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Economical sizing and multi-azimuth layout optimization of grid-connected rooftop photovoltaic systems using mixed-integer programming

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APPLIED ENERGY 2023年 335卷

作者： Alharbi, Abdulaziz Awwad, Zeyad Habib, Abdulelah de Weck, Olivier MIT Ctr Complex Engn Syst KACST Riyadh Saudi Arabia MIT Dept Aeronaut & Astronaut Cambridge MA 02139 USA

Solar energy is expected to be a significant contributor to meet the increasing global energy demand. Rooftop photovoltaic (PV) systems account for a substantial portion of the global solar energy potential. However, optimizing the size and layout of these systems remains challenging. Existing approaches either focus on maximizing energy generation, heavily restrict the space of potential layouts, ignore inverter-type implications, or neglect practical aspects, such as minimizing self-shading. This paper presents a mixed-integer programming (MIP) model to address these limitations for PV systems installed on flat rooftops. The proposed model optimizes the net present value (NPV) and can produce multi-azimuth layouts while accounting for practical considerations, including mitigating self-shading, and ensuring rooftop walkability. The proposed model is adapted for systems that utilize micro-inverters or string-inverters. Two case studies are conducted to evaluate the performance of the proposed model. In one case study, the model is applied to a residential area. It is numerically shown that in some instances of capital costs and billing policies, the use of multi-azimuth layouts could significantly improve the NPV compared to the use of single-azimuth layouts with parallel rows of panels. The proposed model solutions are compared to an existing optimized installation in the second case study. The proposed model multi-azimuth layout solution improves the NPV by 10.17%. When restricted to single-azimuth layouts, the proposed model produces the same design as that of the existing installation in only a few seconds.

关键词： Optimization mixed-integer programming Photovoltaic system sizing optimization Photovoltaic system layout optimization

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On mixed-integer programming Formulations for the Unit Commitment Problem

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INFORMS JOURNAL ON COMPUTING 2020年第4期32卷 857-876页

作者： Knueven, Bernard Ostrowski, James Watson, Jean-Paul Sandia Natl Labs Discrete Math & Optimizat Albuquerque NM 87185 USA Univ Tennessee Ind & Syst Engn Knoxville TN 37996 USA Sandia Natl Labs Data Sci & Cyber Analyt Livermore CA 94551 USA

We provide a comprehensive overview of mixed-integer programming formulations for the unit commitment (UC) problem. UC formulations have been an especially active area of research over the past 12 years due to their practical importance in power grid operations, and this paper serves as a capstone for this line of work. We additionally provide publicly available reference implementations of all formulations examined. We computationally test existing and novel UC formulations on a suite of instances drawn from both academic and real-world data sources. Driven by our computational experience from this and previous work, we contribute some additional formulations for both generator production upper bounds and piecewise linear production costs. By composing new UC formulations using existing components found in the literature and new components introduced in this paper, we demonstrate that performance can be significantly improved-and in the process, we identify a new state-of-the-art UC formulation.

关键词： unit commitment mixed-integer programming mathematical programming formulations

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Optimal Operational Planning of a Gas Turbine Combined Heat and Power Plant Based on the mixed-integer programming

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IFAC Proceedings Volumes 1988年第11期21卷 371-377页

作者： K. Ito R. Yokoyama S. Akagi T. Yamaguchi Y. Matsumoto Dept. of Mech. Eng. for Indu. Mach and Syst. Faculty of Eng. Osaka Univ. Suita Osaka Japan Technical Research Center. The Kansai Electric Power Co. Inc. Amagasaki Hyogo Japan

A planning method is proposed for determining the optimal operational policy of a gas turbine combined heat and power plant connected with distributed heat supply plants at several districts. For the purpose of the efficient planning, a hierarchical approach is adopted. At the first level, the optimal operational policy is determined for each heat supply plant so as to minimize the required amount of input energy. At the second level, the optimal operational policy is determined for the combined heat and power plant so as to minimize its operational cost. These optimization problems are formulated respectively as a mixed-integer quadratic programming problem and a mixed-integer linear one, and they are both solved by applying the branch and bound method. Lastly, the effectiveness of the proposed method is ascertained through a case study.

