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A mixed integer programming approach to the tensor complementarity problem

JOURNAL OF GLOBAL OPTIMIZATION 2019年第4期73卷 789-800页

作者： Du, Shouqiang Zhang, Liping Qingdao Univ Sch Math & Stat Qingdao 266071 Peoples R China Tsinghua Univ Dept Math Sci Beijing 100084 Peoples R China

The tensor complementarity problem is a special instance of nonlinear complementarity problems, which has many applications. How to solve the tensor complementarity problem, via analyzing the structure of the related tensor, is one of very important research issues. In this paper, we propose a mixed integer programming approach for solving the tensor complementarity problem. We reformulate the tensor complementarity problem as an equivalent mixed integer feasibility problem. Based on the reformulation, some conditions for the solution existence and some solution properties of the tensor complementarity problem are given. We also prove that the tensor complementarity problem, corresponding to a positive definite diagonal tensor, has a unique solution. Finally, numerical results are reported to indicate the efficiency of the proposed algorithm.

关键词： Tensor complementarity problem mixed integer programming Unique solution Positive definite 15A69 90C11

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Automatic Generation of mixed integer programming for Scheduling Problems Based on Colored Timed Petri Nets

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2018年第2期E101A卷 367-372页

作者： Porco, Andrea Veronica Ushijima, Ryosuke Nakamura, Morikazu Univ Ryukyus Grad Course Sci & Engn Nishihara Okinawa 9030213 Japan Univ Ryukyus Dept Engn Comp Sci & Intelligent Syst Nishihara Okinawa 9030213 Japan

This paper proposes a scheme for automatic generation of mixed-integer programming problems for scheduling with multiple resources based on colored timed Petri nets. Our method reads Petri net data modeled by users, extracts the precedence and conflict relations among transitions, information on the available resources, and finally generates a mixed integer linear programming for exactly solving the target scheduling problem. The mathematical programing problems generated by our tool can be easily inputted to well-known optimizers. The results of this research can extend the usability of optimizers since our tool requires just simple rules of Petri nets but not deep mathematical knowledge.

关键词： scheduling problem mixed integer programming Petri nets colored timed Petri net automatic generation

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Deep Reinforcement Learning Acceleration for Real-Time Edge Computing mixed integer programming Problems

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IEEE ACCESS 2022年 10卷 18526-18543页

作者： Gerogiannis, Gerasimos Birbas, Michael Leftheriotis, Aimilios Mylonas, Eleftherios Tzanis, Nikolaos Birbas, Alexios Univ Patras Dept Elect & Comp Engn Patras 26500 Greece Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA

In this work, we present the design and implementation of an ultra-low latency Deep Reinforcement Learning (DRL) FPGA based accelerator for addressing hard real-time mixed integer programming problems. The accelerator exhibits ultra-low latency performance for both training and inference operations, enabled by training-inference parallelism, pipelined training, on-chip weights and replay memory, multi-level replication-based parallelism and DRL algorithmic modifications such as distribution of training over time. The design principles can be extended to support hardware acceleration for other relevant DRL algorithms (embedding the experience replay technique) with hard real time constraints. We evaluate the accuracy of the accelerator in a task offloading and resource allocation problem stemming from a Mobile Edge Computing (MEC/5G) scenario. The design has been implemented on a Xilinx Zynq Ultrascale+ MPSoC ZCU104 evaluation kit using High Level Synthesis. The accelerator achieves near optimal performance and exhibits a 10-fold decrease in training-inference execution latency when compared to a high-end CPU-based implementation.

关键词： Training Inference algorithms Real-time systems Artificial neural networks Task analysis Resource management Field programmable gate arrays Accelerator deep reinforcement learning edge computing FPGA high level synthesis mixed integer programming 5G

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Classification of Dantzig-Wolfe reformulations for binary mixed integer programming problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2010年第2期204卷 251-254页

作者： Jans, Raf HEC Montreal & GERAD Montreal PQ H3T 2A7 Canada

In this note, we provide a classification of Dantzig-Wolfe reformulations for Binary mixed integer programming Problems. We specifically focus on modeling the binary conditions in the convexification approach to the Dantzig-Wolfe decomposition. For a general Binary mixed integer programming problem, an extreme point of the overall problem does not necessarily correspond to an extreme point of the subproblem. Therefore, the binary conditions cannot in general be imposed on the new master problem variables but must be imposed on the original binary variables. In some cases, however, it is possible to impose the binary restrictions directly on the new master problem variables. The issue of imposing binary conditions on the original variables versus the master problem variables has not been discussed systematically for MIP problems in general in the literature and most of the research has been focused on the pure binary case, The classification indicates in which cases you can, and cannot, impose binary conditions on the new master problem variables. (C) 2009 Elsevier B.V. All rights reserved.

