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Multi-energy systems fast optimization: A new formulation in linear programming for temperatures and magnitudes of thermal power flows in heating systems

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ENERGY AND BUILDINGS 2025年 336卷

作者： Hachez, Jonathan Latiers, Arnaud Berger, Benjamin Bram, Svend Ecole Cent Arts & Metiers Brussels Belgium Vrije Univ Brussel VUB Fac Engn Thermo & Fluid Dynam FLOW Pleinlaan 2 B-1050 Brussels Belgium Vrije Univ Brussel VUB Brussels Inst Thermal Fluid Syst & Clean Energy BR Ave FD Rooseveltlaan 50 B-1050 Brussels Belgium Univ Libre Bruxelles ULB Ave FD Rooseveltlaan 50 B-1050 Brussels Belgium Destore SPRL Nivelles Belgium

Geopolitical events and environmental pressures can force regions to speed up their energy transition, as seen in the European Union (EU) shift towards sustainable smart energy systems in response to its current socioeconomic and geopolitical situation and to climate change. Among the assets that are envisaged are District Heating Network (DHN), Heat Pump (HP), Thermal Energy Storage (TES), and Photovoltaic Panels (PV).To ensure optimal equipment sizing, the widely adopted method is Mixed Integer linear programming (MILP) with a fixed supply temperature. Unfortunately, using MILP to optimize the design and operation considering variable supply temperature is not done in the literature because it is time-consuming. However, this article's linear programming (LP) formulation uses temperature levels to optimize the supply temperature and reaches optimality within 20 min. It improves the Coefficient of Performance (COP) of HP and increases the energetic density of TES. A specific case study examines a residential building with PV connected to a 5th generation DHN, showing that electric self-production can reach 58%, Seasonal Coefficient of Performance (SCOP) stands at 4.1, and electric self-consumption rate reaches 81 %. This formulation is more complete for optimizing low-temperature DHN, as it accounts for the sensitivity of equipment performance to network temperatures, considering the availability of renewable energy sources.

关键词： Optimization linear programming Multi-energy systems Thermal network

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An Efficient Hyperbolic Kernel Function Yielding the Best Known Iteration Bounds for linear programming

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Acta Mathematicae Applicatae Sinica 2025年第1期41卷 133-151页

作者： Imene TOUIL Wided CHIKOUCHE Djamel BENTERKI Amina ZERARI LMPA Mohammed Seddik Ben Yahia UniversityPO Box 98Ouled Aissa18000 JijelAlgeria LMFN Ferhat Abbas UniversitySetif 19000Algeria

Interior-point methods(IPMs) for linear programming(LP) are generally based on the logarithmic barrier function. Peng et al.(J. Comput. Technol. 6: 61–80, 2001) were the first to propose non-logarithmic kernel functions(KFs) for solving IPMs. These KFs are strongly convex and smoothly coercive on their ***, Bai et al.(SIAM J. Optim. 15(1): 101–128, 2004) introduced the first KF with a trigonometric barrier term. Since then, no new type of KFs were proposed until 2020, when Touil and Chikouche(Filomat. 34(12):3957–3969, 2020;Acta Math. Sin.(Engl. Ser.), 38(1): 44–67, 2022) introduced the first hyperbolic KFs for semidefinite program(ming(SD)P). They( establishe)d that the iteration complexities of algorithms based on their proposed KFs are O(n2/3log(n/ε) and O(n3/4log(n/ε)) for large-update methods, respectively. The aim of this work is to improve the complexity result for large-update method. In fact, we present a new parametric KF with a hyperbolic barrier term. By simple tools, we show that the worst-case iteration complexity of our algorithm for the large-update method is O(√n log n log(n/ε)) iterations. This coincides with the currently best-known iteration bounds for IPMs based on all existing kind of *** algorithm based on the proposed KF has been tested. Extensive numerical simulations on test problems with different sizes have shown that this KF has promising results.

