메뉴 건너뛰기




Volumn 219, Issue 18, 2013, Pages 9652-9669

An improved version of the augmented s-constraint method (AUGMECON2) for finding the exact pareto set in multi-objective integer programming problems

Author keywords

Exact pareto set; Multi objective programming; Constraint method

Indexed keywords

COMBINATORIAL OPTIMIZATION; DECISION MAKING; HEURISTIC METHODS; MATHEMATICAL PROGRAMMING; MULTIOBJECTIVE OPTIMIZATION; OPTIMIZATION; PARETO PRINCIPLE;

EID: 84893644172     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2013.03.002     Document Type: Article
Times cited : (465)

References (57)
  • 1
  • 3
    • 67349211166 scopus 로고    scopus 로고
    • Effective implementation of the ε-constraint method in multi-objective mathematical programming problems
    • G. Mavrotas, Effective implementation of the ε-constraint method in multi-objective mathematical programming problems, Appl. Math. Comput. 213 (2009) 455-465.
    • (2009) Appl. Math. Comput. , vol.213 , pp. 455-465
    • Mavrotas, G.1
  • 4
    • 33750695134 scopus 로고    scopus 로고
    • Constructing robust crew schedules with bicriteria optimization
    • DOI 10.1002/mcda.321
    • M. Ehrgott, D.M. Ryan, Constructing robust crew schedules with bicriteria optimization, J. Multi-Criteria Decis. Anal. 11 (2002) 139-150. (Pubitemid 36854021)
    • (2002) Journal of Multicriteria Decision Analysis , vol.11 , Issue.3 , pp. 139-150
    • Ehrgott, M.1    Ryan, D.M.2
  • 5
    • 27144455754 scopus 로고    scopus 로고
    • An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method
    • DOI 10.1016/j.ejor.2004.08.029, PII S0377221704005715
    • M. Laumanns, L Thiele, E. Zitzler, An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method, Eur. J. Oper. Res. 169 (2006) 932-942. (Pubitemid 41492025)
    • (2006) European Journal of Operational Research , vol.169 , Issue.3 , pp. 932-942
    • Laumanns, M.1    Thiele, L.2    Zitzler, E.3
  • 6
    • 34247172120 scopus 로고    scopus 로고
    • Finding representative systems for discrete bicriterion optimization problems
    • DOI 10.1016/j.orl.2006.03.019, PII S0167637706000745
    • H.W. Hamacher, CR Pedersen, S. Ruzika, Finding representative systems for discrete bicriterion optimization problems, Oper. Res. Lett. 35 (2007) 336-344. (Pubitemid 46589655)
    • (2007) Operations Research Letters , vol.35 , Issue.3 , pp. 336-344
    • Hamacher, H.W.1    Pedersen, C.R.2    Ruzika, S.3
  • 9
    • 70350574016 scopus 로고    scopus 로고
    • Solving multi-objective, multi-constraint knapsack problems using mathematical programming and evolutionary algorithms
    • K. Florios, G. Mavrotas, D. Diakoulaki, Solving multi-objective, multi-constraint knapsack problems using mathematical programming and evolutionary algorithms, Eur. J. Oper. Res. 203 (2010) 14-21.
    • (2010) Eur. J. Oper. Res. , vol.203 , pp. 14-21
    • Florios, K.1    Mavrotas, G.2    Diakoulaki, D.3
  • 10
    • 34547282708 scopus 로고    scopus 로고
    • A survey of recent developments in multiobjective optimization
    • A. Chinchuluun, P.M. Pardalos, A survey of recent developments in multiobjective optimization, Ann. Oper. Res. 154 (2007) 29-50.
    • (2007) Ann. Oper. Res. , vol.154 , pp. 29-50
    • Chinchuluun, A.1    Pardalos, P.M.2
  • 11
    • 0041394612 scopus 로고
    • Linear multiple objective programs with zero-one variables
    • G.R. Bitran, Linear multiple objective programs with zero-one variables, Math. Program. 13 (1977) 121-139.
