The weighted sum method for multi-objective optimization: New insights

Structural and Multidisciplinary Optimization

Volumn 41, Issue 6, 2010, Pages 853-862

  Marler, R Timothy ^a   Arora, Jasbir S ^a  

^a IA United States   (United States)

Author keywords

Multi objective optimization; Preferences; Weighted sum

Indexed keywords

APRIORI; FUNCTION VALUES; PARETO-OPTIMAL SETS; WEIGHTED SUM; WEIGHTED SUM METHOD;

MULTIOBJECTIVE OPTIMIZATION;

EID: 77952953568     PISSN: 1615147X     EISSN: 16151488     Source Type: Journal    
DOI: 10.1007/s00158-009-0460-7     Document Type: Article

References (39)

1. TW Athan PY Papalambros 1996 A note on weighted criteria methods for compromise solutions in multi-objective optimization Eng Optim 27 155 176 10.1080/03052159608941404
2. W Chen MM Wiecek J Zhang 1999 Quality utility-a compromise programming approach to robust design J Mech Des 121 179 187 10.1115/1.2829440
3. I Das JE Dennis 1997 A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems Struct Optim 14 63 69 10.1007/BF01197559
4. I Das JE Dennis 1998 Normal-boundary intersection: a new method for generating the Pareto surface in nonlinear multicriteria optimization problems SIAM J Optim 8 631 657 0911.90287 10.1137/S1052623496307510 1627156
5. RT Eckenrode 1965 Weighting multiple criteria Manage Sci 12 180 192 10.1287/mnsc.12.3.180
6. Gembicki FW (1974) Performance and sensitivity optimization: a vector index approach. PhD dissertation, Case Western Reserve University, Cleveland, OH
7. Gennert MA, Yuille AL (1988) Determining the optimal weights in multiple objective function optimization. In: Second international conference on computer vision (held in Los Alamos, CA), Institute of Electrical and Electronics Engineers, Piscataway, NJ, pp 87-89
8. AM Geoffrion 1968 Proper efficiency and the theory of vector maximization J Math Anal Appl 22 618 630 0181.22806 10.1016/0022-247X(68)90201-1 229453
9. Goicoechea A, Hansen DR, Duckstein L (1982) Multiobjective decision analysis with engineering and business applications. Wiley, New York
10. BF Hobbs 1980 A comparison of weighting methods in power plant siting Decis Sci 11 725 737 10.1111/j.1540-5915.1980.tb01173.x
11. JM Holtzman H Halkin 1966 Directional convexity and the maximum principle for discrete systems SIAM J Control 4 263 275 0152.09302 10.1137/0304023 199008
12. C-H Huang J Galuski CL Bloebaum 2007 Multi-objective Pareto concurrent subspace optimization for multidisciplinary design AIAA J 45 1894 1906 10.2514/1.19972 (Pubitemid 47436968)
13. Hwang C-L, Yoon K (1981) Multiple attribute decision making, methods and applications: a state-of-the-art survey. In: Beckmann M, Kunzi HP (eds) Lecture notes in economics and mathematical systems, no 186. Springer, Berlin
14. Kassaimah SA, Mohamed AM, Kolkailah FA (1995) Bi-criteria optimum design of laminated plates under uniform load and shear. In: Proceedings of the 27th international SAMPLE technical conference (held in Albuquerque, NM), 27, pp 731-737
15. J Koski 1985 Defectiveness of weighting method in multicriterion optimization of structures Commun Appl Numer Methods 1 333 337 0586.73148 10.1002/cnm.1630010613
16. J Koski R Silvennoinen 1987 Norm methods and partial weighting in multicriterion optimization of structures Int J Numer Methods Eng 24 1101 1121 0613.73090 10.1002/nme.1620240606 890415
17. Lin JG (1975) Three methods for determining Pareto-optimal solutions of multiple-objective problems. In: Ho YC, Mitter SK (eds) Directions in large-scale systems. Plenum, New York
