메뉴 건너뛰기




Volumn 60, Issue 8-9, 2011, Pages 1091-1104

A new scalarization and numerical method for constructing the weak Pareto front of multi-objective optimization problems

Author keywords

efficient set; multi objective optimization; nonconvex optimization; nonsmooth optimization; numerical methods; Pareto front; Tchebychev scalarization

Indexed keywords


EID: 84858203481     PISSN: 02331934     EISSN: 10294945     Source Type: Journal    
DOI: 10.1080/02331934.2011.587006     Document Type: Article
Times cited : (33)

References (28)
  • 1
    • 61349142526 scopus 로고    scopus 로고
    • Multiobjective optimization through a series of single-objective formulations
    • Audet, C, Savard, G and Zghal, W. 2008. Multiobjective optimization through a series of single-objective formulations. SIAM J. Optim., 19: 188-210.
    • (2008) SIAM J. Optim , vol.19 , pp. 188-210
    • Audet, C.1    Savard, G.2    Zghal, W.3
  • 2
    • 80053059185 scopus 로고    scopus 로고
    • Optimization over the efficient set of multi-objective convex optimal control problems
    • Bonnel, H and Kaya, CY. 2010. Optimization over the efficient set of multi-objective convex optimal control problems. J. Optim. Theory Appl., 147: 93-112.
    • (2010) J. Optim. Theory Appl , vol.147 , pp. 93-112
    • Bonnel, H.1    Kaya, C.Y.2
  • 3
    • 29144490009 scopus 로고    scopus 로고
    • On a modified subgradient algorithm for dual problems via sharp augmented Lagrangian
    • Burachik, RS, Gasimov, RN, Ismayilova, NA and Kaya, CY. 2006. On a modified subgradient algorithm for dual problems via sharp augmented Lagrangian. J. Global Optim., 34: 55-78.
    • (2006) J. Global Optim , vol.34 , pp. 55-78
    • Burachik, R.S.1    Gasimov, R.N.2    Ismayilova, N.A.3    Kaya, C.Y.4
  • 4
    • 57249108749 scopus 로고    scopus 로고
    • An update rule and a convergence result for a penalty function method
    • Burachik, RS and Kaya, CY. 2007. An update rule and a convergence result for a penalty function method. J. Indust. Man. Optim., 3: 381-398.
    • (2007) J. Indust. Man. Optim , vol.3 , pp. 381-398
    • Burachik, R.S.1    Kaya, C.Y.2
  • 5
    • 84976498696 scopus 로고    scopus 로고
    • A deflected subgradient algorithm using a general augmented Lagrangian duality with implications on penalty methods
    • In: Burachik RS, Yao JC, editors Berlin, Heidelberg: Springer Verlag
    • Burachik, RS and Kaya, CY. 2010. "A deflected subgradient algorithm using a general augmented Lagrangian duality with implications on penalty methods". In Variational Analysis and Optimization, Edited by: Burachik, RS and Yao, JC. 109-132. Berlin, Heidelberg: Springer Verlag.
    • (2010) Variational Analysis and Optimization , pp. 109-132
    • Burachik, R.S.1    Kaya, C.Y.2
  • 6
    • 77249134734 scopus 로고    scopus 로고
    • An inexact modified subgradient algorithm for nonconvex optimization
    • Burachik, RS, Kaya, CY and Mammadov, M. 2010. An inexact modified subgradient algorithm for nonconvex optimization. Comput. Optim. Appl., 45: 1-24.
    • (2010) Comput. Optim. Appl , vol.45 , pp. 1-24
    • Burachik, R.S.1    Kaya, C.Y.2    Mammadov, M.3
  • 7
    • 0032348480 scopus 로고    scopus 로고
    • Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems
    • Das, I and Dennis, JE. 1998. Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM J. Optim., 8: 631-657.
    • (1998) SIAM J. Optim , vol.8 , pp. 631-657
    • Das, I.1    Dennis, J.E.2
  • 10
    • 70450211203 scopus 로고    scopus 로고
    • An Adaptive scalarization method in multi-objective optimization
    • Eichfelder, G. 2009. An Adaptive scalarization method in multi-objective optimization. SIAM J. Opt., 19: 1694-1718.
    • (2009) SIAM J. Opt , vol.19 , pp. 1694-1718
    • Eichfelder, G.1
  • 11
    • 70449523371 scopus 로고    scopus 로고
    • Scalarizations for adaptively solving multi-objective optimization problems
    • Eichfelder, G. 2009. Scalarizations for adaptively solving multi-objective optimization problems. Comput. Optim. Appl., 44: 249-273.
    • (2009) Comput. Optim. Appl , vol.44 , pp. 249-273
    • Eichfelder, G.1
  • 12