    • (1977) Math. Program. , vol.13 , pp. 121-139
    • Bitran, G.R.1
  • 12
    • 34250269537 scopus 로고
    • Theory and algorithms for linear multiple objective programs with zero-one variables
    • G.R. Bitran, Theory and algorithms for linear multiple objective programs with zero-one variables, Math. Program. 17 (1979) 362-390.
    • (1979) Math. Program. , vol.17 , pp. 362-390
    • Bitran, G.R.1
  • 13
    • 0020114131 scopus 로고
    • Algorithm for the multiple objective integer linear programming problem
    • DOI 10.1016/0377-2217(82)90182-5
    • D. Klein, E. Hannan, An algorithm for the multiple objective integer linear programming problem, Eur. J. Oper. Res. 9 (1982) 378-385. (Pubitemid 12512194)
    • (1982) European Journal of Operational Research , vol.9 , Issue.4 , pp. 378-385
    • Klein, D.1    Hannan, E.2
  • 15
    • 25844501652 scopus 로고    scopus 로고
    • A method for generating all efficient solutions of 0-1 multi-objective linear programming problem
    • DOI 10.1016/j.amc.2004.09.091, PII S0096300304008185
    • G.R. Jahanshahloo, F. Hosseinzadeh, N. Shoja, G. Tohidi, A method for generating all efficient solutions of 0-1 multi-objective linear programming problem, Appl. Math. Comput. 169 (2005) 874-886. (Pubitemid 41394326)
    • (2005) Applied Mathematics and Computation , vol.169 , Issue.2 , pp. 874-886
    • Jahanshahloo, G.R.1    Hosseinzadeh, F.2    Shoja, N.3    Tohidi, G.4
  • 16
    • 61349085372 scopus 로고    scopus 로고
    • A multiobjective branch-and-bound framework: Application to the biobjective spanning tree problem
    • F. Sourd, O. Spanjaard, A multiobjective branch-and-bound framework: application to the biobjective spanning tree problem, Inf. J. Comput. 20 (3) (2008) 472-484.
    • (2008) Inf. J. Comput. , vol.20 , Issue.3 , pp. 472-484
    • Sourd, F.1    Spanjaard, O.2
  • 17
    • 33749348467 scopus 로고    scopus 로고
    • An improved algorithm for solving biobjective integer programs
    • DOI 10.1007/s10479-006-0058-z
    • T.K. Ralphs, M.J. Saltzman, M.M. Wiecek, An improved algorithm for solving biobjective integer programs, Ann. Oper. Res. 147 (2006) 43-70. (Pubitemid 44496800)
    • (2006) Annals of Operations Research , vol.147 , Issue.1 , pp. 43-70
    • Ralphs, T.K.1    Saltzman, M.J.2    Wiecek, M.M.3
  • 18
    • 67349171472 scopus 로고    scopus 로고
    • Multi-objective integer programming: A general approach for generating all non-dominated solutions
    • M. Ozlen, M. Azizoglu, Multi-objective integer programming: a general approach for generating all non-dominated solutions, Eur. J. Oper. Res. 199 (2009) 25-35.
    • (2009) Eur. J. Oper. Res. , vol.199 , pp. 25-35
    • Ozlen, M.1    Azizoglu, M.2
  • 19
    • 78751575873 scopus 로고    scopus 로고
    • A two-phase method for multi-objective integer programming and its application to the assignment problem with three objectives
    • A. Przybylski, X. Gandibleux, M. Ehrgott, A two-phase method for multi-objective integer programming and its application to the assignment problem with three objectives, Discrete Optim. 7 (2010) 149-165.
