Visualizing the pareto frontier

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5252 LNCS, Issue , 2008, Pages 213-243

  Lotov, Alexander V ^a   Miettinen, Kaisa ^b  

^a DORODNICYN COMPUTING CENTER   (Russian Federation)

^b UNIVERSITY OF JYVÄSKYLÄ   (Finland)

Author keywords

[No Author keywords available]

Indexed keywords

MULTIOBJECTIVE OPTIMIZATION; VISUALIZATION;

BI OBJECTIVES; MULTI-OBJECTIVE OPTIMIZATION PROBLEM; OBJECTIVE FUNCTIONS; PARETO FRONTIERS; PARETO-OPTIMAL SETS; POINTWISE APPROXIMATION; POLYHEDRAL APPROXIMATION; VISUALIZATION TECHNIQUE;

PARETO PRINCIPLE;

EID: 57049127204     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-88908-3_9     Document Type: Conference Paper

References (81)

1. Abramova, M.: Approximation of a Pareto set on the basis of inexact information. Moscow University Computational Mathematics and Cybernetics 2, 62-69 (1986)
2. Barber, C.B., Dobkin, D.P., Huhdanpaa, H.T.: The quickhull algorithm for convex hulls. ACM Transactions on Mathematical Software 2(4), 469-483 (1996)
3. Benson, H.P.: An outer-approximation algorithm for generating all efficient extreme points in the outcome set of a multiple-objective linear programming problem. Journal of Global Optimization 13, 1-24 (1998)
4. Benson, H.P., Sayin, S.: Toward finding global representations of the efficient set in multiple-objective mathematical programming. Naval Research Logistics 44, 47-67 (1997)
5. Berezkin, V.E., Kamenev, G.K., Lotov, A.V.: Hybrid adaptive methods for approximating a nonconvex multidimensional Pareto frontier. Computational Mathematics and Mathematical Physics 46(11), 1918-1931 (2006)
6. Bushenkov, V.A., Lotov, A.V.: Methods for the Constructing and Application of Generalized Reachable Sets (In Russian). Computing Centre of the USSR Academy of Sciences, Moscow (1982)
7. Bushenkov, V.A., Gusev, D.I., Kamenev, G.K., Lotov, A.V., Chernykh, O.L.: Visualization of the Pareto set in multi-attribute choice problem (In Russian). Doklady of Russian Academy of Sciences 335(5), 567-569 (1993)
8. Chankong, V., Haimes, Y.Y.: Multiobjective Decision Making Theory and Methodology. Elsevier, New York (1983)
9. Chernykh, O.L., Kamenev, G.K.: Linear algorithm for a series of parallel two-dimensional slices of multidimensional convex polytope. Pattern Recognition and Image Analysis 3(2), 77-83 (1993)
10. Chipperfield, A.J., Whideborn, J.F., Fleming, P.J.: Evolutionary algorithms and simulated annealing for MCDM. In: Gal, T., Stewart, T.J., Hanne, T. (eds.) Multicriteria Decision Making: Advances in MCDM Models, Algorithms, Theory and Applications, pp. 16-1-16-32, Kluwer Academic Publishers, Boston (1999)
11. Cleveland, W.S.: The Elements of Graphing Data. Wadsworth, Belmont (1985)
12. Cohon, J., Church, R., Sheer, D.: Generating multiobjective tradeoffs: An algorithm for bicriterion problems. Water Resources Research 15, 1001-1010 (1979)
13. Cohon, J.L.: Multiobjective Programming and Planning. Academic Press, New York (1978)
14. Cooke, R.M., van Noortwijk, J.M.: Generic graphics for uncertainty and sensitivity analysis. In: Schueller, G., Kafka, P. (eds.) Safety and Reliability, Proceedings of ESREL '99, pp. 1187-1192. Balkema, Rotterdam (1999)
15. Das, I., Dennis, J.: Normal boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM Journal on Optimization 8, 631-657 (1998)
16. Evtushenko, Y., Potapov, M.: Methods of Numerical Solutions of Multicriteria Problems. Soviet Mathematics Doklady 34, 420-423 (1987)
17. Gass, S., Saaty, T.: The Computational Algorithm for the Parametric Objective Function. Naval Research Logistics Quarterly 2, 39 (1955)