关键词： linear programming primal-dual interior-point methods kernel functions complexity analysis large and small-update methods

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Evaluation Based on Distance From Average Solution for Circular Pythagorean Fuzzy Schweizer-Sklar Power Aggregation Operators and Their Application in Transportation Problems for linear programming

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IEEE ACCESS 2024年 12卷 154244-154270页

作者： Ali, Zeeshan Siddique, Naila Usman, Muhammad Yin, Shi Senapati, Tapan Esztergar-Kiss, Domokos Moslem, Sarbast Natl Yunlin Univ Sci & Technol Dept Informat Management Touliu 64002 Yunlin Taiwan Govt Viqar Un Nisa Grad Coll Women Dept Stat Rawalpindi 46000 Pakistan Riphah Int Univ Dept Math & Stat Islamabad 44000 Pakistan Hebei Agr Univ Coll Econ & Management Baoding 071000 Peoples R China Southwest Univ Sch Math & Stat Chongqing 400715 Peoples R China Saveetha Inst Med & Tech Sci Saveetha Sch Engn Chennai 602105 India Budapest Univ Technol & Econ Fac Transportat Engn & Vehicle Engn Dept Transport Technol & Econ H-1111 Budapest Hungary Univ Coll Dublin Sch Architecture Planning & Environm Policy Dublin D04 V1W8 Ireland Azerbaijan State Univ Econ UNEC Res Ctr Digital Econ Baku AZ-1001 Azerbaijan

Ranking circular Pythagorean fuzzy sets using distance-based techniques involves calculating the distance between a circular Pythagorean fuzzy set and a reference point that represents either maximum (positive ideal solution) or minimum (negative ideal solution) values. Theoretical design is a major link in the procedure of complex product design, and it is most valuable and dominant to choose the appropriate design scheme, however, there are various kinds and inaccuracies of the evaluation information, and there is a problem of mutual influence among the evaluation criteria, which leads to unreliable decision-making of the optimal solution. In order to evaluate these problems, we concentrate on designing the model of power average/geometric operators based on Schweizer-Sklar operational laws based on the technique of circular Pythagorean fuzzy values. For this, first, we compute the model of Schweizer-Sklar operational laws for circular Pythagorean fuzzy valuable, and then we derive the model of circular Pythagorean fuzzy Schweizer-Sklar power averaging operator, circular Pythagorean fuzzy Schweizer-Sklar power weighted averaging operator, circular Pythagorean fuzzy Schweizer-Sklar power geometric operator, and circular Pythagorean fuzzy Schweizer-Sklar power weighted geometric operator for both t-norm and t-conorm. For the above operators, we also simplify the model of idempotency, monotonicity, and boundedness. Further, we construct the technique of Evaluation Based on the Distance from the Average Solution method based on initiated operators. Additionally, we develop three different procedures for evaluating the problem of transportation for linear programming with the help of a multi-attribute decision-making problem based on the Evaluation Based on Distance from Average Solution method, based on averaging operators, and based on geometric operators. In a sensitive analysis, we compare the proposed techniques with various extant

关键词： Decision making Transportation Fuzzy sets Computational modeling linear programming Software reliability Entropy Analytical models Supply chain management Circular pythagorean fuzzy sets decision-making model EDAS technique linear programming optimization Schweizer-Sklar power aggregation operators transportation problem

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A linear programming-based hyper local search for tuning hyperparameters

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OPERATIONS RESEARCH LETTERS 2025年 61卷

作者： Sinha, Ankur Gunwal, Satender Indian Inst Management Ahmedabad Operat & Decis Sci Ahmadabad 380015 Gujarat India Indian Inst Management Ahmedabad Brij Disa Ctr Data Sci & AI Ahmadabad 380015 Gujarat India Univ Illinois Informat & Decis Sci Chicago IL 60607 USA

We introduce a linear programming-based approach for hyperparameter tuning of machine learning models. The approach finetunes continuous hyperparameters and model parameters through a linear program, enhancing model generalization in the vicinity of an initial model. The proposed method converts hyperparameter optimization into a bilevel program and identifies a descent direction to improve validation loss. The results demonstrate improvements in most cases across regression, machine learning, and deep learning tasks, with test performance enhancements ranging from 0.3% to 28.1%.

