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MULTISTAGE STOCHASTIC programming WITH RECOURSE AS mathematical-programming IN AN L SPACE

SIAM JOURNAL ON CONTROL 1976年第3期14卷 528-537页

作者： OLSEN, P INST DEF ANAL ARLINGTONVA 22202

Multistage stochastic programming with recourse has been formulated in terms of a recursive sequence of parameterized, finite-dimensional mathematical programming problems. It has also been formulated as mathematical ... 详细信息

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关键词： mathematical programming

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The tensor product: A mathematical programming language for FFTs and other fast DSP operations

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IEEE SIGNAL PROCESSING MAGAZINE 1992年第1期9卷 40-48页

作者： Granata, J. Conner, M. Tolimieri, R. CUNY Ctr Large Sclae Computat New York NY 10021 USA CUNY Herbert H Lehman Coll New York NY 10021 USA Univ Connecticut Storrs CT 06269 USA

The use of the tensor product as a tool for modeling and developing digital signal processing algorithms is discussed. A precise mathematical definition of the tensor product is established along with several important properties. Special tensor matrices suited for implementation on various computer architectures are then identified. The notion of the stride permutation matrix is introduced as a method of modeling operand addressing. An important connection between tensor matrices and stride permutations is made explicit. By identifying particular tensor matrices suited for implementation on a given machine the tensor product has been transformed from a mathematical convenience into an extremely useful tool for matching algorithms to computer architectures. Several design examples in which a tensor matrix multiplication is implemented on several radically different types of computer architectures are presented.< >

关键词： Tensile stress mathematical programming Flexible printed circuits Digital signal processing Signal processing algorithms Algorithm design and analysis Computer architecture Computer languages Design optimization Fast Fourier transforms

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Granular contact dynamics using mathematical programming methods

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COMPUTERS AND GEOTECHNICS 2012年 43卷 165-176页

作者： Krabbenhoft, K. Lyamin, A. V. Huang, J. Vicente da Silva, M. Univ Newcastle Ctr Geotech Sci & Engn Callaghan NSW 2308 Australia Univ So Denmark Dept Ind & Civil Engn Odense Denmark Univ Nova Lisboa Dept Civil Engn P-1200 Lisbon Portugal

A class of variational formulations for discrete element analysis of granular media is presented. These formulations lead naturally to convex mathematical programs that can be solved using standard and readily available tools. In contrast to traditional discrete element analysis, the present granular contact dynamics formulation uses an implicit time discretization, thus allowing for large time steps. Moreover, in the limit of an infinite time step, the general dynamic formulation reduces to a static formulation that is useful in simulating common quasi-static problems such as triaxial tests and similar laboratory experiments. A significant portion of the paper is dedicated to exploring the consequences of the associated frictional sliding rule implied by the variational formulation adopted. In this connection, a new interior-point algorithm for general linear complementarity problems is developed and it is concluded that the associated sliding rule, in the context of granular contact dynamics, may be viewed as an artifact of the time discretization and that the use of an associated flow rule at the particle scale level generally is physically acceptable. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Contact dynamics Discrete element method (DEM) mathematical programming Optimization Second-order cone programming

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Integrating machine learning and mathematical programming for efficient optimization of operating conditions in organic Rankine cycle (ORC) based combined systems

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ENERGY 2023年 281卷

作者： Zhou, Jianzhao Chu, Yin Ting Ren, Jingzheng Shen, Weifeng He, Chang Hong Kong Polytech Univ Dept Ind & Syst Engn Hong Kong Peoples R China Chongqing Univ Dept Chem & Chem Engn Chongqing 400044 Peoples R China Sun Yat Sen Univ Guangdong Engn Ctr Petrochem Energy Conservat Sch Mat Sci & Engn Guangzhou 510275 Peoples R China