关键词： mixed integer programming Dantzig-Wolfe decomposition Reformulation

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Parallel mixed integer programming-finite element method technique for global design optimization of power transformers

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IEEE TRANSACTIONS ON MAGNETICS 2008年第6期44卷 1022-1025页

作者： Amoiralis, Eleftherios I. Tsili, Marina A. Georgilakis, Pavlos S. Kladas, Antonios G. Souflaris, Athanassios T. Natl Tech Univ Athens Fac Elect & Comp Engn GR-15780 Athens Greece Tech Univ Crete Dept Prod Engn & Management GR-73100 Khania Greece Schneider Elect AE GR-32011 Elvim Plant Inofyta Greece

Transformer design optimization is determined by minimizing the transformer cost taking into consideration constraints imposed both by international specifications and customer needs. The main purpose of this work is the development and validation of an optimization technique based on a parallel mixed integer nonlinear programming methodology in conjunction with the finite element method, in order to reach a global optimum design of wound core power transformers. The proposed optimization methodology has been implemented into software able to provide a global feasible solution for every given set of initial values for the design variables, rendering it suitable for application in the industrial transformer design environment.

关键词： design methodology finite element methods mixed integer programming optimization methods power transformers

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A flexible mixed integer programming-based system for real-world nurse rostering

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JOURNAL OF SCHEDULING 2022年第1期25卷 59-88页

作者： Boedvarsdottir, Elin Bjoerk Bagger, Niels-Christian Fink Hoffner, Laura Elise Stidsen, Thomas J. R. Tech Univ Denmark Dept Technol Management & Econ Anker Engelundsvej 1 DK-2800 Lyngby Denmark Fink Optimizat ApS Valdemarskrogen 44 DK-2860 Soborg Denmark Dept Data & Dev Support Alleen 15 DK-4180 Soro Region Zealand Denmark

Researchers have studied the nurse rostering problem for multiple decades. Initially, the formulations were rather primitive including only a few necessary restrictions, but down the road, the formulations have become more complex. Nonetheless, a fraction of the research reaches implementation in practice, and many wards still schedule nurses manually. In this article, we introduce a flexible nurse rostering system that employs mathematical optimization to automatically schedule nurses to shifts. We have developed this system in collaboration with practitioners to fully match their needs. The system consists of a comprehensive mixed integer programming (MIP) model along with a flexible framework. In addition to common constraints from the literature, the mathematical formulation includes three new constraints that further encourage healthy work schedules for each nurse. Additionally, we have reformulated some common constraints from the literature and allow for a complex shift structure that matches the needs of real hospital wards. This flexibility results in increased adaptability for different wards with different needs and is crucial to address the complex nurse rostering problem that practitioners face. We have successfully implemented this system in two wards at two Danish hospitals. We present the MIP model along with computational results for 12 real-world rostering instances. Furthermore, we discuss the practical impact of this system and provide general feedback from the practitioners using it. Overall, the results illustrate the capabilities of the system to tackle diverse nurse rostering instances and produce outstanding results.

关键词： Nurse rostering Automatic scheduling mixed integer programming Preference scheduling OR applications in healthcare

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A mixed integer programming approach to a square fully fuzzy linear equation

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2016年第3期31卷 2009-2015页

作者： Ahlatcioglu, Mehmet Albayrak, Inci Kocken, Hale Gonce Ozkok, Beyza Ahlatcioglu Yildiz Tech Univ Dept Math Istanbul Turkey Yildiz Tech Univ Dept Engn Math Istanbul Turkey

In this paper, a new method is proposed to find the feasible (strong) fuzzy solution of a square (n x n) fully fuzzy linear equation system (FFLS) with triangular fuzzy numbers. The main purpose of the proposed method is to remove all the sign restrictions on the parameters and variables. Our method, which is based on the multiplication of two arbitrary triangular fuzzy numbers, converts the FFLS to a mixed integer programming problem. The method is illustrated with numerical examples.

