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An epsilon-constraint method for fully fuzzy multiobjective linear programming

INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS 2020年第4期35卷 600-624页

作者： Perez-Canedo, Boris Luis Verdegay, Jose Miranda Perez, Ridelio Univ Cienfuegos Dept Math Cienfuegos Cuba Univ Granada Dept Comp Sci & Artificial Intelligence Granada Spain

Linear ranking functions are often used to transform fuzzy multiobjective linear programming (MOLP) problems into crisp ones. The crisp MOLP problems are then solved by using classical methods (eg, weighted sum, epsilon-constraint, etc), or fuzzy ones based on Bellman and Zadeh's decision-making model. In this paper, we show that this transformation does not guarantee Pareto optimal fuzzy solutions for the original fuzzy problems. By using lexicographic ranking (LR) criteria, we propose a fuzzy epsilon-constraint method that yields Pareto optimal fuzzy solutions of fuzzy variable and fully fuzzy MOLP problems, in which all parameters and decision variables take on LR fuzzy numbers. The proposed method is illustrated by means of three numerical examples, including a fully fuzzy multiobjective project crashing problem.

关键词： epsilon-constraint method fully fuzzy multiobjective linear programming lexicographic ranking criterion LR fuzzy number project crashing

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A Multi-Objective Model for Home Energy Management System Self-Scheduling using the epsilon-constraint method 14

A Multi-Objective Model for Home Energy Management System Se...

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14th IEEE International Conference on Compatibility, Power Electronics and Power Engineering (CPE-POWERENG)

作者： Javadi, Mohammad Lotfi, Mohamed Osorio, Gerardo J. Ashraf, Abdelrahman Nezhad, Ali Esmaeel Gough, Matthew Catalao, Joao P. S. Univ Porto FEUP Fac Engn P-4200465 Porto Portugal Inst Syst & Comp Engn Technol & Sci INESC TEC P-4200465 Porto Portugal Ontario Tech Univ ERC Oshawa ON L1G 8C4 Canada Univ Beira Interior C MAST Covilha Portugal German Univ Cairo GUC Cairo Egypt Univ Bologna Dept Elect Elect & Informat Engn Bologna Italy

ISBN: (纸本)9781728142180

Self-scheduling of Home Energy Management Systems (HEMS) is one of the most interesting problems for active end-users to reduce their electricity bills. The electricity bill reduction by adopting Demand Response Programs (DRP) considering the flexibility of the end-users is addressed in this paper. The problem is addressed as a multi-objective optimization problem. The first objective function is the minimization of the daily bill, while the second objective aims to minimize the Discomfort Index (DI) regarding shifting the home appliances plugging-in time. The Time-of-Use (ToU) tariff is adopted in this paper and therefore, the end-users can benefit from shifting their flexible loads from peak hours to the off-peak hours and this reduces their bills, accordingly. In this case, the end-users have to change their energy consumption which imposes a level of discomfort on the end-users. Therefore, a two-stage model is proposed in this paper to deal with the mentioned objective functions. The proposed model is represented as standard mixed-integer linear programming (MILP) and for solving this problem the epsilon-constraint method is adopted in this study. The obtained Pareto front from the epsilon-constraint multi-objective framework is fed to the fuzzy satisfying method for final plan selection. These results show that by providing the Pareto set of optimal solutions to the user, they are more informed and can make decisions that better suit their preferences.

关键词： Home Energy Management Systems epsilon-constraint method Multi-objective Optimization

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An exact algebraic ε-constraint method for bi-objective linear integer programming based on test sets

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2020年第2期282卷 453-463页

作者： Isabel Hartillo-Hermoso, Maria Jimenez-Tafur, Haydee Maria Ucha-Enriquez, Jose Univ Seville ETS Ingn Informat Dept Matemat Aplicada 1 Av Reina Mercedes S-N E-41012 Seville Spain Univ Seville Inst Matemat Avda Reina Mercedes S-N E-41012 Seville Spain

A new exact algorithm for bi-objective linear integer problems is presented, based on the classic epsilon-constraint method and algebraic test sets for single-objective linear integer problems. Our method provides the complete Pareto frontier N of non-dominated points and, for this purpose, it considers exactly vertical bar N vertical bar single-objective problems by using reduction with test sets instead of solving with an optimizer. Although we use Grobner bases for the computation of test sets, which may provoke a bottleneck in principle, the computational results are shown to be promising, especially for unbounded knapsack problems, for which any usual branch-and-cut strategy could be much more expensive. Nevertheless, this algorithm can be considered as a potentially faster alternative to IP-based methods when test sets are available. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Multiple objective programming Non-dominated set Pareto set epsilon-constraint method Unbounded Knapsack Problem Algebraic test sets

