The Experts below are selected from a list of 65232 Experts worldwide ranked by ideXlab platform
Jan Weglarz - One of the best experts on this subject based on the ideXlab platform.
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Mathematical Programming formulations for machine scheduling: A survey
European Journal of Operational Research, 1991Co-Authors: Jacek Blazewicz, Moshe Dror, Jan WeglarzAbstract:Abstract Machine scheduling was and still is a rich and promising field for research with applications in manufacturing, logistics, computer architecture, communications, etc. Combinatorial complexity theory has now classified the great majority of known machine scheduling problems as ‘easy’ or ‘very hard’. However, in most cases, Mathematical Programming models have not accompanied the algorithmic developments for solving ‘easy’ scheduling problems, nor have they facilitates solutions for ‘hard’ problems. Nevertheless, the analysis of the Mathematical Programming models for some hard combinatorial problems together with their polyhedral properties has enabled important computational advances for such problems as the TSP. In order to assess the present status and the solution potential of Mathematical Programming formulations for machine scheduling, we have compiled a systematic, consistent survey of formulations. The discussion has been developed in tandem with the classification of a given problem's complexity, since ‘solvability’ (i.e., the status of a problem as P or NP-hard) generally cannot be easily assessed from the formulation itself. A number of excellent survey papers on machine scheduling have appeared over the years (see the reference list), but none of them has been focused on Mathematical formulations. This survey is the first one that attempts to compile a large number of Mathematical Programming formulations for scheduling into a single paper to ease the task of model building and testing scheduling formulations. Both, a newcomer and experienced researcher can use it as a reference point. Ultimately, Mathematical Programming formulations for scheduling problems might be used as a stepping stone to computational advances for some hard problems.
R. Fourer - One of the best experts on this subject based on the ideXlab platform.
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Database structures for Mathematical Programming models
Decision Support Systems, 1997Co-Authors: R. FourerAbstract:Abstract In the design and use of large-scale Mathematical Programming systems, a substantial portion of the effort has no direct relation to the variables and constraints, but is instead concerned with the description, manipulation and display of data. Established principles of database design do not apply directly to Mathematical Programming, however, because there are significant differences of organization and content between the data for an optimization model and the data for a conventional database application such as payroll or order entry. The goal of this work is thus to derive and elucidate fundamental principles of database construction for the specific case of large-scale Mathematical Programming. Alternative formulations of a steel mill planning model, combining aspects of production and network linear Programming, are presented as an example; these formulations are shown to correspond to relational and hierarchical database schemes that have contrasting strengths and weaknesses. A particular implementation of a database system for steel optimization is then introduced and discussed, and a variety of promising generalizations are surveyed.
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Database structures for a class of Mathematical Programming models
Proceedings of the Twenty-Fourth Annual Hawaii International Conference on System Sciences, 1991Co-Authors: R. FourerAbstract:The maintenance of large-scale Mathematical Programming model has long been recognized to involve a substantial task of data management. This paper aims to elucidate some of the principles of database construction for large-scale Mathematical Programming, by use of a linear Programming example that incorporates aspects of production and network models. Two likely algebraic formations are described, and are shown to correspond to relational and hierarchical database schemes that have contrasting strengths and weaknesses.
Alexander Meeraus - One of the best experts on this subject based on the ideXlab platform.
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An extended Mathematical Programming framework
Computers & Chemical Engineering, 2009Co-Authors: Michael C. Ferris, Steven P. Dirkse, Jan-hendrick Jagla, Alexander MeerausAbstract:Abstract Extended Mathematical programs are collections of functions and variables joined together using specific optimization and complementarity primitives. This paper outlines a mechanism to describe such an extended Mathematical program by means of annotating the existing relationships within a model to facilitate higher level structure identification. The structures, which often involve constraints on the solution sets of other models or complementarity relationships, can be exploited by modern large scale Mathematical Programming algorithms for efficient solution. A specific implementation of this framework is outlined that communicates structure from the GAMS modeling system to appropriate solvers in a computationally beneficial manner. Example applications are taken from chemical engineering.
Panos M. Pardalos - One of the best experts on this subject based on the ideXlab platform.
