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Transmission dispatch for loss minimisation using linearised power flow equations in mixed integer programming

INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2014年 62卷 855-861页

作者： Sikiru, Tajudeen H. Jimoh, Adisa A. Hamam, Yskandar Alayli, Yasser Agee, John T. Tshwane Univ Technol Dept Elect Engn Pretoria South Africa LISV Univ Versailles St Quentin En Yvelines Versailles France ESIEE Paris Paris France FSATI Tshwane Univ Technol Pretoria South Africa

Transmission dispatch is a nonlinear optimisation problem due to the nonlinearity of the power flow equations. In the open literature, linearisation of power flow that yields only the active power is used for transmission dispatch problems. The solutions obtained are unacceptable when verified in nonlinear power flow equations, especially for smart grid applications because of the instability issues that result from such formulations. This paper overcomes this limitation by proposing a model that accounts for both active and reactive power in transmission dispatch problem formulations. Furthermore, this paper develops new formulations for transmission dispatch that covers the overall spectrum of operation of a power system network based on the load duration curve rather than the single period considered in the open literature. Transmission dispatch is considered in the context of minimising active power losses in this paper. The advantage of the proposed approach is that it gives acceptable results when verified with nonlinear power flow compared to the classical approach used in transmission dispatch problems. Also, the paper demonstrates that the global set of switchable lines that can minimise the active power losses of a network is obtainable from the multi-period formulations based on the consideration of varying load levels. The results indicate that only this set of switchable lines can reduce losses and ensure the stability of a network, hence useful for smart grid applications. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Transmission dispatch Transmission line switching Active power loss minimisation mixed integer programming Linearised power flow equations

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Decomposition Branching for mixed integer programming

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OPERATIONS RESEARCH 2022年第3期000卷 1854-1872页

作者： Yildiz, Baris Boland, Natashia Savelsbergh, Martin Koc Univ Dept Ind Engn TR-34450 Istanbul Turkey Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA

We introduce a novel and powerful approach for solving certain classes of mixed integer programs (MIPs): decomposition branching. Two seminal and widely used techniques for solving MIPs, branch-and-bound and decomposition, form its foundation. Computational experiments with instances of a weighted set covering problem and a regionalized p-median facility location problem with assignment range constraints demonstrate its efficacy: it explores far fewer nodes and can be orders of magnitude faster than a commercial solver and an automatic Dantzig-Wolfe approach.

关键词： mixed integer programming combinatorial optimization branch-and-bound decomposition algorithms set covering facility location

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Incorporating aspects of habitat fragmentation into long-term forest planning using mixed integer programming

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FOREST ECOLOGY AND MANAGEMENT 2008年第3-4期255卷 440-446页

作者： Ohman, Karin Wikstrom, Peder SLU Dept Forest Resource Management S-90183 Umea Sweden

In forest planning, an understanding of the spatial relationships between compartments has become an increasingly important issue. Effective approaches must, therefore, be developed that include consideration of spatial relationships in planning models. Existing approaches, based on numerical optimization, tend to lack the means effectively to include spatial considerations. Further, many suggested approaches have focused on ways to include adjacency constraints or green-up constraints in forest planning. However, in order to maintain the biodiversity in the forest, methods dealing with, for instance, the problem of fragmentation of old forests, also have to be developed. In this paper, the issue of fragmentation is addressed and incorporated into long-term forest planning. The approach is to attempt to minimize the outer perimeter of areas of old forest. The model presented is formulated on the basis of mixed integer programming, and solved with a branch and bound algorithm. A data set consisting of 924 stands was used to examine the model, which was then evaluated with different requirements for the degree of clustering. The results indicate that the model is effective for the clustering of old forest stands and that it can be solved within a reasonable time despite the large number of constraints and variables. In the case study the loss in net present value as a result of including the issue of fragmentation was a few percent. (c) 2007 Elsevier B.V. All rights reserved.

关键词： mixed integer programming optimization shape index spatial relationships

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A mixed integer programming approach for multi-action planning for threat management

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ECOLOGICAL MODELLING 2020年第0期418卷 108901-000页

作者： Salgado-Rojas, Jose Alvarez-Miranda, Eduardo Hermoso, Virgilio Garcia-Gonzalo, Jordi Weintraub, Andres Univ Politecn Cataluna Dept Stat & Operat Res Barcelona Spain Univ Talca Fac Engn Dept Ind Engn Curico Chile Forest Sci Ctr Catalonia CTFC Solsona Spain Univ Chile Dept Ind Engn Santiago Chile

