Skip to main content
Top

2021 | OriginalPaper | Chapter

11. Interval Multi-objective Optimization

Authors : Chao Jiang, Xu Han, Huichao Xie

Published in: Nonlinear Interval Optimization for Uncertain Problems

Publisher: Springer Singapore

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

By employing an interval approach to describe the uncertainty of parameters in multi-objective optimization, this chapter proposes an interval multi-objective optimization model and also an efficient solution algorithm for this optimization model.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Miettinen K (1999) Nonlinear multiobjective optimization. Kluwer, BostonMATH Miettinen K (1999) Nonlinear multiobjective optimization. Kluwer, BostonMATH
2.
go back to reference Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput 3(4):257–271CrossRef Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput 3(4):257–271CrossRef
3.
go back to reference Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197CrossRef Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197CrossRef
4.
go back to reference Yang BS, Yeun YS, Ruy WS (2002) Managing approximation models in multiobjective optimization. Struct Multidiscip Optim 24(2):141–156CrossRef Yang BS, Yeun YS, Ruy WS (2002) Managing approximation models in multiobjective optimization. Struct Multidiscip Optim 24(2):141–156CrossRef
5.
go back to reference Zitzler E, Thiele L, Bader J (2010) On set-based multiobjective optimization. IEEE Trans Evol Comput 14(1):58–79CrossRef Zitzler E, Thiele L, Bader J (2010) On set-based multiobjective optimization. IEEE Trans Evol Comput 14(1):58–79CrossRef
6.
go back to reference Ali M, Siarry P, Pant M (2012) An efficient differential evolution based algorithm for solving multi-objective optimization problems. Eur J Oper Res 217(2):404–416MathSciNetMATH Ali M, Siarry P, Pant M (2012) An efficient differential evolution based algorithm for solving multi-objective optimization problems. Eur J Oper Res 217(2):404–416MathSciNetMATH
7.
8.
go back to reference Deb K, Abouhawwash M (2016) An optimality theory-based proximity measure for set-based multiobjective optimization. IEEE Trans Evol Comput 20(4):515–528CrossRef Deb K, Abouhawwash M (2016) An optimality theory-based proximity measure for set-based multiobjective optimization. IEEE Trans Evol Comput 20(4):515–528CrossRef
9.
go back to reference Zadeh L (1963) Optimality and non-scalar-valued performance criteria. IEEE Trans Autom Control 8(1):59–60CrossRef Zadeh L (1963) Optimality and non-scalar-valued performance criteria. IEEE Trans Autom Control 8(1):59–60CrossRef
10.
go back to reference Charnes A, Cooper WW, Ferguson RO (1955) Optimal estimation of executive compensation by linear programming. Manage Sci 1(2):138–151MathSciNetCrossRef Charnes A, Cooper WW, Ferguson RO (1955) Optimal estimation of executive compensation by linear programming. Manage Sci 1(2):138–151MathSciNetCrossRef
11.
go back to reference Keeney RL, Raiffa H (1976) Decisions with multiple objectives: preferences and value trade-offs. Wiley, London Keeney RL, Raiffa H (1976) Decisions with multiple objectives: preferences and value trade-offs. Wiley, London
12.
go back to reference Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, New York Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, New York
13.
go back to reference Moh J-S, Chiang D-Y (2000) Improved simulated annealing search for structural optimization. AIAA J 38(10):1965–1973CrossRef Moh J-S, Chiang D-Y (2000) Improved simulated annealing search for structural optimization. AIAA J 38(10):1965–1973CrossRef
14.
go back to reference Liu GP, Han X, Jiang C (2008) A novel multi-objective optimization method based on an approximation model management technique. Comput Methods Appl Mech Eng 197(33):2719–2731CrossRef Liu GP, Han X, Jiang C (2008) A novel multi-objective optimization method based on an approximation model management technique. Comput Methods Appl Mech Eng 197(33):2719–2731CrossRef
15.
go back to reference Li XL, Jiang C, Han X (2011) An uncertainty multi-objective optimization based on interval analysis and its application. China Mech Eng 22(9):1100–1106 Li XL, Jiang C, Han X (2011) An uncertainty multi-objective optimization based on interval analysis and its application. China Mech Eng 22(9):1100–1106 
16.
go back to reference Li XL (2011) Uncertain multi-objective optimization based on non probabilistic convex sets and its application. Master thesis, Hunan University, Changsha Li XL (2011) Uncertain multi-objective optimization based on non probabilistic convex sets and its application. Master thesis, Hunan University, Changsha
17.
go back to reference Liu GP (2008) Multi-objective optimization methods based on the micro genetic algorithm and applications. PhD thesis, Hunan University, Changsha Liu GP (2008) Multi-objective optimization methods based on the micro genetic algorithm and applications. PhD thesis, Hunan University, Changsha
18.
go back to reference Krishnakumar K (1990) Micro-genetic algorithms for stationary and non-stationary function optimization. In: 1989 symposium on visual communications, image processing, and intelligent robotics systems. Philadelphia, PA, United States. Krishnakumar K (1990) Micro-genetic algorithms for stationary and non-stationary function optimization. In: 1989 symposium on visual communications, image processing, and intelligent robotics systems. Philadelphia, PA, United States.
19.
go back to reference Li FY, Li GY, Zheng G (2010) Uncertain multi-objective optimization method based on interval. Chin J Solid Mech 31(1):86–93CrossRef Li FY, Li GY, Zheng G (2010) Uncertain multi-objective optimization method based on interval. Chin J Solid Mech 31(1):86–93CrossRef
20.
go back to reference Jiang C, Bai YC, Han X, Ning HM (2010) An efficient reliability-based optimization method for uncertain structures based on non-probability interval model. Comput, Mater Contin (CMC) 18(1):21–42 Jiang C, Bai YC, Han X, Ning HM (2010) An efficient reliability-based optimization method for uncertain structures based on non-probability interval model. Comput, Mater Contin (CMC) 18(1):21–42
Metadata
Title
Interval Multi-objective Optimization
Authors
Chao Jiang
Xu Han
Huichao Xie
Copyright Year
2021
Publisher
Springer Singapore
DOI
https://doi.org/10.1007/978-981-15-8546-3_11

Premium Partner