    • (2010) Discrete Optim. , vol.7 , pp. 149-165
    • Przybylski, A.1    Gandibleux, X.2    Ehrgott, M.3
  • 20
    • 0015094608 scopus 로고
    • On a bicriterion formulation of the problems of integrated system identification and system optimization
    • Y.Y. Haimes, LS. Lasdon, D.A. Wismer, On a bicriterion formulation of the problems of integrated system identification and system optimization, IEEE Trans. Syst. Man Cybern. 1 (1971) 296-297.
    • (1971) IEEE Trans. Syst. Man Cybern. , vol.1 , pp. 296-297
    • Haimes, Y.Y.1    Lasdon, L.S.2    Wismer, D.A.3
  • 22
    • 49249098311 scopus 로고    scopus 로고
    • Improved ε-constraint method for multiobjective programming
    • M. Ehrgott, S. Ruzika, Improved ε-constraint method for multiobjective programming, J. Optim. Theory Appl. 138 (2008) 375-396.
    • (2008) J. Optim. Theory Appl. , vol.138 , pp. 375-396
    • Ehrgott, M.1    Ruzika, S.2
  • 23
    • 2442646635 scopus 로고    scopus 로고
    • A method for finding the set of non-dominated vectors for multiple objective integer linear programs
    • J. Sylva, A. Crema, A method for finding the set of non-dominated vectors for multiple objective integer linear programs, Eur. J. Oper. Res. 158 (2004) 46-55.
    • (2004) Eur. J. Oper. Res. , vol.158 , pp. 46-55
    • Sylva, J.1    Crema, A.2
  • 24
    • 33847070033 scopus 로고    scopus 로고
    • A method for finding well-dispersed subsets of non-dominated vectors for multiple objective mixed integer linear programs
    • DOI 10.1016/j.ejor.2006.02.049, PII S0377221706003481
    • J. Sylva, A. Crema, A method for finding well-dispersed subsets of non-dominated vectors for multiple objective mixed integer linear programs, Eur. J. Oper. Res. 180 (2007) 1011-1027. (Pubitemid 46275294)
    • (2007) European Journal of Operational Research , vol.180 , Issue.3 , pp. 1011-1027
    • Sylva, J.1    Crema, A.2
  • 26
    • 63449084870 scopus 로고    scopus 로고
    • Approximating the nondominated frontiers of multi-objective combinatorial optimization problems
    • M. Koksalan, B. Lokman, Approximating the nondominated frontiers of multi-objective combinatorial optimization problems, Nav. Res. Logist. 56 (2009)191-198.
    • (2009) Nav. Res. Logist. , vol.56 , pp. 191-198
    • Koksalan, M.1    Lokman, B.2
  • 27
    • 0041739877 scopus 로고
    • A survey of techniques for finding efficient solutions to multi-objective integer linear programming
    • J. Teghem, P.L Kunsch, A survey of techniques for finding efficient solutions to multi-objective integer linear programming, Asia-Pac. J. Oper. Res. 3 (1986) 95-108.
    • (1986) Asia-Pac. J. Oper. Res. , vol.3 , pp. 95-108
    • Teghem, J.1    Kunsch, P.L.2
  • 28
    • 84994926936 scopus 로고
    • Multi-objective combinatorial optimization problems: A survey
    • E.L Ulungu, J. Teghem, Multi-objective combinatorial optimization problems: a survey, J. Multi-Criteria Decis. Anal. 3 (1994) 83-104.
    • (1994) J. Multi-Criteria Decis. Anal. , vol.3 , pp. 83-104
    • Ulungu, E.L.1    Teghem, J.2
  • 29
    • 0022304489 scopus 로고
    • Zero-one programming with multiple criteria
    • L.M. Rasmussen, Zero-one programming with multiple criteria, Eur. J. Oper. Res. 26 (1986) 83-95.
    • (1986) Eur. J. Oper. Res. , vol.26 , pp. 83-95
    • Rasmussen, L.M.1
  • 30
    • 0001322778 scopus 로고    scopus 로고
    • A survey and annotated bibliography of multiobjective combinatorial optimization
    • M. Ehrgott, X. Gandibleux, A survey and annotated bibliography of multiobjective combinatorial optimization, OR Spectr. 22 (2000) 425-460.