Operations optimization in an organic Rankine cycle (ORC) based combined system is important while computationally difficult by using mechanistic models due to complex nonlinearities and constraints. In this study, a hybrid framework integrating machine learning and mathematical programming has been proposed to optimize the operations of the system for the best exergy performance. The combined system is first decomposed into two single ORCs for reducing computational complexity. Classification models and regression models based on artificial neural network (ANN) and linear regression are developed using simulation data, where classifications can be employed for high-throughput screening feasible inputs which meet the mechanistic constraints in ORC. The results demonstrate high performances of machine learning with at least 99% accuracies for classifications and with mean relative errors of less than 1% for regressions. These data-driven models and the relation of two ORCs were then embedded with mathematical programming for optimization and maximum net exergy of 28.66 MW is obtained. By linear expansion of ReLU operators in ANN, mixed-integer linear programming (MILP) based on machine learning models achieve high efficiency with similar to 0.1 s required for optimization compared to mixed-integer nonlinear programming (MINLP) (>1000 s) and heuristic optimization based on mechanistic models (>10 h).

关键词： Organic Rankine cycle Process simulation Optimization Machine learning mathematical programming

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Aggregating classifiers with mathematical programming

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2004年第4期47卷 791-807页

作者： Adem, J Gochet, W Katholieke Univ Leuven Dept Appl Econ B-3000 Louvain Belgium

Bagging and boosting are popular and often successful ways to improve the performance of a classifier by means of aggregation. Classifiers can also be aggregated by means of an efficient and flexible mathematical programming model. This data-based approach guarantees that the aggregated classifier will be at least as good as the best predictor on the design data set for a user-defined criterion function. The mathematical programming approach is evaluated on real-world data sets from different contexts such as medical diagnosis, image segmentation and handwritten digit recognition. The real-world examples show that the approach can outperform both bagging and boosting. (C) 2003 Elsevier B.V. All rights reserved.

关键词： supervised classification bagging boosting mathematical programming computational efficiency

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System network planning expansion using mathematical programming, genetic algorithms and tabu search

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ENERGY CONVERSION AND MANAGEMENT 2008年第6期49卷 1557-1566页

作者： Sadegheih, A. Drake, P. R. Univ Yadz Dept Ind Engn Yadz Iran Univ Liverpool Sch Management E Business & Operat Management Div Liverpool L69 3BX Merseyside England

In this paper, system network planning expansion is formulated for mixed integer programming, a genetic algorithm (GA) and tabu search (TS). Compared with other optimization methods, GAs are suitable for traversing large search spaces, since they can do this relatively rapidly and because the use of mutation diverts the method away from local minima, which will tend to become more common as the search space increases in size. GA's give an excellent trade off between solution quality and computing time and flexibility for taking into account specific constraints in real situations. TS has emerged as a new, highly efficient, search paradigm for finding quality solutions to combinatorial problems. It is characterized by gathering knowledge during the search and subsequently profiting from this knowledge. The attractiveness of the technique comes from its ability to escape local optimality. The cost function of this problem consists of the capital investment cost in discrete form, the cost of transmission losses and the power generation costs. The DC load flow equations for the network are embedded in the constraints of the mathematical model to avoid sub-optimal solutions that can arise if the enforcement of such constraints is done in an indirect way. The solution of the model gives the best line additions and also provides information regarding the optimal generation at each generation point. This method of solution is demonstrated on the expansion of a 10 bus bar system to 18 bus bars. Finally, a steady-state genetic algorithm is employed rather than generational replacement, also uniform crossover is used. (C) 2007 Elsevier Ltd. All rights reserved.

关键词： system planning tabu search genetic algorithm mathematical programming artificial intelligence iterative improvement methods

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Hybrid Nested Partitions and mathematical programming Approach and Its Applications

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2008年第4期5卷 573-586页

作者： Pi, Liang Pan, Yunpeng Shi, Leyuan Univ Wisconsin Dept Ind & Syst Engn Madison WI 53706 USA CombineNet Inc Pittsburgh PA 15222 USA Tsinghua Univ Ctr Intelligent & Networked Syst Beijing 100084 Peoples R China