18. Geoffrion, A.M., Dyer, J.S., Feinberg, A.: An interactive approach for multi-criterion optimization, with an application to the operation of an academic department. Management Science 19(4), 357-368 (1972)
19. Gusev, D. V., Lotov, A. V.: Methods for decision support in finite choice problems (In Russian). In: Ivanilov, J. (ed.) Operations Research. Models, Systems, Decisions, pp. 15-43. Computing Center of Russian Academy of Sciences, Moscow (1994)
20. Haimes, Y.Y., Tarvainen, K., Shima, T., Thadathill, J.: Hierachical Multiobjective Analysis of Large-Scale Systems. Hemisphere Publishing Corporation, New York (1990)
21. Henig, M., Buchanan, J.T.: Generalized tradeoff directions in multiobjective optimization problems. In: Tzeng, G., Wang, H., Wen, U., Yu, P. (eds.) Multiple Criteria Decision Making - Proceedings of the Tenth International Conference, pp. 47-56. Springer, New York (1994)
22. Henig, M., Buchanan, J.T.: Tradeoff directions in multiobjective optimization problems. Mathematical Programming 78(3), 357-374 (1997)
23. Jahn, J.: Vector Optimization. Springer, Berlin (2004)
24. Jewel, T.K.: A Systems Approach to Civil Engineering, Planning, Design. Harper & Row, New York (1990)
25. Kaliszewski, i.: Quantitative Pareto Analysis by Cone Separation Technique. Kluwer, Dordrecht (1994)
26. Kamenev, G.K.: Dual adaptive algorithms for polyhedral approximation of convex bodies. Computational Mathematics and Mathematical Physics 42(8) (2002)
27. Klamroth, K., Tind, J., Wiecek, M.M.: Unbiased approximation in multicriteria optimization. Mathematical Methods of Operations Research 56, 413-437 (2002)
28. Klimberg, R.: GRADS: A new graphical display system for visualizing multiple criteria solutions. Computers & Operations Research 19(7), 707-711 (1992)
29. Krasnoshchekov, P.S., Morozov, V.V., Fedorov, V.V.: Decomposition in design problems (In Russian). Izvestiya Akademii Nauk SSSR, Series Technical Cybernetics (2), 7-17 (1979)
30. Kubotani, H., Yoshimura, K.: Performance evaluation of acceptance probability functions for multiobjective simulated annealing. Computers & Operations Research 30, 427-442 (2003)
31. Larichev, O.: Cognitive validity in design of decision-aiding techniques. Journal of Multi-Criteria Decision Analysis 1(3), 127-138 (1992)
32. Lewandowski, A., Granat, J.: Dynamic BIPLOT as the interaction interface for aspiration based decision support systems. In: Korhonen, P., Lewandowski, A., Wallenius, J. (eds.) Multiple Criteria Decision Support, pp. 229-241. Springer, Berlin (1991)
33. Lomov, B.F.: Philosophical and Theoretical Problems of Psychology. Science Publisher, Moscow (1984)
34. Lotfi, V., Stewart, T.J., Zionts, S.: An aspiration level interactive model for multiple criteria decision making. Computers & Operations Research 19(7), 671-681 (1992)
35. Lotov, A., Berezkin, V., Kamenev, G., Miettinen, K.: Optimal control of cooling process in continuous casting of steel using a visualization-based multi-criteria approach. Applied Mathematical Modelling 29(7), 653-672 (2005)
36. Lotov, A.V.: Exploration of economic systems with the help of reachable sets (In Russian). In: Proceedings of the International Conference on the Modeling of Economic Processes, Erevan, 1974, pp. 132-137. Computing Centre of USSR Academy of Sciences, Moscow (1975)
37. Lotov, A.V.: Coordination of Economic Models by the Attainable Sets Method (In Russian). In: Berlyand, E.L., Barabash, S.B. (eds.) Mathematical Methods for an Analysis of Interaction between Industrial and Regional Systems, pp. 36-44. Nauka, Novosibirsk (1983)