    • (2000) OR Spectr. , vol.22 , pp. 425-460
    • Ehrgott, M.1    Gandibleux, X.2
  • 31
    • 33846316381 scopus 로고    scopus 로고
    • A review of interactive methods for multiobjective integer and mixed-integer programming
    • DOI 10.1016/j.ejor.2006.02.033, PII S0377221706002384
    • M.J. Alves, J. Climaco, A review of interactive methods for multiobjective integer and mixed-integer programming, Eur. J. Oper. Res. 180 (2007) 99-115. (Pubitemid 46123843)
    • (2007) European Journal of Operational Research , vol.180 , Issue.1 , pp. 99-115
    • Alves, M.J.1    Climaco, J.2
  • 32
    • 2642512286 scopus 로고    scopus 로고
    • On the computational efficiency of multiple objective metaheuristics, the knapsack problem case study
    • A. Jaszkiewicz, On the computational efficiency of multiple objective metaheuristics, The knapsack problem case study, Euro. J. Oper. Res. 158 (2004) 418-433.
    • (2004) Euro. J. Oper. Res. , vol.158 , pp. 418-433
    • Jaszkiewicz, A.1
  • 33
    • 0033318858 scopus 로고    scopus 로고
    • Multiobjective evolutionary algorithms a comparative case study and the strength pareto approach
    • DOI 10.1109/4235.797969
    • E. Zitzler, L Thiele, Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach, IEEE Trans. Evol. Comput. 3 (1999) 257-271. (Pubitemid 30544879)
    • (1999) IEEE Transactions on Evolutionary Computation , vol.3 , Issue.4 , pp. 257-271
    • Zitzler Eckart1    Thiele Lothar2
  • 34
    • 0033891465 scopus 로고    scopus 로고
    • Dynamic programming approaches to the multiple criteria knapsack problem
    • DOI 10.1002/(SICI)1520-6750(200002) 47:1<57::AID-NAV4>3.0.CO;2-4
    • K. Klamroth, M.M. Wiecek, Dynamic programming approaches to the multiple criteria knapsack problem, Nav. Res. Logist. 47 (2000) 57-76. (Pubitemid 30542457)
    • (2000) Naval Research Logistics , vol.47 , Issue.1 , pp. 57-76
    • Klamroth, K.1    Wiecek, M.M.2
  • 35
    • 0036966921 scopus 로고    scopus 로고
    • Approximating multiobjective knapsack problems
    • T. Erlebach, H. Kellerer, U. Pferschy, Approximating multiobjective knapsack problems, Manage. Sci. 48 (2002) 1603-1612.
    • (2002) Manage. Sci. , vol.48 , pp. 1603-1612
    • Erlebach, T.1    Kellerer, H.2    Pferschy, U.3
  • 36
    • 79952195180 scopus 로고    scopus 로고
    • Comparative analysis of multiobjective evolutionary algorithms for random and correlated instances of multiobjective d-dimensional knapsack problems
    • R. Shah, P. Reed, Comparative analysis of multiobjective evolutionary algorithms for random and correlated instances of multiobjective d-dimensional knapsack problems, Eur. J. Oper. Res. 211 (2011) 466-479.
    • (2011) Eur. J. Oper. Res. , vol.211 , pp. 466-479
    • Shah, R.1    Reed, P.2
  • 37
    • 84861702197 scopus 로고    scopus 로고
    • The multiobjective multidimensional knapsack problem: A survey and a new approach
    • T. Lust, J. Teghem, The multiobjective multidimensional knapsack problem: a survey and a new approach, Int. Trans. Oper. Res. 19 (2012) 495-520.