Planning for management actions that address threats to biodiversity is important for securing its long term persistence. However, systematic conservation planning (SCP) has traditionally overlooked this aspect and just focused on identifying priority areas without any recommendation on actions needed. This paper develops a mixed integer mathematical programming (MIP) approach for the multi-action management planning problem (MAMP), where the goal is to find an optimal combination of management actions that abate threats, in an efficient way while accounting for connectivity. An extended version of the MAMP model (MAMP-E) is also proposed that adds an expression for minimizing fragmentation between different actions. To evaluate the efficiency of the two models, they were applied to a case study corresponding to a large area of the Mitchell River in Northern Australia, where 45 species of freshwater fish are exposed to the presence of four threats. The evaluation compares our exact MIP approach with the conservation planning software Marxan and the heuristic approach developed in Cattarino et al. (2015). The results obtained show that our MIP models have three advantages over their heuristic counterparts: shorter execution times, higher solutions quality, and a solution quality guarantee. Hence, the proposed MIP methodology provides a more effective framework for addressing the multi-action conservation problem.

关键词： Conservation planning Wildlife management mixed integer programming Conservation management plans

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Scheduling of steelmaking-continuous casting process by integrating deep neural networks with mixed integer programming

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2024年

作者： Shin, Woo-Jin Lee, Sang-Wook Lee, Jun-Ho Song, Min-Ho Kim, Hyun-Jung Korea Adv Inst Sci & Technol Dept Ind & Syst Engn Daejeon 34141 South Korea Chungnam Natl Univ Sch Business Daejeon South Korea POSCO Tech Res Labs Gwangyang Jeollanam Do South Korea

This study addresses the scheduling problem in the steelmaking-continuous casting (SCC) process. The SCC process is a hybrid flow shop with three stages, and we focus on job dispatching in the second stage, the refining stage. Our primary aim is to develop an algorithm applicable to real-world scenarios, mirroring field engineers' decision-making and handling the process's complex features. We propose a deep neural network (DNN)-based approach, trained on engineers' past decisions, achieving up to 97% accuracy. However, DNN alone falls short of outperforming engineers in scheduling objectives, specifically minimizing the total completion time in the refining stage. Hence, we introduce a novel approach combining DNN with mixed integer programming (MIP). In the integrated approach, the DNN initially makes decisions, but when confidence in the accuracy of a DNN-based decision is lacking, as determined by a developed reliability measure, it is supplemented with a decision derived using MIP. Experiments demonstrate that this integration improves scheduling objectives, surpassing engineers' performance. Furthermore, filtering inaccurate decisions enhances the accuracy of the DNN-based decisions. The proposed approach has been successfully implemented in one of South Korea's largest steelmaking companies.

关键词： Scheduling automation artificial intelligence steelmaking process mixed integer programming

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On the optimal modeling and evaluation of job shops with a total weighted tardiness objective: Constraint programming vs. mixed integer programming

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APPLIED MATHEMATICAL MODELLING 2015年第2期39卷 955-964页

作者： Sahraeian, Rashed Namakshenas, Mohammad Shahed Univ Coll Engn Dept Ind Engn Tehran Iran

In this study we consider the mapping of the main characteristics, i.e., the structural properties, of a classical job shop problem onto well-known combinatorial techniques, i.e., positional sets, disjunctive graphs, and linear orderings. We procedurally formulate three different models in terms of mixed integer programming (MIP) and constraint programming (CP) paradigms. We utilize the properties of positional sets and disjunctive graphs to construct tight MIP formulations in an efficient manner. In addition, the properties are retrieved by the polyhedral structures of the linear ordering and they are defined on a disjunctive graph to facilitate the formulation of the CP model and to reduce the number of dominant variables. The proposed models are solved and their computational performance levels are compared with well-known benchmarks in the job shop research area using IBM ILog Cplex software. We provide a more explicit analogy of the applicability of the proposed models based on parameters such as time efficiency, thereby producing strong bounds, as well as the expressive power of the modeling process. We also discuss the results to determine the best formulation, which is computationally efficient and structurally parsimonious with respect to different criteria. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Combinatorics Constraint programming Job shop mixed integer programming Total weighted tardiness

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Comparison of mixed integer programming and fast simulated annealing for optimizing beam weights in radiation therapy

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MEDICAL PHYSICS 1996年第6期23卷 957-964页

作者： Langer, M Morrill, S Brown, R Lee, O Lane, R ONE STONE CORP CAMBRIDGEMA 02140

Two competing methods for assigning intensities to radiation treatment beams were tested. One method was derived from mixed integer programming and the other was based on simulated annealing. The methods faced a common objective and identical constraints. The goal was to maximize the minimum tumor dose while keeping the dose in required fractions of normal organ volumes below a threshold for damage. The minimum tumor doses of the two methods were compared when all the dose-volume constraints were satisfied. A mixed integer linear program gave a minimum tumor dose that was at least 1.8 Gy higher than that given by simulated annealing in 7 of 19 trials. The difference was greater than or equal to 5.4 Gy in 4 of 19 trials. In no case was the mixed integer solution one fraction size (1.8 Gy) worse than that of simulated annealing. The better solution provided by the mixed integer program allows tumor dose to increase without violating the dose-volume limits of normal tissues. (C) 1996 American Association of Physicists in Medicine.