关键词： Bilevel optimization Machine learning Hyperparameter tuning linear programming

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Net-Zero Energy House-Oriented linear programming for the Sizing Problem of Photovoltaic Panels and Batteries

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IEEE ACCESS 2024年 12卷 80429-80441页

作者： Daniel Carnerero, A. Tanaka, Taichi Li, Mengmou Hatanaka, Takeshi Wasa, Yasuaki Hirata, Kenji Ushifusa, Yoshiaki Ida, Takanori Tokyo Inst Technol Sch Engn Dept Syst & Control Engn Tokyo 1528550 Japan Hiroshima Univ Grad Sch Adv Sci & Engn Higashihiroshima 7390046 Japan Waseda Univ Fac Sci & Engn Sch Adv Sci & Engn Dept Elect Engn & Biosci Tokyo 1698555 Japan Univ Toyama Sch Engn Dept Elect & Elect Engn Toyama 9308555 Japan Univ Kitakyushu Fac Econ & Business Adm Fukuoka 8028577 Japan Kyoto Univ Grad Sch Econ Kyoto 6068501 Japan

The global drive towards carbon neutrality has led to a significant increase in the number of power plants based on renewable energy sources (RES). Concurrently, numerous households are adopting RES to generate their own energy, aiming to decrease both electricity costs and carbon footprints. To support these users, many papers have been devoted to developing optimal investment strategies for residential energy systems. However, there is still a significant gap as these studies often neglect important aspects like carbon neutrality. For this reason, in this paper, we explore the concept of net-zero energy houses (ZEHs)-houses designed to have an annual net energy consumption around zero-by presenting a constrained optimization problem to find the optimal number of photovoltaic panels and the optimal size of the battery system for home integration. Solving this constrained optimization problem is difficult due to its nonconvex constraints. Nevertheless, by applying a series of transformations, we reveal that it is possible to find an equivalent linear programming (LP) problem which is computationally tractable. The attainment of ZEH can be tackled by introducing a single constraint in the optimization problem. Additionally, we propose a sharing economy approach to the investment problem, offering a strategy that could potentially reduce investment costs and facilitate the attainment of ZEH more efficiently. Finally, we apply the proposed frameworks to a neighborhood in Japan as a case study, demonstrating the potential for long-term ZEH attainment. The results show that, under the right incentive, users can achieve ZEH, reduce their electricity costs and have a minimal impact on the main grid.

关键词： Batteries Investment Costs Optimization Renewable energy sources Photovoltaic systems Power system dynamics Net zero linear programming Net-zero energy houses optimization linear programming

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A novel reliability assessment method for distribution networks based on linear programming considering distribution automation and distributed generation

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IET RENEWABLE POWER GENERATION 2024年第3期18卷 412-425页

作者： Li, Junhui Kong, Huichao Wang, Wenzhong Sun, Liming Xiao, Wencong Wang, Ziyao Dongguan Power Supply Bur Power Grid Planning Ctr Dongguan Peoples R China Guangzhou Shuimu Qinghua Technol Co Ltd Guangzhou Peoples R China South China Univ Technol Sch Elect Power Engn Guangzhou Peoples R China South China Univ Technol Guangzhou Peoples R China

The primary methods of assessing the reliability of distribution networks comprise analytic and simulation methods. However, both approaches require the identification and computation of network topology, which precludes their expression in explicit, continuous functions, consequently impeding the incorporation of reliability constraints into planning and operational optimization models. To tackle this restriction, the present work puts forth a novel linear-programming-based reliability assessment method that is mathematically formulated, considering distribution automation (DA) and distributed generations (DGs), consisting of both conventional and renewable energy sources. In this paper, the clustering method and the scenario-based method are used to model DGs. Next, a mixed integer linear programming (MILP) model, considering the DA and DGs with the System Average Interruption Duration Index (SAIDI) as the optimization objective, is proposed. Finally, the feasibility and effectiveness of the proposed method are verified in a 37-node distribution network system.