    • (2012) Int. Trans. Oper. Res. , vol.19 , pp. 495-520
    • Lust, T.1    Teghem, J.2
  • 38
    • 0036671292 scopus 로고    scopus 로고
    • On the performance of multiple-objective genetic local search on the 0/1 knapsack problem-A comparative experiment
    • DOI 10.1109/TEVC.2002.802873, PII 1011092002802873
    • A. Jaszkiewicz, On the performance of multiple-objective genetic local search on the 0/1 knapsack problem - a comparative experiment, IEEE Trans. Evol. Comput. 6 (2002) 402-412. (Pubitemid 35032741)
    • (2002) IEEE Transactions on Evolutionary Computation , vol.6 , Issue.4 , pp. 402-412
    • Jaszkiewicz, A.1
  • 39
    • 85174591806 scopus 로고    scopus 로고
    • An adaptive scheme to generate the pareto front based on the epsilon-constraint method
    • J. Branke, K. Deb, K. Miettinen, R. Steuer (Eds.) URN: urn: nbn: de:0030-drops-2465, URL
    • M. Laumanns, L Thiele, E. Zitzler, An adaptive scheme to generate the Pareto front based on the epsilon-constraint method, in: J. Branke, K. Deb, K. Miettinen, R. Steuer (Eds.), Practical Approaches to Multi-Objective Optimization, Dagstuhl Seminar Proceedings, Vol. 04461, 2005. URN: urn: nbn: de:0030-drops-2465, URL: http://drops.dagstuhl.de/opus/volltexte/2005/246.
    • (2005) Practical Approaches to Multi-Objective Optimization, Dagstuhl Seminar Proceedings , vol.4461
    • Laumanns, M.1    Thiele, L.2    Zitzler, E.3
  • 41
    • 71649116216 scopus 로고    scopus 로고
    • Evolutionary, constructive and hybrid procedures for the bi-objective set packing problem
    • X. Delorme, X. Gandibleux, F. Degoutin, Evolutionary, constructive and hybrid procedures for the bi-objective set packing problem, Eur. J. Oper. Res. 204 (2010)206-217.
    • (2010) Eur. J. Oper. Res. , vol.204 , pp. 206-217
    • Delorme, X.1    Gandibleux, X.2    Degoutin, F.3
  • 42
    • 84862992079 scopus 로고    scopus 로고
    • Multi-directional local search
    • F. Tricoire, Multi-directional local search, Comput. Oper. Res. 39 (2012) 3089-3101.
    • (2012) Comput. Oper. Res. , vol.39 , pp. 3089-3101
    • Tricoire, F.1
  • 43
    • 0023825684 scopus 로고
    • Computational experience concerning payoff tables and minimum criterion values over the efficient set
    • DOI 10.1016/0377-2217(88)90257-3
    • H. Isermann, R.E. Steuer, Computational experience concerning payoff tables and minimum criterion values over the efficient set, Eur. J. Oper. Res. 33 (1987)91-97. (Pubitemid 18546738)
    • (1988) European Journal of Operational Research , vol.33 , Issue.1 , pp. 91-97
    • Isermann, H.1    Steuer, R.E.2
  • 44
    • 0022734986 scopus 로고
    • Estimates of the minimum nondominated criterion values in multiple-criteria decision-making
    • DOI 10.1016/0167-188X(86)90003-0
    • M.I. Dessouky, M. Ghiassi, W.J. Davis, Estimates of the minimum nondominated criterion values in multiple criteria decision making, Eng. Costs Prod. Econ. 10 (1986) 95-104. (Pubitemid 16608559)
    • (1986) Engineering costs and production economics , vol.10 , Issue.2 , pp. 95-104
    • Dessouky, M.I.1    Ghiassi, M.2    Davis, W.J.3
  • 45
    • 63349087616 scopus 로고    scopus 로고
    • A method for nadir point estimation in MOLP problems
    • B. Metev, V. Vassilev, A method for nadir point estimation in MOLP problems, Cyberne. Inf. Technol. 3 (2003) 15-24.