关键词： radiation therapy planning optimization mixed integer programming simulated annealing dose-volume limits

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Optimization of radiosurgery treatment planning via mixed integer programming

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MEDICAL PHYSICS 2000年第5期27卷 995-1004页

作者： Lee, EK Fox, T Crocker, I Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA Emory Univ Sch Med Dept Radiat Oncol Atlanta GA 30322 USA

An automated optimization algorithm based on mixed integer programming techniques is presented for generating high-quality treatment plans for LINAC radiosurgery treatment. The physical planning in radiosurgery treatment involves selecting among a large collection of beams with different physical parameters an optimal beam configuration (geometries and intensities) to deliver the clinically prescribed radiation dose to the tumor volume while sparing the nearby critical structure and normal tissue. The proposed mixed integer programming models incorporate strict dose restrictions on tumor volume, and constraints on the desired number of beams, isocenters, couch angles, and gantry angles. The model seeks to deliver full prescription dose coverage and uniform radiation dose to the tumor volume while minimizing the excess radiation to the periphery normal tissue. In particular, it ensures that proximal normal tissues receive minimal dose via rapid dose fall-off. Preliminary numerical tests on a single patient case indicate that this approach can produce exceptionally high-quality plans in a fraction of the time required using the procedure currently employed by clinicians. The resulting plans provide highly uniform prescription dose to the tumor volume while drastically reducing the irradiation received by the proximal critical normal tissue. (C) 2000 American Association of Physicists in Medicine. [S0094-2405(00)00505-8].

关键词： radiosurgery treatment planning computational optimization mixed integer programming automated optimization computer-assisted treatment planning

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Operating value optimisation using simulation and mixed integer programming

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INTERNATIONAL JOURNAL OF MINING RECLAMATION AND ENVIRONMENT 2014年第1期28卷 25-46页

作者： Salama, Abubakary Nehring, Micah Greberg, Jenny Lulea Univ Technol Dept Civil Min & Environm Engn Div Min & Geotech Engn S-95187 Lulea Sweden Univ Queensland Sch Mech & Min Engn St Lucia Qld Australia

Mining operations around the world will increasingly need to operate at greater depths. This significantly influences the complexity of ore extraction and ore transportation to the surface. The increase in mine depth leads to increases in haulage distance from mine areas to the mine surface. This results in an increase in energy costs to haul material further. Due to the increasing cost of future operations, the choice of the haulage method becomes an important factor in the optimisation of the mine plan. The haulage process is one of the most energy intensive activities in a mining operation, and thus, one of the main contributors to energy cost. This paper presents the comparison of the operating values of the mine plans at depth levels of 1000, 2000 and 3000m for diesel and electric trucks, shaft and belt conveyor haulage systems for the current and a predicted future energy price scenario. The aim is to analyse the impact of energy requirements associated with each haulage method, as well as the use of alternative sequencing techniques as mine depth increases. This study is carried out using a combination of discrete event simulation and mixed integer programming (MIP) as a tool to improve decision-making in the process of generating and optimising the mine plans. Results show that energy cost increases across each haulage method at both current and future energy prices, with increasing depth. This study thus provides a broad and up to date analysis of the impact on operating values that may be experienced with the use of the main haulage systems available at present. Also, the study shows how the combination of discrete event simulation and MIP generates a good tool for decision support.

关键词： discrete event simulation mixed integer programming deep mining haulage energy

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An optimal control approach to nonlinear mixed integer programming problems

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 1998年第3期36卷 87-105页

作者： Lee, HWJ Teo, KL Cai, XQ Chinese Univ Hong Kong Dept Syst Engn & Engn Management Shatin NT Hong Kong Curtin Univ Technol Sch Math & Stat Perth WA 6001 Australia

Motivated by the recent developments of the Control Parametrization Enhancing Technique (CPET), a novel method for solving a general class of nonlinear mixed integer programming problems is introduced in this paper. By imposing appropriate dynamics as well as a set of statistical variance type of functional constraints, a problem with mixed integer decision variables is first transformed into a discrete-valued optimal control problem, and then transformed, by applying CPET, into a standard optimization problem involving only continuous values. (C) 1998 Elsevier Science Ltd. All rights reserved.

关键词： nonlinear discrete optimization mixed integer programming optimal control control parametrization enhancing technique

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