关键词： Computer-aided systet design power generation heat systems gas turbines optimization hierarchical systems district heating and cooling optimal operation mixed-integer programming

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A Survey on mixed-integer programming Techniques in Bilevel Optimization

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EURO JOURNAL ON COMPUTATIONAL OPTIMIZATION 2021年 9卷

作者： Kleinert, Thomas Labbe, Martine Ljubic, Ivana Schmidt, Martin Friedrich Alexander Univ Erlangen Nurnberg Discrete Optimizat Cauerstr 11 D-91058 Erlangen Germany Energie Campus Nurnberg Further Str 250 D-90429 Nurnberg Germany Univ Libre Bruxelles Dept Comp Sci Blvd TriompheCP212 B-1050 Brussels Belgium Inria Lille Nord Europe Parc Sci Haute Borne 40Av Halley Bat APk Plaza F-59650 Villeneuve Dascq France ESSEC Business Sch Paris F-95021 Cergy Pontoise France Trier Univ Dept Math Univ Ring 15 D-54296 Trier Germany

Bilevel optimization is a field of mathematical programming in which some variables are constrained to be the solution of another optimization problem. As a consequence, bilevel optimization is able to model hierarchical decision processes. This is appealing for modeling real-world problems, but it also makes the resulting optimization models hard to solve in theory and practice. The scientific interest in computational bilevel optimization increased a lot over the last decade and is still growing. Independent of whether the bilevel problem itself contains integer variables or not, many state-of-the-art solution approaches for bilevel optimization make use of techniques that originate from mixed-integer programming. These techniques include branch-and-bound methods, cutting planes and, thus, branch-and-cut approaches, or problem-specific decomposition methods. In this survey article, we review bilevel-tailored approaches that exploit these mixed-integer programming techniques to solve bilevel optimization problems. To this end, we first consider bilevel problems with convex or, in particular, linear lower-level problems. The discussed solution methods in this field stem from original works from the 1980's but, on the other hand, are still actively researched today. Second, we review modern algorithmic approaches to solve mixed-integer bilevel problems that contain integrality constraints in the lower level. Moreover, we also briefly discuss the area of mixed-integer nonlinear bilevel problems. Third, we devote some attention to more specific fields such as pricing or interdiction models that genuinely contain bilinear and thus nonconvex aspects. Finally, we sketch a list of open questions from the areas of algorithmic and computational bilevel optimization, which may lead to interesting future research that will further propel this fascinating and active field of research.

关键词： Bilevel optimization mixed-integer programming Applications Branch-and-bound Branch-and-cut Survey

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Research on obstetric ward planning combining lean thinking and mixed-integer programming

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INTERNATIONAL JOURNAL FOR QUALITY IN HEALTH CARE 2021年第3期33卷 mzab101页

作者： Mu, Dongmei Li, Hua Zhao, Danning Ju, Yuanhong Li, Yuewei Jilin Univ Sch Publ Hlth 1163 Xinmin St Changchun 130000 Jilin Peoples R China Jilin Univ First Hosp Dept Clin Res 1 Xinmin St Changchun 130000 Jilin Peoples R China Jilin Univ First Hosp Dept Abdominal Ultrasound 1 Xinmin St Changchun 130000 Jilin Peoples R China Jilin Univ Sch Nursing 965 Xinjiang St Changchun 130000 Jilin Peoples R China