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An Extended C&CG Algorithm for Solving Two-Stage Robust Optimization of Economic and Feasible Scheduling

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2025年第2期205卷 1-29页

作者： Chen, Ruibin Bao, Zhejing Lu, Lingxia Yu, Miao Zhejiang Univ Hangzhou Peoples R China

The extensively researched column-and-constraint-generation (C&CG) algorithm, which utilizes the KKT (Karush-Kuhn-Tucker) condition or duality theory to reformulate the subproblem, encounters challenges when solving two-stage robust optimization (TSRO) problems with extreme parameters that could adversely affect the feasibility of the second-stage decision. After the analysis of the original C&CG algorithm, an extended C&CG algorithm with multiple subproblems is proposed to overcome the challenges, which decompose a TSRO model into the master problem and several subproblems searching for the worst-case scenarios. A simple linear case is given to show the shortcoming of the traditional C&CG algorithm and the advantage of the extended C&CG algorithm. Then, a TSRO model for the scheduling optimization of electricity system considering the optimal power flow (OPF) is proposed, in order to explore the effectiveness of the extended C&CG algorithm in handling the general optimization problem while considering the feasibility. Finally, the proposed solving method is validated by case studies.

关键词： Column and constraint generation Two-stage robust optimization Feasibility check epsilon-constraint method

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Bi-Objective Optimization of a Flow Shop Scheduling Problem Under Time-of-Use Tariffs

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2025年 22卷 7679-7695页

作者： Wang, Xinyue Chu, Feng Ren, Tao Bai, Danyu Univ Paris Saclay Univ Evry Lab IBISC F-91025 Paris France Northeastern Univ Software Coll Shenyang 110819 Peoples R China Dalian Maritime Univ Sch Maritime Econ & Management Dalian 116026 Peoples R China

Time-of-use (ToU) tariffs flexibly offer markedly cheap electricity prices to industrial and residential users during off-peak periods, encouraging them to shift their peak electricity demands in valley periods. Although ToU tariffs play a crucial role in balancing electricity supply and demand, especially in energy-intensive industries, the best trade-off between industrial performance and energy costs has not been well explored. Manufacturing consumes a substantial amount of energy, primarily in the form of electricity, leading to imbalances in power consumption. The flow shop scheduling (FSS) model is one of the most prevalent models in manufacturing. To explore the significant role of ToU tariffs in manufacturing, this study addresses a bi-objective FSS problem under ToU tariffs. The objective is to find the optimal balance between customer satisfaction and total electricity cost. A tight mixed integer programming model is developed to solve this NP-hard problem using business optimizers. On the bases of the problem properties demonstrated in this study, valid inequalities are designed to reduce the solution space of the problem. For small-scale instances, an improved $\varepsilon $ -constraint method is presented to find the Pareto front. For medium and large-scale instances, a two-stage fruit fly optimization (TFFO) algorithm is developed to obtain the near Pareto front. Experimental results demonstrate the efficiency and effectiveness of the proposed model and algorithms. Note to Practitioners-Scheduling for complex systems remains a formidable challenge in manufacturing. Energy cost saving is a major objective for all energy-intensive industries. Effective scheduling is crucial for businesses achieving eco-friendly performance, especially under ToU tariffs. This study aims to provide efficient scheduling model and methods that can guide decision-makers in fostering ecological transitions. The $\varepsilon $ -constraint method can find globally optimal soluti

关键词： Flow shop scheduling time-of-use electricity tariffs mixed integer programming fruit fly optimization metaheuristic epsilon-constraint method Flow shop scheduling time-of-use electricity tariffs mixed integer programming fruit fly optimization metaheuristic

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ε-constraint procedures for Pareto front optimization of large size discrete time/cost trade-off problem

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2025年第3期322卷 753-769页

作者： Aminbakhsh, Saman Sonmez, Rifat Atan, Tankut Atilim Univ Civil Engn Ankara Turkiye Middle East Tech Univ Civil Engn Ankara Turkiye Bahcesehir Univ Ind Engn Istanbul Turkiye