38. Lotov, A.V.: Generalized reachable sets method in multiple criteria problems. In: Lewandowski, A., Stanchev, I. (eds.) Methodology and Software for Interactive Decision Support, pp. 65-73. Springer, Berlin (1989)
39. Lotov, A.V., Kamenev, G.K., Berezkin, V.E.: Approximation and Visualization of Pareto-Efficient Frontier for Nonconvex Multiobjective Problems. Doklady Mathematics 66(2), 260-262 (2002)
40. Lotov, A.V., Bushenkov, V.A., Kamenev, G.K.: Interactive Decision Maps. Approximation and Visualization of Pareto Frontier. Kluwer Academic Publishers, Boston (2004)
41. Louie, P., Yeh, W., Hsu, N.: Multiobjective Water Resources Management Planning. Journal of Water Resources Planning and Management 110(1), 39-56 (1984)
42. Mareschal, B., Brans, J.-P.: Geometrical representation for MCDA. European Journal of Operational Research 34(1), 69-77 (1988)
43. Mattson, C.A., Messac, A.: Pareto frontier based concept selection under uncertainty, with visualization. Optimization and Engineering 6, 85-115 (2005)
44. McClure, D.E., Vitale, R.A.: Polygonal approximation of plane convex bodies. Journal of Mathematical Analysis and Applications 51(2), 326-358 (1975)
45. McQuaid, M.J., Ong, T.-H., Chen, H., Nunamaker, J.F.: Multidimensional scaling for group memory visualization. Decision Support Systems 27, 163-176 (1999)
46. Meisel, W.S.: Tradeoff decision in multiple criteria decision making. In: Cochrane, J., Zeleny, M. (eds.) Multiple Criteria Decision Making, pp. 461-476. University of South Carolina Press, Columbia (1973)
47. Miettinen, K.: Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, Boston (1999)
48. Miettinen, K.: Graphical illustration of Pareto optimal solutions. In: Tanino, T., Tanaka, T., Inuiguchi, M. (eds.) Multi-Objective Programming and Goal Programming: Theory and Applications, pp. 197-202. Springer, Berlin (2003)
49. Miettinen, K., Mäkelä, M.M.: On generalized trade-off directions in nonconvex multiobjective optimization. Mathematical Programming 92, 141-151 (2002)
50. Miettinen, K., Mäkelä, M.M.: Characterizing general trade-off directions. Mathematical Methods of Operations Research 57, 89-100 (2003)
51. Miettinen, K., Mäkelä, M.M.: Synchronous approach in interactive multiobjective optimization. European Journal of Operational Research 170(3), 909-922 (2006)
52. Miettinen, K., Lotov, A.V., Kamenev, G.K., Berezkin, V.E.: Integration of two multiobjective optimization methods for nonlinear problems. Optimization Methods and Software 18, 63-80 (2003)
53. Miettinen, K., Molina, J., González, M., Hernández- Díaz, A., Caballero, R.: Using box indices in supporting comparison in multiobjective optimization. European Journal of Operational Research. To appear (2008), doi:10.1016/j.ejor.2008.05.103
54. Miller, G.A.: The magical number seven, plus or minus two: Some limits of our capacity for processing information. Psychological Review 63, 81-97 (1956)
55. Nefedov, V.N.: On the approximation of Pareto set. USSR Computational Mathematics and Mathematical Physics 24, 19-28 (1984)
56. Nefedov, V.N.: Approximation of a set of Pareto-optimal solutions. USSR Computational Mathematics and Mathematical Physics 26, 99-107 (1986)
57. Olson, D.: Decision Aids for Selection Problems. Springer, New York (1996)
58. Popov, N.: Approximation of a Pareto set by the convolution method. Moscow University Computational Mathematics and Cybernetics (2), 41-48 (1982)