Large-scale discrete optimization problems are difficult to solve, especially when different kinds of real constraints are considered. Conventionally, standard mathematical programming is a general approach for discrete optimization, but may suffer from the unacceptable long solution time in applications. On the other hand, some heuristics/metaheuristics methods are more powerful in finding approximate solutions efficiently, but mostly are problem and constraint dependent. In this paper, we develop a new Hybrid Nested Partitions and mathematical programming Approach, which creates compliance between mathematical programming and the heuristics/metaheuristics methods. Potentially applicable to many different types of problems, the hybrid approach can provide approximate solutions efficiently, and in the meantime can easily handle different kinds of constraints. The applications of the hybrid approach to the local pickup and delivery problem (LPDP) and the discrete facility location problem (DFLP) are presented in this paper.

关键词： Discrete facility location problem discrete optimization problem mathematical programming nested partitions pickup and delivery problem

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A BRANCH AND BOUND ALGORITHM FOR EXTREME POINT mathematical-programming PROBLEMS

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DISCRETE APPLIED MATHEMATICS 1985年第3期11卷 265-280页

作者： SEN, S SHERALI, HD VIRGINIA POLYTECH INST & STATE UNIV DEPT IND ENGN & OPERAT RESBLACKSBURGVA 24061

This paper deals with a class of nonconvex mathematical programs called Extreme Point mathematical Programs. This class is a generalization of zero-one integer programs and is a special case of the Generalized Lattice Point Problem, and finds applications in various areas such as production scheduling, load balancing, and concave programming. The current work existing on this class of problems is limited to certain dual types of extreme point ranking methods (which do not find a feasible solution until optimality) and some non-convergent cutting plane algorithms. No computational experience exists. This paper develops a finitely convergent branch and bound algorithm for solving the problem. The principles involved in the design of this algorithm are quite general and apply to a wider class of mathematical programs including the Generalized Lattice Point Problem. A random problem generator is described which is capable of generating problems of varying levels of difficulty. Computational experience on such problems is provided.

关键词： mathematical programming

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History of mathematical programming in the USSR: analyzing the phenomenon

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mathematical programming 2002年第3期91卷 401-416页

作者： Polyak, BT Inst Control Sci Moscow Russia

I am not a historian;these are just reminiscences of a person involved in the development of optimization theory and methods in the former USSR. I realize that my point of view may be very personal;however, I am tryin... 详细信息

关键词： mathematical programming

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Synthesis of mass exchange networks: A novel mathematical programming approach

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COMPUTERS & CHEMICAL ENGINEERING 2018年 115卷 226-232页

作者： Angel Velazquez-Guevara, Miguel Ramon Uribe-Ramirez, Agustin Israel Gomez-Castro, Fernando Maria Ponce-Ortega, Jose Hernandez, Salvador Gabriel Segovia-Hernandez, Juan Arturo Alfaro-Ayala, Jorge de Jesus Ramirez-Minguela, Jose Univ Guanajuato Dept Ingn Quim Div Ciencias Nat & Exactas Campus GuanajuatoNoria Alta S-N Col Noria Alta Guanajuato 36050 Mexico Univ Michoacana Fac Ingn Quim Div Estudios Posgrad Francisco J Mugica S-N Morelia 58060 Michoacan Mexico

Mass integration is an efficient tool to prevent pollution derived from chemical processes. In recent years, several advances have been reported in methodologies for the design of mass exchange networks (MENs), using approaches as the pinch point and mathematical programming. Recently, simultaneous design and optimization methodologies have been proposed. The design methods based on simultaneous optimization offer the possibility of synthetizing MENs in a single step, formulating the synthesis problem as a mixed-integer nonlinear programming problem (MINLP). In this work, a MINLP model for the synthesis of mass exchange networks is presented. The model is based on a superstructure represented with disjunctions. The proposed superstructure is obtained from a state-task-network representation and is applied to a process for copper removal from an etching process. The obtained mass exchange network showed a lower total annual cost than the networks previously reported for the same process. (c) 2018 Elsevier Ltd. All rights reserved.

关键词： Mass exchange networks State-task-network representation mathematical programming

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