The discrete time/cost trade-off problem (DTCTP) optimizes the project duration and/or cost while considering the trade-off between activity durations and their direct costs. The complete and non-dominated time-cost profile over the set of feasible project durations is achieved within the framework of Pareto front problem. Despite the importance of Pareto front optimization in project and portfolio management, exact procedures have achieved very limited success in solving the problem for large size instances. This study develops exact procedures based on combinations of mixed-integer linear programming (MILP), epsilon-constraint method, network and problem reduction techniques, and present new bounding strategies to solve the Pareto problem for large size instances. This study also provides new large size benchmark problem instances aiming to represent the size of real-life projects for the DTCTP. The new instances, therefore, are generated to include up to 990 activities and nine execution modes. Computational experiments reveal that the procedures presented herein can remarkably outperform the state-of-the-art exact methods. The new exact procedures enabled obtaining the optimal Pareto front for instances with serial networks that include more than 200 activities for the first time.

关键词： Discrete time/cost trade-off problem Pareto front Large instances Multi-objective optimization epsilon-constraint method

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Reliability-aware multi-objective approach for predictive asset management: A Danish distribution grid case study

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APPLIED ENERGY 2024年 358卷

作者： Mirshekali, Hamid Mortensen, Lasse Kappel Shaker, Hamid Reza Univ Southern Denmark Maersk Mc Kinney Moeller Inst Fac Engn SDU Ctr Energy Informat Odense Denmark

The transition towards sustainable practices and a reliable electricity grid accommodates the rising electri-fication of the heating and transportation sectors. Aging, environmental factors, and operational conditions of electrical grid infrastructure contribute to a higher likelihood of faults. This leads to a reduced level reliability, emphasizing the importance of renewing electrical grid infrastructure, particularly underground cables. Optimally replacing cables is essential, taking into account various factors like reducing the fault probability, minimizing the cost of power outages, and enhancing reliability within the budgetary constraint. This paper introduces an innovative methodology to predictive asset management for replacing underground cables using multi-objective optimization approach. Three objective functions are formulated: number replaced cables, cost of power outages, and interruption-related index, which is determined through metrics SAIFI, SAIDI, and ASIDI. These objectives are modeled as mixed-integer programming creating a multi-objective optimization problem, which is addressed using the epsilon-constraint approach. The optimization model identifies the cables that should be replaced within the budget constraint, aiming to optimize the objectives. The effectiveness of this approach is assessed using a real Danish distribution grid. The findings indicate that, compared to methods based on the cable age, fault vulnerability, and risk assessment, the proposed method demonstrates superior performance in terms of reliability metrics and power outage cost.

关键词： epsilon-constraint method Multi-objective optimization Predictive asset management Underground cable

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Optimizing tree selection for planning cable yarding operations: a multi-objective modelling approach

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FOREST ECOLOGY AND MANAGEMENT 2025年 578卷

作者： Sforza, Francesco Ziesak, Martin Lingua, Emanuele Starke, Michael Univ Padua Dept Land Environm Agr & Forestry Viale Univ 16 I-35020 Padua Legnaro Italy Bern Univ Appl Sci Sch Agr Forest & Food Sci HAFL Langgasse 85 CH-3052 Bern Switzerland

When planning timber harvesting in mountainous areas, selecting the trees to extract is highly challenging. This is due to the need to consider both the forest management plan as well as feasibility aspects of the logging operation. Additionally, the choice using cable yarding systems in steep and difficult terrain increases the complexity and related costs of the harvesting process. The protective function of mountain forests against natural hazards adds another layer of consideration. Decision-makers must strike a balance between maintaining the protective function of the forest directly after cutting and on a long term, while maximizing the economic efficiency of the harvesting operation. In this study, we have developed an optimization model for tree selection using linear mixed programming. The model relies on high-resolution airborne laser scanning data to create a forest inventory through individual tree detection. Constituting the Pareto frontier, by optimizing two primary objectives, 15 optimal trade-off solutions could be identified when minimizing the harvesting area and maximizing the economic benefit of timber harvesting. Four of the solutions were identified, which maintain the maximum protective effect of the remaining forest, with a cumulative basal area ranging from 33.3 to 33.9 m(2)ha(-1), while significantly reducing the economic loss from 17 % to 79.6 % when emphasizing the economic benefit maximization. Furthermore, the model presented four solutions that keep the protective effect above the minimum threshold (cumulative basal area > 30 m(2)ha(-1)) while also resulting in positive economic benefits from harvesting. This model presents a method that integrates a multi-objective approach to decision making, considering the practical constraints of cable yarding technology in the process of tree selection in mountainous areas.