59. Pryke, A., Mostaghim, S., Nazemi, A.: Heatmap Visualization of Population Based Multi Objective Algorithms. In: Obayashi, S., Deb, K., Poloni, C, Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 361-375. Springer, Heidelberg (2007)
60. Reuter, H.: An approximation method for the efficiency set of multiobjective programming problems. Optimization 21, 905-911 (1990)
61. Roy, B.: Decisions avec critères multiples. Metra International 11(1), 121-151 (1972)
62. Ruzika, S., Wiecek, M.M.: Survey paper: Approximation methods in multiobjective programming. Journal of Optimization Theory and Applications 126(3), 473-501 (2005)
63. Sawaragi, Y., Nakayama, H., Tanino, T.: Theory of Multiobjective Optimization. Academic Press, Orlando (1985)
64. Sayin, S.: A Procedure to Find Discrete Representations of the Efficient Set with Specified Coverage Errors. Operations Research 51, 427-436 (2003)
65. Schandl, B., Klamroth, K., Wiecek, M.M.: Introducing oblique norms into multiple criteria programming. Journal of Global Optimization 23, 81-97 (2002a)
66. Schandl, B., Klamroth, K., Wiecek, M.M.: Norm-based approximation in multicriteria programming. Computers and Mathematics with Applications 44, 925-942 (2002b)
67. Schütze, O., Jourdan, L., Legrand, T., Talbi, E.-G., Wojkiewicz, J.L.: A multiobjective approach to the design of conducting polymer composites for electromagnetic shielding. In: Obayashi, S., Deb, K., Poloni, C, Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 590-603. Springer, Heidelberg (2007)
68. Simon, H.: Reason in Human Affairs. Stanford University Press, Stanford (1983)
69. Smirnov, M. : The logical convolution of the criterion vector in the problem of approximating Pareto set. Computational Mathematics and Mathematical Physics 36, 605-614 (1996)
70. Sobol, I.M., Statnikov, R.B.: Choice of Optimal Parameters in Multiobjective Problems (In Russian). Nauka Publishing House, Moscow (1981)
71. Solanki, R.S., Appino, P.A., Cohon, J.L.: Approximating the noninferior set in multiobjective linear programming problems. European Journal of Operational Research 68, 356-373 (1993)
72. Statnikov, R.B., Matusov, J.: Multicriteria Optimization and Engineering. Chapman and Hall, Boca Raton (1995)
73. Steuer, R.E., Harris, F.W.: Intra-set point generation and filtering in decision and criterion space. Computers & Operations Research 7, 41-58 (1980)
74. Suppaptnarm, A., Steffen, K.A., Parks, G.T., Clarkson, P.J.: Simulated annealing: An alternative approach to true multiobjective optimization. Engineering Optimization 33(1), 59-85 (2000)
75. Trinkaus, H.L., Hanne, T.: knowcube: a visual and interactive support for multicriteria decision making. Computers & Operations Research 32, 1289-1309 (2005)
76. Vetschera, R.: A preference preserving projection technique for MCDM. European Journal of Operational Research 61(1-2), 195-203 (1992)
77. Voinalovich, V.: External Approximation to the Pareto Set in Criterion Space for Multicriterion Linear Programming Tasks. Cybernetics and Computing Technology 1, 135-142 (1984)
78. Wierzbicki, A.P.: On the role of intuition in decision making and some ways of multicriteria aid of intuition. Journal of Multi-Criteria Decision Analysis 6(2), 65-76 (1997)
79. Wierzbicki, A.P., Nakamori, Y.: Creative Space. Springer, Berlin (2005)
80. Yu, P.L.: Cone convexity, cone extreme points and nondominated solutions in decision problems with multiple objectives. Journal of Optimization Theory and Applications 14(3), 319-377 (1974)
81. Yu, P.L.: Multiple-Criteria Decision Making Concepts, Techniques and Extensions. Plenum Press, New York (1985)