关键词： distributed generation distribution automation distribution networks linear programming reliability assessment

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Optimal pivot path of the simplex method for linear programming based on reinforcement learning

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Science China Mathematics 2024年第6期67卷 1263-1286页

作者： Anqi Li Tiande Guo Congying Han Bonan Li Haoran Li School of Mathematical Sciences University of Chinese Academy of SciencesBeijing100049China

Based on the existing pivot rules,the simplex method for linear programming is not polynomial in the worst ***,the optimal pivot of the simplex method is *** this paper,we propose the optimal rule to find all the shortest pivot paths of the simplex method for linear programming problems based on Monte Carlo tree ***,we first propose the SimplexPseudoTree to transfer the simplex method into tree search mode while avoiding repeated basis ***,we propose four reinforcement learning models with two actions and two rewards to make the Monte Carlo tree search suitable for the simplex ***,we set a new action selection criterion to ameliorate the inaccurate evaluation in the initial *** is proved that when the number of vertices in the feasible region is C_(n)^(m),our method can generate all the shortest pivot paths,which is the polynomial of the number of *** addition,we experimentally validate that the proposed schedule can avoid unnecessary search and provide the optimal pivot ***,this method can provide the best pivot labels for all kinds of supervised learning methods to solve linear programming problems.

关键词： simplex method linear programming pivot rules reinforcement learning

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Iterative MILP algorithm to find alternate solutions in linear programming models

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OPTIMIZATION AND ENGINEERING 2024年第4期25卷 2401-2424页

作者： Kakkad, Dev A. Grossmann, Ignacio E. Springub, Bianca Galanopoulos, Christos de Assis, Leonardo Salsano Tran, Nga Wassick, John M. Carnegie Mellon Univ Dept Chem Engn 5000 Forbes Ave Pittsburgh PA 15213 USA Aurubis AG Hamburg 20539 Germany

We address in this paper linear programming (LP) models in which it is desired to find a finite set of alternate optima. An LP may have multiple alternate solutions with the same objective value or with increasing objective values. For many real life applications, it can be interesting to have a pool of solutions to compare what operations should be executed and what is the cost/benefit of doing it. To obtain a specified number of these alternate solutions in the increasing order of objective values, we propose an iterative MILP algorithm in which we successively add integer cuts on inactive constraints. We demonstrate the application and effectiveness of this algorithm on a 2 dimensional LP and on small and large supply chain problems. The proposed iterative MILP algorithm provides an effective approach for finding a specified number of alternate optima in LP models, which provides a useful tool in a variety of applications as for instance in supply chain optimization problems.

关键词： Supply chain network linear programming Mixed integer linear programming Alternate optima

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An infeasible interior-point arc-search method with Nesterov's restarting strategy for linear programming problems

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2024年第2期88卷 643-676页

作者： Iida, Einosuke Yamashita, Makoto Tokyo Inst Technol Dept Math & Comp Sci Tokyo Japan

An arc-search interior-point method is a type of interior-point method that approximates the central path by an ellipsoidal arc, and it can often reduce the number of iterations. In this work, to further reduce the number of iterations and the computation time for solving linear programming problems, we propose two arc-search interior-point methods using Nesterov's restarting strategy which is a well-known method to accelerate the gradient method with a momentum term. The first one generates a sequence of iterations in the neighborhood, and we prove that the proposed method converges to an optimal solution and that it is a polynomial-time method. The second one incorporates the concept of the Mehrotra-type interior-point method to improve numerical performance. The numerical experiments demonstrate that the second one reduced the number of iterations and the computational time compared to existing interior-point methods due to the momentum term.

关键词： Interior point method Arc-search Nesterov's restarting method linear programming

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A fuzzy rough-interval linear programming model for booster optimization in water distribution systems

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ENGINEERING OPTIMIZATION 2024年

作者： Wang, Yumin Du, Yuanyang Southeast Univ Sch Energy & Environm Nanjing Peoples R China City Univ Hong Kong MA Int Studies Hongkong Peoples R China

In this article, a fuzzy rough-interval linear programming (FRILP) approach is proposed to deal with the uncertainty expressed by the fuzzy rough set in the optimization of booster cost under uncertainty. The FRILP model was applied to two cases to verify its effectiveness in booster optimization under uncertainty. The optimal upper and lower approximation intervals of the injection mass and booster cost in the fuzzy rough set were obtained and the effects of booster number and location were analysed. The results indicated that with an increase in booster number, the injection mass generally decreased, and booster cost decreased or increased. The nodal chlorine concentration also decreased and was distributed uniformly under a scenario with more boosters. Locating the booster far from the source resulted in more uniform chlorine distribution. The results could help managers design booster schemes with consideration of technical and economic factors comprehensively under uncertainty.

关键词： Water distribution system fuzzy rough-interval set linear programming

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