关键词： Linear equation system fuzzy number fuzzy decision making mixed integer programming

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Projected mixed integer programming formulations for unit commitment problem

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2015年 68卷 195-202页

作者： Yang, Linfeng Jian, Jinbao Wang, Yuanyuan Dong, Zhaoyang Guangxi Univ Sch Comp Elect & Informat Nanning 530004 Peoples R China Yulin Normal Univ Sch Math & Informat Sci Yulin 537000 Peoples R China Changsha Univ Sci & Technol Sch Elect & Informat Engn Hunan Prov Key Lab Smart Grids Operat & Control Changsha 410076 Hunan Peoples R China Univ Sydney Sch Elect & Informat Engn Sydney NSW 2006 Australia

The thermal unit commitment (UC) problem is a large-scale mixed integer quadratic programming (MIQP), which is difficult to solve efficiently, especially for large-scale instances. This paper presents a projected reformulation for UC problem. After projecting the power output of unit onto [0,1], a novel MIQP reformulation, denoted as P-MIQP, can be formed. The obtained P-MIQP is tighter than traditional MIQP formulation of UC problem. And the reduced problem of P-MIQP, which is eventually solved by solvers such as CPLEX, is compacter than that of traditional MIQP. In addition, two mixed integer linear programming (MILP) formulations can be obtained from traditional MIQP and our P-MIQP of UC by replacing the quadratic terms in the objective functions with a sequence of piece-wise perspective-cuts. Projected MILP is also tighter and compacter than the traditional MILP due to the same reason of MIQP. The simulation results for realistic instances that range in size from 10 to 200 units over a scheduling period of 24 h show that the projected reformulation yields tight and compact mixed integer programming UC formulations, which are competitive with currently traditional ones. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Unit commitment Tight Compact Project mixed integer programming

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A mixed integer programming MODEL FOR MULTIPLE-CLASS DISCRIMINANT ANALYSIS

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INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGY & DECISION MAKING 2011年第4期10卷 589-612页

作者： Sun, Minghe Univ Texas San Antonio Coll Business Dept Management Sci & Stat San Antonio TX 78249 USA

A mixed integer programming model is proposed for multiple-class discriminant and classification analysis. When multiple discriminant functions, one for each class, are constructed with the mixed integer programming model, the number of misclassified observations in the sample is minimized. This model is an extension of the linear programming models for multiple-class discriminant analysis but may be considered as a generalization of mixed integer programming formulations for two-class classification analysis. Properties of the model are studied. The model is immune from any difficulties of many mathematical programming formulations for two-class classification analysis, such as nonexistence of optimal solutions, improper solutions, and instability under linear data transformation. In addition, meaningful discriminant functions can be generated under conditions where other techniques fail. Examples are provided. Results on publically accessible datasets show that this model is very effective in generating powerful discriminant functions.

关键词： Discriminant analysis classification mixed integer programming optimization nonparametric procedures

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Network-Wide Optimization of Traffic Signals Using mixed integer programming

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JOURNAL OF ROBOTICS AND MECHATRONICS 2014年第5期26卷 607-615页

作者： Kamal, Md. Abdus Samad Imura, Jun-ichi Hayakawa, Tomohisa Ohata, Akira Aihara, Kazuyuki Japan Sci & Technol Agcy Meguro Ku 4-6-1 Komaba Tokyo 1538505 Japan Univ Tokyo Inst Ind Sci Meguro Ku Tokyo 1538505 Japan Tokyo Inst Technol Dept Mech & Environm Informat Meguro Ku Tokyo 1528552 Japan Toyota Motors Corp Shizuoka 4101107 Japan Univ Tokyo Inst Ind Sci Meguro Ku Tokyo 1538505 Japan

In this paper a network-wide traffic signal control scheme in a model predictive control framework using mixed integer programming is presented. A concise model of traffic is proposed to describe a signalized road network considering conservation of traffic. In the model, the traffic of two sections that belong to a traffic signal group of a junction are represented by a single continuous variable. Therefore, the number of variables required to describe traffic in the network becomes half compared with the models that describe section wise traffic flows. The traffic signal at the junction is represented by a binary variable to express a signal state either green or red. The proposed model is transformed into a mixed logical dynamical system to describe the traffic flows in a finite horizon, and traffic signals are optimized using mixed integer linear programming (MILP) for a given performance index. The scheme simultaneously optimizes all traffic signals in a network in the context of model predictive control by successively extending or terminating a green or red signal of each junction. Consequently, traffic signal patterns with the optimal free parameters, i.e., the cycle times, the split times and the offsets, are realized. Use of the proposed concise traffic model significantly reduces the computation time of the scheme without compromising the performance as it is evaluated on a small road network and compared with a previously proposed scheme.

关键词： traffic signal control hybrid dynamical systems mixed integer programming model predictive control

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