Equispaced Pareto front construction for constrained bi-objective optimization

Mathematical and Computer Modelling

Volumn 57, Issue 9-10, 2013, Pages 2122-2131

  Pereyra, Victor ^a   Saunders, Michael ^b   Castillo, Jose ^c  

^a WEIDLINGER ASSOCIATES INC   (United States)

^b Stanford University   (United States)

^c SAN DIEGO STATE UNIVERSITY   (United States)

Author keywords

Constrained optimization; Mesh design; Multiobjective optimization; Parallel global method; Pareto fronts

Indexed keywords

BI-OBJECTIVE OPTIMIZATION; GLOBAL METHODS; HOMOTOPY CONTINUATION; LARGE-SCALE APPLICATIONS; MESH DESIGNS; PARETO FRONT; UNCONSTRAINED PROBLEMS; VARIATIONAL APPROACHES;

MOTION COMPENSATION; MULTIOBJECTIVE OPTIMIZATION; PARETO PRINCIPLE; PARTIAL DIFFERENTIAL EQUATIONS;

CONSTRAINED OPTIMIZATION;

EID: 84875667752     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2010.12.044     Document Type: Article

References (25)

1. K. Deb, A. Pratap, S. Agarwal, T. Meyarivan, A fast and elitist multi-objective genetic algorithm: NSGA-II. KanGAL Report 2000-01, Indian Institute of Technology, Kanpur, 2000.
2. Rakowska J., Haftka R.T., Watson L.T. Tracing the efficient curve for multi-objective control-structure optimization. SIAM J. Optim. 1993, 3:654-667.
3. Rheinboldt W.C., Burkardt J. PITCON: a program for a locally parametrized continuation process. ACM TOMS 1983, 9:236-241.
4. O. Schutze, A. Dell'Aere, M. Dellnitz, On continuation methods for the numerical treatment of multi-objective optimization problems, in: Dagstuhl Seminar Proceedings 04461, Practical Approaches to Multi-Objective Optimization, 2005.
5. Das I., Dennis J.E. Normal-boundary intersection: an alternate approach for generating Pareto-optimal points in multicriteria optimization problems. SIAM J. Optim. 1998, 8:631-657.
6. Pereyra V. Fast computation of equispaced Pareto manifolds and Pareto fronts for multiobjective optimization problems. Math. Comput. Simulation 2009, 79:1935-1947.
7. Ortega J.M., Rheinboldt W.C. Iterative Solution of Nonlinear Equations in Several Variables 1970, Academic Press, New York.
8. Keller H.B. Global homotopies and Newton methods. Recent Advances in Numerical Analysis 1978, 73-94. C. de Boor, G.H. Golub (Eds.).
9. P.E. Gill, W. Murray, M.A. Saunders, User's guide to SNOPT version 7: software for large-scale nonlinear programming. 2006 (accessed 09.10.08). http://www.scicomp.ucsd.edu/~peg/Software.html.
10. Kim I.Y., de Weck O.L. Adaptive weighted-sum method for bi-objective optimization: Pareto front generation. Struct. Multidiscip. Optim. 2005, 23:149-158.
11. Handbook of Grid Generation 1998, CRC Press. J.F. Thomson, B.K. Soni, N.P. Weatherill (Eds.).
12. Castillo J. A discrete variational grid generation method. SIAM J. Sci. Stat. Comput. 1991, 12:454-468.
13. Leyffer S. A complementarity constraint formulation of convex multiobjective optimization problems. INFORMS J. Comput. 2009, 21:257-267.
14. Sayin S. Measuring the quality of discrete representations of efficient sets in multiple objective mathematical programming. Math. Program 2000, 87:543-560.
15. G. Eichfelder, Parametergesteuerte Lösung nichtlinearer multikriterieller Optimierungsprobleme (Parameter-Controlled Solving of Nonlinear Multi-Objective Optimization Problems) Ph.D. Dissertation, University of Erlangen-Nurnberg, Germany, 2006.
16. Eichfelder G. Adaptive Scalarization Methods in Multiobjective Optimization 2008, Springer.
17. Pascoletti A., Serafini P. Scalarizing vector optimization problems. J. Optim. Theory Appl. 1984, 42:499-524.
18. G. Eichfelder, Personal communication.
19. Eichfelder G. ε-constraint method with adaptive parameter control and an application to intensity-modulated radiotherapy. Multicriteria Decision Making and Fuzzy Systems: Theory, Methods and Applications 2006, 25-42. Shaker, Aachen. K.-H. Küfer, H. Rommelfanger, C. Tammer, K. Winkler (Eds.).
20. Eichfelder G. A constraint method in nonlinear multi-objective optimization. Lecture Notes in Economics and Mathematical Systems 2009, vol. 618. V. Barichard (Ed.).
21. Alonso J.J., LeGresley P., Pereyra V. Aircraft design optimization. Math. Comput. Simulation 2009, 79:1948-1958.
22. A.W. Iorio, X. Li, Rotated test problems for assessing the performance of multiobjective optimization algorithms, in: Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, Seattle, WA, 2006, pp. 683-690.
23. P.J. Roache, W.M. Moeny, S. Steinberg, Interactive electric field calculations for lasers, in: 17th AIAA Fluid Dynamics, Plasma Dynamics, and Lasers Conference, Snowmass, CO, 1984, Paper 84-1655, 1984.
24. Pereyra V. Asynchronous distributed solution of large-scale nonlinear inversion problems. J. Appl. Numer. Math. 1999, 30:31-40. (special issue) (V. Pereyra and J. Castillo (Eds.)).
25. Pereyra V. Ray tracing methods for inverse problems. Inverse Problems 2000, 16:R1-R35.