Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-02T18:50:18.113Z Has data issue: false hasContentIssue false
  • English
  • Français

An optimization approach to order of magnitude reasoning

Published online by Cambridge University Press:  27 February 2009

Jayant R. Kalagnanam  and
Urmila M. Diwekar
Jayant R. Kalagnanam
Affiliation:
Center for Energy & Environmental Studies, Department of Engineering & Public Policy, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A.
Urmila M. Diwekar
Affiliation:
Center for Energy & Environmental Studies, Department of Engineering & Public Policy, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

An approach for transforming the order of magnitude relation between two variables into an algebraic equality or inequality constraint is provided. In order to derive the order of magnitude relation between any two variables, a nonlinear optimization problem is solved for the minimum and maximum values of the ratio between the two variables, subject to two classes of constraints. The first class of constraints corresponds to the quantitative model and the second class of constraints corresponds to the qualitative model. The optimization approach is shown to provide more precise inferences as compared to the conventional constraint satisfaction approaches. Moreover, this approach provides a crucial step in developing unified frameworks that allow the incorporation of qualitative information at various levels of abstraction into numerical frameworks used for reasoning with quantitative models.

Keywords

O(M) ReasoningAl and Optimization
Type
Research Article
Information
AI EDAM , Volume 8 , Issue 3 , Summer 1994 , pp. 207 - 217
Copyright
Copyright © Cambridge University Press 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Aelion, V., Kalagnanam, J.R., & Powers, G.J. (1992). Evaluation of operating procedures based on stationary-state stability. Ind. Res. Chem. Res. 31, 2532–2538.CrossRefGoogle Scholar
Berleant, D., & Kuipers, B. (1990). Combined qualitative and numerical simulation with Q3. Proceedings of the Workshop on Qualitative Physics, Lugano, Switzerland, 140–152.Google Scholar
Biegler, L.T. (1983). Simultaneous modular simulation and optimization. Proceedings of Second International Conference on Foundations of Computer Aided Process Design (Westerberg, A. W., & Chien, H.H., Eds.), 369–384. Cast Publications, Ann Arbor, Michigan.Google Scholar
Dague, P., Deves, P., & Raiman, O. (1987). Troubleshooting: When modeling is the trouble. Proceedings of AAAI-87, Seattle, WA, 600–605.Google Scholar
Dague, P. (1993a). Symbolic reasoning with relative orders of magnitude. Proceedings of IJCAI-93, Chambery, France, 1059–1114.Google Scholar
Dague, P. (1993b). Numerical reasoning with relative orders of magnitude. Proceedings of AAAI-93, San Diego, CA, 541–547.Google Scholar
de Kleer, J., & Brown, J.S. (1984). A qualitative physics based on confluences. Artif. Intel. 24, 7–84.Google Scholar
Forbes, K.D. (1984). Qualitative process theory. Artif. Intel., 24, 85–168.CrossRefGoogle Scholar
Forbus, K.D., & Falkenhainer, B. (1990). Self-explanatory simulations: An integration of qualitative and quantitative knowledge. Proceedings of AAAI-90, Boston, MA, 380–387.Google Scholar
Hamscher, W.C. (1991). Modeling digital circuits for troubleshooting. Artif. Intel. 51, 223–272.CrossRefGoogle Scholar
Hoffman, M.O., Cost, T.L., & Whitley, M. (1992). Diagnostic reasoning for shuttle main engine. AI EDAM, 131–148.Google Scholar
Kuipers, B. (1987). Abstraction by time-scale in qualitative simulation, Proceedings of AAAI-87, Seattle, WA, 621–626.Google Scholar
Lang, Y.D., & Biegler, L.T. (1987). A unified algorithm for flowsheet optimization. Comput. Chem. Engrg. 11, 143.Google Scholar
Lhomme, O. (1993). Consistency techniques for numeric CSPs. Proceedings of IJCAI-93, Chambery, France, 232–238.Google Scholar
Mavrovouniotis, M.L., & Stephanopoulos, G. (1987). Reasoning with orders of magnitude and approximate relations. Proceedings of AAAI-87, Seattle, WA, 626–630.Google Scholar
Mavrovouniotis, M.L., & Stephanopoulos, G. (1988). Formal order-of-magnitude reasoning in process engineering. Comput. Chem. Engrg. 12, 867–880.CrossRefGoogle Scholar
Oyeleye, O.O., & Kramer, M.A. (1987). Qualitative simulation of process plants. Proc. of 10th IFAC World Cong. Autom. Contr. 6, 324–329.Google Scholar
Raiman, O. (1986). Order of magnitude reasoning. Proceedings of AAAI-86, Philadelphia, PA, 100–104.Google Scholar
Raiman, O. (1991). Order of magnitude reasoning. Artif. Intel. 51, 11–38.CrossRefGoogle Scholar
Raman, R., & Grossman, I.E. (1991). Relation between MILP modelling and logical inference for chemical process synthesis. Comput. Chem. Engrg. 15(2), 73–84.Google Scholar
Struss, P. (1990). Mathematical aspects of qualitative reasoning. In Readings in Qualitative Reasoning, pp. 288–305. Morgan Kaufmann, San Mateo, CA.Google Scholar
Subrahmanian, E., Rychener, M.D., Wiss, J.W., & Lasky, S.J. (1988). Diagnosis of a complex machine: Integration of evidential with causal reasoning and simulation. Proceedings of 1988 ASME Int. Conf. on Computers in Engineering, San Francisco, CA, American Society for Mechanical Engineers.Google Scholar
Ulerich, N.C. (1990). Diagraph and fault tree technique for on-line process diagnosis. Ph.D. Thesis. Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA.Google Scholar
Venkatasubrahmanian, V., & Rich, S.H. (1987). Integrating heuristic and deep-level knowledge in expert systems for process fault diagnosis. Proceedings of AAAI Workshop AI in Process Engineering, New York, Columbia University.Google Scholar
Williams, B.C. (1991). A theory of interactions: Unifying qualitative and quantitative algebraic reasoning. Artif. Intel. 51, 39–94.Google Scholar