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

Structural and Multidisciplinary Optimization - Tập 41 Số 6 - Trang 853-862 - 2010
R. Timothy Marler1,2, Jasbir S. Arora3,2
1111 ERF, The University of Iowa, Iowa City, IA, 52242, USA
2Center for Computer Aided Design, College of Engineering
3238 ERF, The University of Iowa, Iowa City, IA, 52242, USA

Tóm tắt

Từ khóa


Tài liệu tham khảo

Athan TW, Papalambros PY (1996) A note on weighted criteria methods for compromise solutions in multi-objective optimization. Eng Optim 27:155–176

Chen W, Wiecek MM, Zhang J (1999) Quality utility—a compromise programming approach to robust design. J Mech Des 121:179–187

Das I, Dennis JE (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

Das I, 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

Eckenrode RT (1965) Weighting multiple criteria. Manage Sci 12:180–192

Gembicki FW (1974) Performance and sensitivity optimization: a vector index approach. PhD dissertation, Case Western Reserve University, Cleveland, OH

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

Geoffrion AM (1968) Proper efficiency and the theory of vector maximization. J Math Anal Appl 22:618–630

Goicoechea A, Hansen DR, Duckstein L (1982) Multiobjective decision analysis with engineering and business applications. Wiley, New York

Hobbs BF (1980) A comparison of weighting methods in power plant siting. Decis Sci 11:725–737

Holtzman JM, Halkin H (1966) Directional convexity and the maximum principle for discrete systems. SIAM J Control 4:263–275

Huang C-H, Galuski J, Bloebaum CL (2007) Multi-objective Pareto concurrent subspace optimization for multidisciplinary design. AIAA J 45:1894–1906

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

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

Koski J (1985) Defectiveness of weighting method in multicriterion optimization of structures. Commun Appl Numer Methods 1:333–337

Koski J, Silvennoinen R (1987) Norm methods and partial weighting in multicriterion optimization of structures. Int J Numer Methods Eng 24:1101–1121

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

Marler RT (2009) A study of multi-objective optimization methods for engineering applications. VDM, Saarbrucken

Marler RT, Arora JS (2004) Survey of multi-objective optimization methods for engineering. Struct Multidiscipl Optim 26:369–395

Marler RT, Arora JS (2005) Transformation methods for multi-objective optimization. Eng Optim 37:551–569

Messac A, Mattson CA (2002) Generating well-distributed sets of Pareto points for engineering design using physical programming. Eng Optim 3:431–450

Messac A, Sukam CP, Melachrinoudis E (2000a) Aggregate objective functions and Pareto frontiers: required relationships and practical implications. Optim Eng 1:171–188

Messac A, Sundararaj GJ, Tappeta RV, Renaud JE (2000b) Ability of objective functions to generate points on nonconvex Pareto frontiers. AIAA J 38(6):1084–1091

Messac A, Ismail-Yahaya A, Mattson CA (2003) The normalized normal constraint method for generating the Pareto frontier. Struct Multidiscipl Optim 25:86–98

Miettinen K (1999) Nonlinear multiobjective optimization. Kluwer Academic, Boston

Proos KA, Steven GP, Querin OM, Xie YM (2001) Multicriterion evolutionary structural optimization using the weighted and the global criterion methods. AIAA J 39:2006–2012

Rao JR, Roy N (1989) Fuzzy set theoretic approach of assigning weights to objectives in multicriteria decision making. Int J Syst Sci 20:1381–1386

Saaty TL (1977) A scaling method for priorities in hierarchies, multiple objectives and fuzzy sets. J Math Psychol 15:234–281

Saaty TL (2003) Decision-making with the AHP: why is the principal eigenvalue necessary. Eur J Oper Res 145:85–91

Saaty TL, Hu G (1998) Ranking by eigenvector versus other methods in the analytic hierarchy process. Appl Math Lett 11:121–125

Saramago SFP, Steffen V Jr (1998) Optimization of the trajectory planning of robot manipulators taking into account the dynamics of the system. Mech Mach Theory 33:883–894

Stadler W (1995) Caveats and boons of multicriteria optimization. Microcomput Civ Eng 10:291–299

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

Steuer RE (1989) Multiple criteria optimization: theory, computation, and application. Krieger, Malabar

Tappeta RV, Renaud JE, Messac E, Sundararaj GJ (2000) Interactive physical programming: tradeoff analysis and decision making in multicriteria optimization. AIAA J 38:917–926

Voogd H (1983) Multicriteria evaluation for urban and regional planning. Pion, London

Yoon KP, Hwang C-L (1995) Multiple attribute decision making, an introduction. Sage, London

Zadeh LA (1963) Optimality and non-scalar-valued performance criteria. IEEE Trans Automat Contr AC-8:59–60

Zhang K-S, Han Z-H, Li W-J, Song W-P (2008) Bilevel adaptive weighted sum method for multidisciplinary multi-objective optimization. AIAA J 46:2611–2622