Background: In recent years, there are many studies on scheduling methods of patient flow, nurse scheduling, bed allocation, operating room scheduling and other problems, but there is no report on the research methods of how to plan ward allocation from a more macroscopic perspective. Objective: Refine and stratify the obstetric ward to provide more accurate medical service for pregnant women and improve the work efficiency of obstetricians and midwives. The problem of how to allocate the number of each type of ward is modeled as a mixed integer programming problem, which maximizes the patient flow of pregnant women in obstetric hospitals. Methods: The obstetric wards are divided into observation ward, cesarean section ward and natural delivery ward according to lean thinking. CPLEX is used to solve the mixed-integer programming problem of ward allocation. In R software, multivariate Generalized Linear Models (GLM) regression model is used to analyze the influence of each factor on patient flow. Results: The maximum patient flow of each case was obtained by CPLEX, which was 19-25% higher than that of patients without refinement, stratification and planning. GLM regression analysis was carried out on the abovementioned data, and the positive and negative correlation factors were obtained. Conclusion: According to lean thinking, obstetric wards are divided into three types of wards. Obstetricians and midwives work more efficiently and get more rest time. Pregnant women also enjoy more detailed medical services. By modeling the delivery ward allocation problem as a mixed-integer programming problem, we can improve the capacity of the service in obstetric hospitals from a macro perspective. Through GLM regression model analysis, it is conducive to improve the obstetric hospital capacity from the perspective of positive and negative correlation factors.

关键词： obstetric ward planning lean thinking mixed-integer programming clinical pathway CPLEX

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Area aggregation in map generalisation by mixed-integer programming

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INTERNATIONAL JOURNAL OF GEOGRAPHICAL INFORMATION SCIENCE 2010年第12期24卷 1871-1897页

作者： Haunert, Jan-Henrik Wolff, Alexander Leibniz Univ Hannover Inst Kartog & Geoinformat Hannover Germany Tech Univ Eindhoven Fac Wiskunde Informat NL-5600 MB Eindhoven Netherlands

Topographic databases normally contain areas of different land cover classes, commonly defining a planar partition, that is, gaps and overlaps are not allowed. When reducing the scale of such a database, some areas become too small for representation and need to be aggregated. This unintentionally but unavoidably results in changes of classes. In this article we present an optimisation method for the aggregation problem. This method aims to minimise changes of classes and to create compact shapes, subject to hard constraints ensuring aggregates of sufficient size for the target scale. To quantify class changes we apply a semantic distance measure. We give a graph theoretical problem formulation and prove that the problem is NP-hard, meaning that we cannot hope to find an efficient algorithm. Instead, we present a solution by mixed-integer programming that can be used to optimally solve small instances with existing optimisation software. In order to process large datasets, we introduce specialised heuristics that allow certain variables to be eliminated in advance and a problem instance to be decomposed into independent sub-instances. We tested our method for a dataset of the official German topographic database ATKIS with input scale 1:50,000 and output scale 1:250,000. For small instances, we compare results of this approach with optimal solutions that were obtained without heuristics. We compare results for large instances with those of an existing iterative algorithm and an alternative optimisation approach by simulated annealing. These tests allow us to conclude that, with the defined heuristics, our optimisation method yields high-quality results for large datasets in modest time.

关键词： map generalisation aggregation combinatorial optimisation mixed-integer programming NP-hardness

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A mixed integer-Linear programming Model for Solving the Hydroelectric Unit Maintenance Scheduling Problem

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IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING 2025年

作者： Tang, Yuehao Changjiang Inst Technol 9 Wenhua Ave Wuhan Peoples R China

This paper presents an optimization modeling approach utilizing mixed integer Linear programming (MILP) techniques to address the hydroelectric unit maintenance scheduling problem for British Columbia Hydro and Power Authority (BC Hydro) systems. The research leverages specialized linear formulations and algorithms to solve the combinatorial maintenance problem in large-scale hydroelectric systems. The primary objective is to determine the optimal timing and sequencing for each unit outage within the system, ensuring system productivity, reliability, and operability. The proposed method involves a detailed MILP formulation that considers various constraints. A novel 'maintenance shape' algorithm is designed to handle the nonlinearity arising from the maintenance continuity preference, ensuring that all units' maintenance activities within each plant are arranged sequentially without breaks. Results from the case study illustrate the systematic effects of unit maintenance on BC Hydro's competitiveness in the electricity market. The model can be extended to include more plants and reservoirs, providing a valuable tool for BC Hydro and similar utilities in strategically managing their maintenance operations. (c) 2025 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

