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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust optimization. Princeton University Press
Bishop CM (2006) Pattern recognition and Machine learning. Springer, NewYork, p 738
Blankenship JW, Falk JE (1976) Infinitely constrained optimization problems. J Optim Theory Appl 19(2):261–281
Campi MC, Garatti S, Prandini M (2009) The scenario approach for systems and control design. Annu Rev Control 33(2):149–157
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
Gilboa I (2009) Theory of decision under uncertainty. Cambridge University Press
Girosi F, Poggio T (1990) Networks and the best approximation property. Biol Cybern 63(3):169–176
Haimes YY, Wismer DA (1972) A computational approach to the combined problem of optimization and parameter identification. Automatica 8(5):337–346
Hartman EJ, Keeler JD, Kowalski JM (1990) Layered neural networks with Gaussian hidden units as universal approximations. Neural Comput 2(2):210–215
Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2(5):359–366
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
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)
McGrew DR, Haimes YY (1974) Parameter solution to the joint system and optimization problem. J Optim Theory Appl 13(5):582–605
Myers RH, Montgomery DC (1995) Response surface methodology: process and product optimization using designed experiments. Wiley Interscience
Roberts PD (1977) Multilevel approaches to the combined problem of system optimization and parameter identification. Int J Syst Sci 8(3):273–299
Shimizu K, Aiyoshi E (1980) Necessary conditions for min-max problems and algorithms by relaxation procedure. IEEE Trans Autom Control 25(1):62–66
Shimizu K, Aiyoshi E (1982) A new solution to optimization-satisfaction problems by a penalty method. Automatica 18(1):37–46
Takeda A, Mitsugi H, Kanamori T (2013) A unified classification model based on robust optimization. Neural Comput 12(3):759–804
Vapnik V (2008) The nature of statistical learning theory. Springer
Xu H, Caramanis C, Mannor S (2009) Robustness and regularization of support vector machine. J Mach Learn Res 10(51):1485–1510
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-981-19-7776-3_2
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-19-7775-6
Online ISBN: 978-981-19-7776-3
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)