AN ADAPTIVE SCALARIZATION METHOD IN MULTIOBJECTIVE OPTIMIZATION

被引：80

作者：

Eichfelder, Gabriele ^{[1
]}

机构：

[1] Univ Erlangen Nurnberg, Dept Math, D-91058 Erlangen, Germany

来源：

SIAM JOURNAL ON OPTIMIZATION | 2009年 / 19卷 / 04期

关键词：

multicriteria optimization; vector optimization; approximation; sensitivity; scalarization approaches; INTENSITY-MODULATED RADIOTHERAPY; NONDOMINATED SOLUTIONS; ALGORITHM; APPROXIMATION; OPTIMALITY; POINTS;

D O I：

10.1137/060672029

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents a new method for the numerical solution of nonlinear multiobjective optimization problems with an arbitrary partial ordering in the objective space induced by a closed pointed convex cone. This algorithm is based on the well-known scalarization approach by Pascoletti and Serafini and adaptively controls the scalarization parameters using new sensitivity results. The computed image points give a nearly equidistant approximation of the whole Pareto surface. The effectiveness of this new method is demonstrated with various test problems and an applied problem from medicine.

引用

页码：1694 / 1718

页数：25

共 59 条

[1] Intensity modulated radiotherapy treatment planning by use of a barrier-penalty multiplier method [J].

Alber, M. ;

Reemtsen, R. .

OPTIMIZATION METHODS & SOFTWARE, 2007, 22 (03) :391-411

[2] Equilibrium analysis in financial markets with countably many securities [J].

Aliprantis, CD ;

Florenzano, M ;

Martins-da-Rocha, VF ;

Tourky, R .

JOURNAL OF MATHEMATICAL ECONOMICS, 2004, 40 (06) :683-699

[3]

ALT W, 1991, BAYREUTHER MATH SCHR, V35, P1

[4]

[Anonymous], MULTICRITERIA DECISI

[5] GENERALIZATION OF DOMINATION STRUCTURES AND NONDOMINATED SOLUTIONS IN MULTICRITERIA DECISION-MAKING [J].

BERGSTRESSER, K ;

CHARNES, A ;

YU, PL .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1976, 18 (01) :3-13

[6]

BERNAU H, 1987, METHODEN VERFAHREN M, V34, P21

[7] Three new metrics to measure the convergence of metaheuristics towards the Pareto frontier and the aesthetic of a set of solutions in biobjective optimization [J].

Collette, Y ;

Siarry, P .

COMPUTERS & OPERATIONS RESEARCH, 2005, 32 (04) :773-792

[8] A multiobjective gradient-based dose optimization algorithm for external beam conformal radiotherapy [J].

Cotrutz, C ;

Lahanas, M ;

Kappas, C ;

Baltas, D .

PHYSICS IN MEDICINE AND BIOLOGY, 2001, 46 (08) :2161-2175

[9] Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems [J].

Das, I ;

Dennis, JE .

SIAM JOURNAL ON OPTIMIZATION, 1998, 8 (03) :631-657

[10]

Deb K, 2001, LECT NOTES COMPUT SC, V1993, P284

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