    • 33750704919 scopus 로고    scopus 로고
    • Generating ε{lunate}-efficient solutions in multiobjective programming
    • Engau, A and Wiecek, MM. 2007. Generating ε{lunate}-efficient solutions in multiobjective programming. Euro. J. Oper. Res., 177: 1566-1579.
    • (2007) Euro. J. Oper. Res , vol.177 , pp. 1566-1579
    • Engau, A.1    Wiecek, M.M.2
  • 13
    • 70349581299 scopus 로고    scopus 로고
    • Obtaining the efficient set of nonlinear biobjective optimization problems via interval branch-and-bound methods
    • Fernández, J and Boglárka, T. 2009. Obtaining the efficient set of nonlinear biobjective optimization problems via interval branch-and-bound methods. Comput. Optim. Appl., 42: 393-419.
    • (2009) Comput. Optim. Appl , vol.42 , pp. 393-419
    • Fernández, J.1    Boglárka, T.2
  • 15
    • 45849106161 scopus 로고    scopus 로고
    • Generating the weakly efficient set of nonconvex multiobjective problems
    • Gourion, D and Luc, DT. 2008. Generating the weakly efficient set of nonconvex multiobjective problems. J. Global Optim., 41: 517-538.
    • (2008) J. Global Optim , vol.41 , pp. 517-538
    • Gourion, D.1    Luc, D.T.2
  • 16
    • 41549151558 scopus 로고    scopus 로고
    • Finding preferred subsets of Pareto optimal solutions
    • Kao, GK and Jacobson, SH. 2008. Finding preferred subsets of Pareto optimal solutions. Comput. Optim. Appl., 40: 73-95.
    • (2008) Comput. Optim. Appl , vol.40 , pp. 73-95
    • Kao, G.K.1    Jacobson, S.H.2
  • 19
    • 0032251894 scopus 로고    scopus 로고
    • Convergence properties of the Nelder-Mead simplex method in low dimensions
    • Lagarias, JC, Reeds, JA, Wright, MH and Wright, PE. 1998. Convergence properties of the Nelder-Mead simplex method in low dimensions. SIAM J. Optim., 9: 112-147.
    • (1998) SIAM J. Optim , vol.9 , pp. 112-147
    • Lagarias, J.C.1    Reeds, J.A.2    Wright, M.H.3    Wright, P.E.4
  • 20
    • 27844551838 scopus 로고    scopus 로고
    • Scalarizing functions for generating the weakly efficient solution set in convex multiobjective problems
    • Luc, DT, Phong, TQ and Volle, M. 2005. Scalarizing functions for generating the weakly efficient solution set in convex multiobjective problems. SIAM J. Optim., 15: 987-1001.
    • (2005) SIAM J. Optim , vol.15 , pp. 987-1001
    • Luc, D.T.1    Phong, T.Q.2    Volle, M.3
  • 22
    • 38649117240 scopus 로고    scopus 로고
    • Box-constrained multi-objective optimization: A gradient-like method without 'a priori' scalarization
    • Miglierina, E, Melho, E and Recchioni, MC. 2008. Box-constrained multi-objective optimization: A gradient-like method without 'a priori' scalarization. Euro. J. Oper. Res., 188: 662-682.
    • (2008) Euro. J. Oper. Res , vol.188 , pp. 662-682
    • Miglierina, E.1    Melho, E.2    Recchioni, M.C.3
  • 23
    • 70450173608 scopus 로고    scopus 로고
    • A successive approach to compute the bounded Pareto front of practical multiobjective optimization problems
    • Mueller-Gritschneder, D, Graeb, H and Schlichtmann, U. 2009. A successive approach to compute the bounded Pareto front of practical multiobjective optimization problems. SIAM J. Optim., 20: 915-934.
    • (2009) SIAM J. Optim , vol.20 , pp. 915-934
    • Mueller-Gritschneder, D.1    Graeb, H.2    Schlichtmann, U.3
  • 24
    • 0035401160 scopus 로고    scopus 로고
    • Comments on properties of the minmax solutions in goal programming
    • Ogryczak, W. 2001. Comments on properties of the minmax solutions in goal programming. Euro. J. Oper. Res., 132: 17-21.
    • (2001) Euro. J. Oper. Res , vol.132 , pp. 17-21
    • Ogryczak, W.1
  • 28
    • 56949095415 scopus 로고    scopus 로고
    • A method for generating a well-distributed Pareto set in nonlinear multiobjective optimization
    • Utyuzhnikov, SV, Fantini, P and Guenov, MD. 2009. A method for generating a well-distributed Pareto set in nonlinear multiobjective optimization. J. Comput. Appl. Math., 223: 820-841.
    • (2009) J. Comput. Appl. Math , vol.223 , pp. 820-841
    • Utyuzhnikov, S.V.1    Fantini, P.2    Guenov, M.D.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.