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Systematic modeling of discrete-continuous optimization models through generalized disjunctive programming

AICHE JOURNAL 2013年第9期59卷 3276-3295页

作者： Grossmann, Ignacio E. Trespalacios, Francisco Carnegie Mellon Univ Dept Chem Engn Ctr Adv Proc Decis Making Pittsburgh PA 15213 USA

Discrete-continuous optimization problems are commonly modeled in algebraic form as mixed-integer linear or nonlinear programming models. Since these models can be formulated in different ways, leading either to solvable or nonsolvable problems, there is a need for a systematic modeling framework that provides a fundamental understanding on the nature of these models. This work presents a modeling framework, generalized disjunctive programming (GDP), which represents problems in terms of Boolean and continuous variables, allowing the representation of constraints as algebraic equations, disjunctions and logic propositions. An overview is provided of major research results that have emerged in this area. Basic concepts are emphasized as well as the major classes of formulations that can be derived. These are illustrated with a number of examples in the area of process systems engineering. As will be shown, GDP provides a structured way for systematically deriving mixed-integer optimization models that exhibit strong continuous relaxations, which often translates into shorter computational times. (c) 2013 American Institute of Chemical Engineers AIChE J, 59: 3276-3295, 2013

关键词： optimization mixed-integer programming logic-based optimization

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logic-based granular prototyping

Logic-based granular prototyping

引用

26th Annual International Computer Software and Applications Conference

作者： Bargiela, A Pedrycz, W Hirota, K Nottingham Trent Univ Dept Comp & Math Nottingham NG1 4BU England

ISBN: (纸本)0769517277

A fuzzy logic based similarity measure is introduced as a criterion for the identification of structure in data. An important characteristic of the proposed approach is that cluster prototypes are formed and evaluated in the course of the optimization without any a-priori assumptions about the number of clusters. The intuitively straightforward compound optimization criterion of maximizing the overall similarity between data and the prototypes while minimizing the similarity between the prototypes has been adopted. It is shown that the partitioning of the pattern space obtained in the course of the optimization is more intuitive than the one obtained for the standard FCM. The local properties of clusters (in terms of the ranking order of features in the multidimensional pattern space) are captured by the weight vector associated with each cluster prototype, The weight vector is then used for the construction of interpretable information granules.

关键词： granular prototyping clustering logic-based optimization data mining

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