary multi-criterion optimisation. In Conference on Evolutionary Multi-Criterion Optimization (EMO 2003), volume 2632 of LNCS, pp. 16-30. Berlin: Springer.
    • (2003) , vol.2632 , pp. 16-30
    • Purshouse, R.C.1    Fleming, P.J.2
  • 33
    • 84901459041 scopus 로고    scopus 로고
    • Evolutionary many-objective optimisation: An exploratory analysis
    • In Congress on Evolutionary Computation (CEC 2003), Piscataway, NJ: IEEE Press
    • Purshouse, R. C., and Fleming, P. J. (2003b). Evolutionary many-objective optimisation: An exploratory analysis. In Congress on Evolutionary Computation (CEC 2003), pp. 2066-2073. Piscataway, NJ: IEEE Press.
    • (2003) , pp. 2066-2073
    • Purshouse, R.C.1    Fleming, P.J.2
  • 34
    • 0031102641 scopus 로고    scopus 로고
    • Prioritizing and scheduling road projects by genetic algorithm
    • Qiu, M. (1997). Prioritizing and scheduling road projects by genetic algorithm. Mathematics and Computers in Simulation, 43:569-574.
    • (1997) Mathematics and Computers in Simulation , vol.43 , pp. 569-574
    • Qiu, M.1
  • 35
    • 37249034215 scopus 로고    scopus 로고
    • Non-linear dimensionality reduction procedures for certain large-dimensional multi-objective optimization problems: Employing correntropy and a novel maximum variance unfolding
    • In Conference on Evolutionary Multi-Criterion Optimization (EMO 2007), LNCS, Berlin: Springer
    • Saxena, D. K., and Deb, K. (2007). Non-linear dimensionality reduction procedures for certain large-dimensional multi-objective optimization problems: Employing correntropy and a novel maximum variance unfolding. In Conference on Evolutionary Multi-Criterion Optimization (EMO 2007), volume 4403 of LNCS, pp. 772-787. Berlin: Springer.
    • (2007) , vol.4403 , pp. 772-787
    • Saxena, D.K.1    Deb, K.2
  • 37
    • 0029723340 scopus 로고    scopus 로고
    • A tight analysis of the greedy algorithm for set cover
    • In Symposium on Theory of Computing (STOC 1996), New York: ACM
    • Slavík, P. (1996). A tight analysis of the greedy algorithm for set cover. In Symposium on Theory of Computing (STOC 1996), pp. 435-441. New York: ACM.
    • (1996) , pp. 435-441
    • Slavík, P.1
  • 38
    • 37249022930 scopus 로고    scopus 로고
    • Robust multi-objective optimization in high dimensional spaces
    • In Conference on Evolutionary Multi-Criterion Optimization (EMO 2007), LNCS, Berlin: Springer
    • Sülflow, A., Drechsler, N., and Drechsler, R. (2007). Robust multi-objective optimization in high dimensional spaces. In Conference on Evolutionary Multi-Criterion Optimization (EMO 2007), volume 4403 of LNCS, pp. 715-726. Berlin: Springer.
    • (2007) , vol.4403 , pp. 715-726
    • Sülflow, A.1    Drechsler, N.2    Drechsler, R.3
  • 40
    • 37248999403 scopus 로고    scopus 로고
    • Pareto-, aggregation-, and indicator-based methods in many-objective optimization
    • In S. Obayashi, K.Deb, C. Poloni, T. Hiroyasu, and T. Murata (Eds.), Conference on Evolutionary Multi-Criterion Optimization (EMO 2007), LNCS, Berlin: Springer
    • Wagner, T., Beume, N., and Naujoks, B. (2007). Pareto-, aggregation-, and indicator-based methods in many-objective optimization. In S. Obayashi, K.Deb, C. Poloni, T. Hiroyasu, and T. Murata (Eds.), Conference on Evolutionary Multi-Criterion Optimization (EMO 2007), volume 4403 of LNCS, pp. 742-756. Berlin: Springer.
    • (2007) , vol.4403 , pp. 742-756
    • Wagner, T.1    Beume, N.2    Naujoks, B.3
  • 41
    • 24344451332 scopus 로고    scopus 로고
    • A new analysis of the LebMeasure algorithm for calculating hypervolume
    • In Conference on Evolutionary Multi-Criterion Optimization (EMO 2005), volume 3410 of LNCS, Berlin: Springer
    • While, L. (2005). A new analysis of the LebMeasure algorithm for calculating hypervolume. In Conference on Evolutionary Multi-Criterion Optimization (EMO 2005), volume 3410 of LNCS, pp. 326-340. Berlin: Springer.
    • (2005) , vol.3410 , pp. 326-340
    • While, L.1
  • 42
    • 27144534854 scopus 로고    scopus 로고
    • Heuristics for optimising the calculation of hypervolume for multi-objective optimisation problems
    • In Congress on Evolutionary Computation (CEC 2005), Piscataway, NJ: IEEE Press
    • While, L., Bradstreet, L., Barone, L., and Hingston, P. (2005). Heuristics for optimising the calculation of hypervolume for multi-objective optimisation problems. In Congress on Evolutionary Computation (CEC 2005), pp. 2225-2232. Piscataway, NJ: IEEE Press.
    • (2005) , pp. 2225-2232
    • While, L.1    Bradstreet, L.2    Barone, L.3    Hingston, P.4
  • 44
    • 0002024151 scopus 로고
    • Random Orders
    • Winkler, P. (1985). Random orders. Order, 1:317-331.
    • (1985) Order , vol.1 , pp. 317-331
    • Winkler, P.1
  • 45
    • 37249040048 scopus 로고    scopus 로고
    • The hypervolume indicator revisited: On the design of pareto-compliant indicators via weighted integration
    • In S. Obayashi, K. Deb, C. Poloni, T. Hiroyasu, and T. Murata (Eds.), Conference on Evolutionary Multi-Criterion Optimization (EMO 2007), LNCS, Berlin: Springer
    • Zitzler, E., Brockhoff, D., and Thiele, L. (2007). The hypervolume indicator revisited: On the design of pareto-compliant indicators via weighted integration. In S. Obayashi, K. Deb, C. Poloni, T. Hiroyasu, and T. Murata (Eds.), Conference on Evolutionary Multi-Criterion Optimization (EMO 2007), volume 4403 of LNCS, pages 862-876. Berlin: Springer.
    • (2007) , vol.4403 , pp. 862-876
    • Zitzler, E.1    Brockhoff, D.2    Thiele, L.3
  • 46
    • 35048846146 scopus 로고    scopus 로고
    • Indicator-based selection in multiobjective search
    • In Conference on Parallel Problem Solving from Nature (PPSNVIII), LNCS, Berlin: Springer
    • Zitzler, E., and Künzli, S. (2004). Indicator-based selection in multiobjective search. In Conference on Parallel Problem Solving from Nature (PPSNVIII), volume 3242 of LNCS, pp. 832-842. Berlin: Springer.
    • (2004) , vol.3242 , pp. 832-842
    • Zitzler, E.1    Künzli, S.2


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