Abstract
In many optimization problems there may exist multiple ways in which a particular hierarchical optimization problem can be modeled. In addition, the diversity of hierarchical optimization problems requires different types of multilevel relations between sub-problems. Thus, the approximate and accurate representations and solutions can be integrated. That is, to address the how partial solutions of sub-problems can be reintegrated to build a solution for the main problem. The nature of relations between components differs from one decomposition strategy to another. In this paper, we will investigate the possible links and relationships that may appear between sub-problems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Hertz, A., Lahrichi, N.: A patient assignment algorithm for home care services. Journal of the Operational Research Society 60, 481–495 (2009)
Newell, A., Shaw, C., Simon, H.: The process of creative thinking. In: Gruber, H.E., Terrell, G., Wertheimer, M. (eds.) Contemporary Approaches to Creative Thinking, pp. 63–119. Atherton, New York (1993)
Swamy, C.: The effectiveness of Stackelberg strategies and tolls for network congestion games. In: SODA, pp. 1133–1142 (2007)
Reyniers, D., Tapiero, C.: The Delivery and Control of Quality in Supplier-Producer Contracts. Management Science 41(10), 1581–1590 (1995)
Korzhyk, D, Conitzer, V., Parr, R.: Complexity of computing optimal stackelberg strategies in security resource allocation games. In: The Procedings of the National Conference on Artificial Intelligence (AAAI), Atlanta, GA, USA pp. 805–810 (2002)
Bacchus, F., Yang, Q.: The expected value of hierarchical problem-solving. In: AAAI 1992 Proceedings of the Tenth National Conference on Artificial Intelligence, pp. 369–374 (1992)
Kretinin, K., Egorov, I., Fedechkin, K.: Multi-level robust design optimization fan. In: Workshop CEAS, VrijeUniversiteit Brussels (VUB), Brussels, Belgium (2010)
Leitmann, G.: On general Stackelberg Strategies. Journal of optimization theory and applications 26(4), 637–643 (1978)
Kim, H., Kumar, D., Chen, W., Papalambros, P.: Target feasibility achievement in enterprisedriven hierarchical multidisciplinary design. In: AIAA-2004-4546, 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, New York (2004)
Jemai, J., Chaieb, M., Mellouli, K.: The home care scheduling problem: A modeling and solving issue. In: Proceedings of the 5th International Conference on Modeling, Simulation and Applied Optimization (ICMSAO) (2013)
Sobieski, J., Hafka, R.: Interdisciplinary and multilevel optimum design. In: Mota Soares, C.A. (ed.) Computer Aided Optimal Design: Structural and Mechanical Systems NATO ASI Series. Springer, Berlin, Heidelberg Berlin (1987)
Michalek, J., Papalambros, P.: Weights, norms, and notation in analytical target cascading. Journal of Mechanical Design 127(3), 499–501 (2005)
Bracken, J., McGill, J.: Mathematical programs with optimization problems in the constraints. Operations Research 21, 37–44 (1973)
El-Beltagy, M., John Keane, J.: A comparison of various optimization algorithms on a multilevel problem. Engineering Applications of Artificial Intelligence 12(8), 639–654 (1999)
Mesarovic, M., Takahara, Y., Macko, D.: Theory of Hierarchical Multilevel Systems. Academic Press, New York, USA (1970)
Michelena, N., Park, H., Papalambros, P.: Convergence properties of analytical target cascading. AIAA Journal 41(5), 897–905 (2003)
Braun, R., Kroo, I.: Development and application of the collaborative optimization architecture in a multidisciplinary design environment multidisciplinary design optimization: State of the art. SIAM, 98–116 (1995)
Azarm, S., Li, W.-C.: Multi-level design optimization using global monotonicity analysis. Journal of Mechanical Design 111(2), 259–263 (1989)
Tosserams, S., Etman, L., Rooda, J.: An augmented Lagrangian relaxation for analytical target cascading using the alternating directions method of multipliers. Structural and Multidisciplinary Optimization 31(3), 176–189 (2006)
Roughgarden, T.: Stackelberg scheduling strategies. SIAM J. Comput. 33(2), 332–350 (2004)
Paul Ramasubramanian, P., Kannan, A.: Intelligent Multi-Agent Based Multivariate Statistical Framework for Database Intrusion Prevention System. International Arab Journal of Information Technology 2(3), 239–247 (2005)
Bhaskar, U., Fleischer, L., Anshelevich, E.: A stackelberg strategy for routing flow over time. In: Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 192–201 (2010)
Korilis, Y., Lazar, A., Orda, A.: Achieving network optima using stackelberg routing strategies. IEEE/ACM Trans. Netw. 5(1), 161–173 (1997)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Chaieb, M., Jemai, J., Mellouli, K. (2015). On the Relationships Between Sub Problems in the Hierarchical Optimization Framework. In: Ali, M., Kwon, Y., Lee, CH., Kim, J., Kim, Y. (eds) Current Approaches in Applied Artificial Intelligence. IEA/AIE 2015. Lecture Notes in Computer Science(), vol 9101. Springer, Cham. https://doi.org/10.1007/978-3-319-19066-2_23
Download citation
DOI: https://doi.org/10.1007/978-3-319-19066-2_23
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19065-5
Online ISBN: 978-3-319-19066-2
eBook Packages: Computer ScienceComputer Science (R0)