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Modelling-Driven Optimization Problems with Uncertainty Tolerance and Their Solution Strategies: A Risk-Management Perspective in the Circulating and Spiral-up Systems Approach

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Innovative Systems Approach for Facilitating Smarter World

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Abstract

Working in the framework of the circulating and spiral-up systems approach, we attempt to embed modelling procedures, used to construct approximate models of input–output relationships at the induction stage, into optimization problems formulated at the abduction stage. In particular, for cases in which uncertainty is present in real systems, we show that, by considering worst-case scenarios from a risk-management perspective, we can formulate optimization problems with embedded modelling procedures that might be termed robust modelling. As a solution strategy for these problems, we consider a constraint-relaxation method—the scenario approach—and discuss how this strategy fits into the framework of the circulating and spiral-up systems approach.

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References

  • Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust optimization. Princeton University Press

    Book  MATH  Google Scholar 

  • Bishop CM (2006) Pattern recognition and Machine learning. Springer, NewYork, p 738

    MATH  Google Scholar 

  • Blankenship JW, Falk JE (1976) Infinitely constrained optimization problems. J Optim Theory Appl 19(2):261–281

    Article  MathSciNet  MATH  Google Scholar 

  • Campi MC, Garatti S, Prandini M (2009) The scenario approach for systems and control design. Annu Rev Control 33(2):149–157

    Article  Google Scholar 

  • Freund Y, Schapire RE (1997) A decision-theoretic generation of on-line learning and application to boosting. J Comput Syst Sci 55(1):119–139

    Article  MATH  Google Scholar 

  • Gilboa I (2009) Theory of decision under uncertainty. Cambridge University Press

    Book  MATH  Google Scholar 

  • Girosi F, Poggio T (1990) Networks and the best approximation property. Biol Cybern 63(3):169–176

    Article  MathSciNet  MATH  Google Scholar 

  • Haimes YY, Wismer DA (1972) A computational approach to the combined problem of optimization and parameter identification. Automatica 8(5):337–346

    Article  MATH  Google Scholar 

  • Hartman EJ, Keeler JD, Kowalski JM (1990) Layered neural networks with Gaussian hidden units as universal approximations. Neural Comput 2(2):210–215

    Article  Google Scholar 

  • Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2(5):359–366

    Article  MATH  Google Scholar 

  • Kaihara T (2021) New trends in systems approaches to realized smarter world. In: Kaihara T, Kita H, Takahashi S (eds) Innovative systems approach for designing smarter world. Springer, Singapore, pp 1–15

    Chapter  Google Scholar 

  • Kitayama S, Yasuda K, Yamazaki K (2008) The integrative optimization by RBF network and particle swarm optimization. IEEJ Trans Electron Inf Syst 128(4):636–645. (in Japanese)

    Google Scholar 

  • McGrew DR, Haimes YY (1974) Parameter solution to the joint system and optimization problem. J Optim Theory Appl 13(5):582–605

    Article  MathSciNet  MATH  Google Scholar 

  • Myers RH, Montgomery DC (1995) Response surface methodology: process and product optimization using designed experiments. Wiley Interscience

    MATH  Google Scholar 

  • Roberts PD (1977) Multilevel approaches to the combined problem of system optimization and parameter identification. Int J Syst Sci 8(3):273–299

    Article  MathSciNet  MATH  Google Scholar 

  • Shimizu K, Aiyoshi E (1980) Necessary conditions for min-max problems and algorithms by relaxation procedure. IEEE Trans Autom Control 25(1):62–66

    Article  MathSciNet  MATH  Google Scholar 

  • Shimizu K, Aiyoshi E (1982) A new solution to optimization-satisfaction problems by a penalty method. Automatica 18(1):37–46

    Article  MathSciNet  MATH  Google Scholar 

  • Takeda A, Mitsugi H, Kanamori T (2013) A unified classification model based on robust optimization. Neural Comput 12(3):759–804

    Article  MathSciNet  MATH  Google Scholar 

  • Vapnik V (2008) The nature of statistical learning theory. Springer

    MATH  Google Scholar 

  • Xu H, Caramanis C, Mannor S (2009) Robustness and regularization of support vector machine. J Mach Learn Res 10(51):1485–1510

    MathSciNet  MATH  Google Scholar 

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Aiyoshi, E., Yasuda, K., Tamura, K. (2023). Modelling-Driven Optimization Problems with Uncertainty Tolerance and Their Solution Strategies: A Risk-Management Perspective in the Circulating and Spiral-up Systems Approach. In: Kaihara, T., Kita, H., Takahashi, S., Funabashi, M. (eds) Innovative Systems Approach for Facilitating Smarter World. Design Science and Innovation. Springer, Singapore. https://doi.org/10.1007/978-981-19-7776-3_2

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