Abstract
Numerous industrial problems can be modelled as MINLP (Mixed Integer NonLinear Programming) problems combining both numeric and integer variables: design of water transmission networks, automobile, aircraft, etc. [1]. These problems are really hard to solve since they combine both the combinatorial nature of mixed integer programming and the intrinsic difficulty of nonlinear programs. Several methods were proposed to solve these problems: branch-and-bound, extended cutting plane methods, and generalised Bender’s decomposition, etc. But industrial applications need more than solving problems. Problems can be dynamic, this implies that constraints may be added or removed dynamically. Moreover, if no solution is found, the user often needs to know why the problem is over-constrained, or why the expected solution is inconsistent.
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References
Bussieck, M.R., Pruessner, A.: Mixed-integer nonlinear programming. In: SIAG/OPT Newsletter: Views & News (2003)
Jussien, N., Lhomme, O.: Dynamic domain splitting for numeric CSP. In: European Conference on Artificial Intelligence, pp. 224–228 (1998)
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© 2004 Springer-Verlag Berlin Heidelberg
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Rochart, G. (2004). Explanations and Numeric CSPs. In: Wallace, M. (eds) Principles and Practice of Constraint Programming – CP 2004. CP 2004. Lecture Notes in Computer Science, vol 3258. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30201-8_84
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DOI: https://doi.org/10.1007/978-3-540-30201-8_84
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