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Mathematical Programming in Machine Learning
2013Co-Authors: O. Erhun Kundakcioglu, Panos M. PardalosAbstract:There have been dramatic improvements in the algorithms and techniques used in machine learning over the last twenty years. Numerous methods have been developed that utilize Mathematical Programming techniques that are well known to operations researchers. Because understanding of the fundamentals of Mathematical Programming is essential for theoretical computer scientists, this book intends to provide this audience a strong introduction to the analysis and Mathematical Programming techniques used in machine learning. Additionally, the book offers operations researchers various examples of machine learning's applications to optimization and modeling. Its Primary Audience for Work are: Researchers and practitioners in fields of Computer Science and Operations Research.
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Mathematical Programming Techniques for Sensor Networks
Algorithms, 2009Co-Authors: Alexey Sorokin, Nikita Boyko, Vladimir Boginski, Stan Uryasev, Panos M. PardalosAbstract:This paper presents a survey describing recent developments in the area of Mathematical Programming techniques for various types of sensor network applications. We discuss Mathematical Programming formulations associated with these applications, as well as methods for solving the corresponding problems. We also address some of the challenges arising in this area, including both conceptual and computational aspects.
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7 Mathematical Programming — A computational perspective
Handbook of Statistics, 1993Co-Authors: William W. Hager, Reiner Horst, Panos M. PardalosAbstract:Publisher Summary Mathematical Programming studies the properties of optimization problems and techniques for computing their solution. A typical optimization problem has the form where the real-valued function f(x) is called either the “objective function” or the “cost function” and C is the constraint set. Because maximizing f(x) is equivalent to minimizing -f(x) , a maximization problem can always be posed as a minimization problem. The chapter focuses on the case where x is a vector with n components. Although in practice the constraint set C can be contained in an infinite dimensional space, the infinite dimensional problem must be discretized when a solution is computed numerically leading to a finite dimensional problem. Consequently the theory associated with finite dimensional optimization is relevant to infinite dimensional problems. Moreover, many finite dimensional algorithms extent directly to infinite dimensions. Mathematical Programming has many applications in statistics. A linear program is a Mathematical Programming problem in which the cost function is linear and the constraint set is a polytope. The simplex method is one of the most popular methods for solving linear Programming problems. A quadratic program is a Mathematical Programming problem in which the cost function is quadratic and the constraint set is a polytope. A special class of algorithms for the linear complementarity problem has been developed based on iterative matrix splitting techniques. Because of the connection between quadratic Programming and the linear complementarity problem, these techniques are also applicable to the corresponding quadratic programs.
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Mathematical Programming Formulations for Problems in Genomics and Proteomics
Data Mining in Biomedicine, 1Co-Authors: Cláudio N. Meneses, Carlos A. S. Oliveira, Panos M. PardalosAbstract:Computational biology problems generally involve the determination of discrete structures over biological configurations determined by genomic or proteomic data. Such problems present great opportunities for application of Mathematical Programming techniques. We give an overview of formulations employed for the solution of problems in genomics and proteomics. In particular, we discuss Mathematical Programming formulations for string comparison and selection problems, with high applicability in biological data processing.
Jacek Blazewicz - One of the best experts on this subject based on the ideXlab platform.
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Mathematical Programming formulations for machine scheduling: A survey
European Journal of Operational Research, 1991Co-Authors: Jacek Blazewicz, Moshe Dror, Jan WeglarzAbstract:Abstract Machine scheduling was and still is a rich and promising field for research with applications in manufacturing, logistics, computer architecture, communications, etc. Combinatorial complexity theory has now classified the great majority of known machine scheduling problems as ‘easy’ or ‘very hard’. However, in most cases, Mathematical Programming models have not accompanied the algorithmic developments for solving ‘easy’ scheduling problems, nor have they facilitates solutions for ‘hard’ problems. Nevertheless, the analysis of the Mathematical Programming models for some hard combinatorial problems together with their polyhedral properties has enabled important computational advances for such problems as the TSP. In order to assess the present status and the solution potential of Mathematical Programming formulations for machine scheduling, we have compiled a systematic, consistent survey of formulations. The discussion has been developed in tandem with the classification of a given problem's complexity, since ‘solvability’ (i.e., the status of a problem as P or NP-hard) generally cannot be easily assessed from the formulation itself. A number of excellent survey papers on machine scheduling have appeared over the years (see the reference list), but none of them has been focused on Mathematical formulations. This survey is the first one that attempts to compile a large number of Mathematical Programming formulations for scheduling into a single paper to ease the task of model building and testing scheduling formulations. Both, a newcomer and experienced researcher can use it as a reference point. Ultimately, Mathematical Programming formulations for scheduling problems might be used as a stepping stone to computational advances for some hard problems.