关键词： hydro system unit maintenance mixed-integer programming

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Computing the Pareto frontier of a bi-objective bi-level linear problem using a multiobjective mixed-integer programming algorithm

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OPTIMIZATION 2012年第3期61卷 335-358页

作者： Alves, Maria Joao Dempe, Stephan Judice, Joaquim J. Univ Coimbra Fac Econ INESCC Coimbra Portugal TU Bergakad Freiberg Fak Math & Informat D-09596 Freiberg Germany Univ Coimbra Dept Matemat Inst Telecomunicacoes Coimbra Portugal

In this article, we study the bi-level linear programming problem with multiple objective functions on the upper level (with particular focus on the bi-objective case) and a single objective function on the lower level. We have restricted our attention to this type of problem because the consideration of several objectives at the lower level raises additional issues for the bi-level decision process resulting from the difficulty of anticipating a decision from the lower level decision maker. We examine some properties of the problem and propose a methodological approach based on the reformulation of the problem as a multiobjective mixed 0-1 linear programming problem. The basic idea consists in applying a reference point algorithm that has been originally developed as an interactive procedure for multiobjective mixed-integer programming. This approach further enables characterization of the whole Pareto frontier in the bi-objective case. Two illustrative numerical examples are included to show the viability of the proposed methodology.

关键词： bi-level programming multiobjective mixed-integer programming

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A mixed-integer programming model of registration signalling and paging in a mobile communication network

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INTERNATIONAL JOURNAL OF COMMUNICATION NETWORKS AND DISTRIBUTED SYSTEMS 2021年第4期26卷 367-397页

作者： Khazaelpour, Payam Sobhani, Ahmad Roshani, Afshan Univ Ghent Dept Ind Syst Engn & Prod Design Ghent Belgium Oakland Univ Sch Business Adm Rochester MI USA Oakland Univ Dept Ind & Syst Engn Rochester MI USA

Handling traffic delays in a mobile communication network (MCN) is a principal problem due to time and cost expenses. Delays limit mobile coverage. Therefore, optimisation techniques and tools are applied to minimise delays. However, there is still a high chance that at some points the network will lose its integral connectivity and delays happen. Delays prohibit call transmissions and produce several breaks. System breaks/delays cause call pending for a connection. Accordingly, network partitioning happens, thus leads to disconnection. This paper proposes a mixed-integer programming (MIP) to minimise network delays while a reliable trade-off between registration signalling (RS) and paging (P) coverage distances is maintained. The proposed MIP is NP-hard. For this reason, a metaheuristic approach, genetic algorithm (GA), is developed and compared with it. MIP validation is endorsed by GA approximations in different random trials and comparative analysis investigates GA performance metrics in a numerical example.

关键词： genetic algorithm mixed-integer programming MIP integrated mobile network optimisation IMNO registration signalling paging relaxed mixed-integer programming RMIP linear programming mobile switching service centre MSSC

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SelfSplit parallelization for mixed-integer linear programming

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COMPUTERS & OPERATIONS RESEARCH 2018年 93卷 101-112页

作者： Fischetti, Matteo Monaci, Michele Salvagnin, Domenico Univ Padua DEI Padua Italy Univ Bologna DEI Bologna Italy

SelfSplit is a simple static mechanism to convert a sequential tree-search code into a parallel one. In this paradigm, tree-search is distributed among a set of identical workers, each of which is able to autonomously determine-without any communication with the other workers-the job parts it has to process. SelfSplit already proved quite effective in parallelizing Constraint programming solvers. In the present paper we investigate the performance of SelfSplit when applied to a mixed-integer Linear programming (MILP) solver. Both ad-hoc and general purpose MILP codes have been considered. Computational results show that SelfSplit, in spite of its simplicity, can achieve good speedups even in the MILP context. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Parallel computing Enumerative algorithms mixed-integer programming Computational analysis

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