18. Marler RT (2009) A study of multi-objective optimization methods for engineering applications. VDM, Saarbrucken
19. RT Marler JS Arora 2004 Survey of multi-objective optimization methods for engineering Struct Multidiscipl Optim 26 369 395 10.1007/s00158-003-0368-6 2057377
20. RT Marler JS Arora 2005 Transformation methods for multi-objective optimization Eng Optim 37 551 569 10.1080/03052150500114289 2164916 (Pubitemid 41311780)
21. A Messac CA Mattson 2002 Generating well-distributed sets of Pareto points for engineering design using physical programming Eng Optim 3 431 450 1079.90627 10.1023/A:1021179727569
22. A Messac CP Sukam E Melachrinoudis 2000 Aggregate objective functions and Pareto frontiers: required relationships and practical implications Optim Eng 1 171 188 0992.90062 10.1023/A:1010035730904 1919916
23. A Messac GJ Sundararaj RV Tappeta JE Renaud 2000 Ability of objective functions to generate points on nonconvex Pareto frontiers AIAA J 38 6 1084 1091 10.2514/2.1071
24. A Messac A Ismail-Yahaya CA Mattson 2003 The normalized normal constraint method for generating the Pareto frontier Struct Multidiscipl Optim 25 86 98 10.1007/s00158-002-0276-1 2018726
25. Miettinen K (1999) Nonlinear multiobjective optimization. Kluwer Academic, Boston
26. KA Proos GP Steven OM Querin YM Xie 2001 Multicriterion evolutionary structural optimization using the weighted and the global criterion methods AIAA J 39 2006 2012 10.2514/2.1193
27. JR Rao N Roy 1989 Fuzzy set theoretic approach of assigning weights to objectives in multicriteria decision making Int J Syst Sci 20 1381 1386 0679.90079 10.1080/00207728908910222 1005682
28. TL Saaty 1977 A scaling method for priorities in hierarchies, multiple objectives and fuzzy sets J Math Psychol 15 234 281 0372.62084 10.1016/0022-2496(77)90033-5 682619
29. TL Saaty 2003 Decision-making with the AHP: why is the principal eigenvalue necessary Eur J Oper Res 145 85 91 1012.90015 10.1016/S0377-2217(02) 00227-8 1947158
30. TL Saaty G Hu 1998 Ranking by eigenvector versus other methods in the analytic hierarchy process Appl Math Lett 11 121 125 0942.91020 10.1016/S0893-9659(98)00068-8 1631150
31. SFP Saramago V Steffen Jr 1998 Optimization of the trajectory planning of robot manipulators taking into account the dynamics of the system Mech Mach Theory 33 883 894 1049.70618 10.1016/S0094-114X(97)00110-9 1653337
32. W Stadler 1995 Caveats and boons of multicriteria optimization Microcomput Civ Eng 10 291 299 10.1111/j.1467-8667.1995.tb00291.x
33. Stadler W, Dauer JP (1992) Multicriteria optimization in engineering: a tutorial and survey. In: Kamat MP (ed) Structural optimization: status and promise. American Institute of Aeronautics and Astronautics, Washington, DC
34. Steuer RE (1989) Multiple criteria optimization: theory, computation, and application. Krieger, Malabar
35. RV Tappeta JE Renaud E Messac GJ Sundararaj 2000 Interactive physical programming: tradeoff analysis and decision making in multicriteria optimization AIAA J 38 917 926 10.2514/2.1048
36. Voogd H (1983) Multicriteria evaluation for urban and regional planning. Pion, London
37. Yoon KP, Hwang C-L (1995) Multiple attribute decision making, an introduction. Sage, London
38. LA Zadeh 1963 Optimality and non-scalar-valued performance criteria IEEE Trans Automat Contr AC- 8 59 60 10.1109/TAC.1963.1105511
39. K-S Zhang Z-H Han W-J Li W-P Song 2008 Bilevel adaptive weighted sum method for multidisciplinary multi-objective optimization AIAA J 46 2611 2622 10.2514/1.36853