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Erschienen in:
2015 | OriginalPaper | Buchkapitel
Uncertainty Relationship Analysis for Multi-Parametric Programming in Optimization
verfasst von : Tianxing Cai, Qiang Xu
Erschienen in: Advances in Global Optimization
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Abstract
Uncertainties exist at all levels of the industrial design and manufacturing. Hitherto, all the studies that handle multi-parametric programming (mp-LP, mp-QP, mp-NLP, mp-MILP, and mp-MINLP) treat uncertainties to be independent of each other; while under some circumstances, there might exist some kinds of quantitative relationship among them. There is still a lack of research studies on the relationship between these uncertainties, which can help simply the complexity of multi-parametric optimization problems in terms of reducing the dimension of uncertainty space or the region of uncertainty space.
This paper presents multiple types of relationships among uncertainty parameters, which can be generalized into two categories: strong relationship and weak relationship. The strong relationship can be used to reduce the dimension of uncertainty space while the weak relationship can be used to reduce the region of uncertainty space. With the combination of the above relationships, different kinds of multi-parametric programming problems can be solved more efficiently and effectively toward global optimality.