关键词： Linear programming epsilon-constraint method Protective forest Forest management Timber harvest Economic benefit

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Optimal operational and carbon neutrality strategies for private hospitals: A multi-objective approach considering patient flow

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TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW 2025年 198卷

作者： Li, Haoran Wu, Yiwei Xin, Baogui Xu, Min Wu, Shining Shandong Univ Sci & Technol Coll Econ & Management Qingdao 266590 Peoples R China Hong Kong Polytech Univ Dept Logist & Maritime Studies Hong Kong 999077 Peoples R China Hong Kong Polytech Univ Dept Ind & Syst Engn Hong Kong 999077 Peoples R China

Hospitals are now the fifth-largest source of global greenhouse gas (GHG) emissions. Despite this significant impact, the critical goal of achieving carbon neutrality is often overlooked in optimization studies on healthcare operations management. To address this gap, this paper proposes a novel multi-objective decision-making framework for private hospitals that balances patient health, environmental impact, and economic performance. This study tackles the intricate challenge of multi-objective optimization that maximizes patient utility and hospital profit while simultaneously minimizing net carbon emissions. An exact algorithm based on the epsilon-constraint method is employed to optimize hospital operational decisions by discretizing patient utility and net carbon emission targets into linear constraints on the non-concave profit objective. This approach guarantees Pareto-optimal solutions, thus enabling hospital decision-makers to select their preferred options among the three criteria: patient utility, environmental sustainability, and hospital profitability, while exploring the resulting trade-offs. Additionally, this study discusses the impacts of hospital operational decision changes on these objectives, particularly under scenarios where patient flow increases waiting time due to limited hospital capacity. To validate the practical significance of the proposed multi-objective optimization model and evaluate the effectiveness of the proposed algorithm, two case studies and sensitivity analyses are conducted. The results demonstrate that this approach effectively supports hospital decision-makers in making informed decisions that balance patient utility, carbon neutrality, and hospital profitability objectives.

关键词： Healthcare operations management Multi-objective optimization epsilon-constraint method Carbon neutrality Patient flow

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Optimization, validation and analyses of a hybrid PV-battery-diesel power system using enhanced electromagnetic field optimization algorithm and ε-constraint

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ENERGY REPORTS 2024年 11卷 5335-5349页

作者： Zhu, Chaoyang Zhang, Yunxiang Wang, Mengxia Deng, Jinxin Cai, Yiwei Wei, Wei Guo, Mengxing Univ China Inst Social Innovat & Publ Culture Commun Beijing 100000 Peoples R China Int Inst Engn Psychol Denver CO 80201 USA Univ Illinois Champaign Urbana Champaign IL 61801 USA Hainan Vocat Univ Sci & Technol Haikou 570100 Hainan Peoples R China Shenzhen High level Talents Dev Promot Assoc Shenzhen 518000 Guangdong Peoples R China CDA Int Accelerator Shenzhen 518000 Guangdong Peoples R China Shenzhen Res Inst Beijing Inst Technol Shenzhen 518000 Guangdong Peoples R China Univ Wollongong Wollongong NSW 2522 Australia Xian Univ Technol Sch Comp Sci & Engn Xian 710048 Shaanxi Peoples R China Shandong Open Univ Jinan 250000 Shandong Peoples R China

This study introduces and assesses a hybrid renewable energy system tailored for a practical, off-grid location. The integrated power system comprises a diesel generator, photovoltaic panels, battery storage system, and a converter. The primary objective is to formulate a system exhibiting optimal performance concerning cost, carbon emissions, and load satisfaction, necessitating a three-objective optimization approach. Leveraging the epsilon-constraint method alongside an enhanced optimization algorithm, the study compares the enhanced algorithm against its original version and established optimization algorithms using intricate benchmark functions. Outcomes indicate the enhanced algorithm's superiority, manifested through minimal error and standard deviation. Subsequently, the enhanced hybrid optimization method is employed to optimize the design and operation of the proposed power system, considering economic, environmental, and technical facets. Rigorous sensitivity analyses ascertain the system cost's responsiveness to varying parameters. To validate the efficacy of the proposed optimization approach, a parallel optimization of the hybrid power system is conducted using HOMER software. Results demonstrate that the proposed hybrid optimization method not only meets defined limits but also minimizes carbon emissions, emphasizing its effectiveness in designing sustainable and efficient off-grid energy systems.

关键词： Multi-objective optimization Enhanced electromagnetic field optimization algorithm epsilon-constraint method Hybrid renewable energy system Photovoltaic

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