    • (2003) Cyberne. Inf. Technol. , vol.3 , pp. 15-24
    • Metev, B.1    Vassilev, V.2
  • 46
    • 63349099255 scopus 로고    scopus 로고
    • An exact method for computing the nadir values in multiple objective linear programming
    • M.J. Alves, J.P. Costa, An exact method for computing the nadir values in multiple objective linear programming, Eur. J. Oper. Res. 198 (2009) 637-646.
    • (2009) Eur. J. Oper. Res. , vol.198 , pp. 637-646
    • Alves, M.J.1    Costa, J.P.2
  • 47
    • 55949128545 scopus 로고    scopus 로고
    • An algorithm for optimizing a linear function over an integer efficient set
    • J.M. Jorge, An algorithm for optimizing a linear function over an integer efficient set, Eur. J. Oper. Res. 195 (2009) 98-103.
    • (2009) Eur. J. Oper. Res. , vol.195 , pp. 98-103
    • Jorge, J.M.1
  • 49
    • 2942547409 scopus 로고    scopus 로고
    • SPEA2: Improving the strength pareto evolutionary algorithm for multiobjective optimization
    • K. Giannakoglou, D. Tsahalis, J. Periaux, K. Papailiou, T. Fogarty (Eds.) Spain
    • E. Zitzler, M. Laumanns, L Thiele, SPEA2: improving the strength pareto evolutionary algorithm for multiobjective optimization, in: K. Giannakoglou, D. Tsahalis, J. Periaux, K. Papailiou, T. Fogarty (Eds.), Evolutionary Methods for Design, Optimization, and Control, Barcelona, CIMNE, Spain, 2002, pp. 19-26.
    • (2002) Evolutionary Methods for Design, Optimization, and Control, Barcelona, CIMNE , pp. 19-26
    • Zitzler, E.1    Laumanns, M.2    Thiele, L.3
  • 53
    • 28444484954 scopus 로고    scopus 로고
    • Multi-criteria branch and bound: A vector maximization algorithm for Mixed 0-1 Multiple Objective Linear Programming
    • DOI 10.1016/j.amc.2005.01.038, PII S0096300305000809
    • G. Mavrotas, D. Diakoulaki, Multi-criteria branch & bound: a vector maximization algorithm for mixed 0-1 multiple objective linear programming, Appl. Math. Comput. 171 (2005) 53-71. (Pubitemid 41737288)
    • (2005) Applied Mathematics and Computation , vol.171 , Issue.1 , pp. 53-71
    • Mavrotas, G.1    Diakoulaki, D.2
  • 55
    • 35248851504 scopus 로고    scopus 로고
    • PISA - A platform and programming language independent interface for search algorithms
    • C. Fonseca, P. Fleming, E. Zitzler, K. Deb, L Thiele (Eds.) Springer, Heidelberg
    • S. Bleuler, M. Laumanns, L Thiele, E. Zitzler, PISA - a platform and programming language independent interface for search algorithms, in: C. Fonseca, P. Fleming, E. Zitzler, K. Deb, L Thiele (Eds.), Evolutionary Multi-Criterion Optimization, Springer, Heidelberg, 2003, pp. 494-508.
    • (2003) Evolutionary Multi-Criterion Optimization , pp. 494-508
    • Bleuler, S.1    Laumanns, M.2    Thiele, L.3    Zitzler, E.4
  • 57
    • 35848970555 scopus 로고    scopus 로고
    • Selection among ranked projects under segmentation, policy and logical constraints
    • DOI 10.1016/j.ejor.2007.03.010, PII S0377221707003074
    • G. Mavrotas, D. Diakoulaki, A. Kourentzis, Selection among ranked projects under segmentation, policy and logical constraints, Eur. J. Oper. Res. 187 (2008)177-192. (Pubitemid 350061096)
    • (2008) European Journal of Operational Research , vol.187 , Issue.1 , pp. 177-192
    • Mavrotas, G.1    Diakoulaki, D.2    Kourentzis, A.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.