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IEEE Power and Energy Society General Meeting

作者： Boran Zhou Quanyuan Jiang College of Electrical Engineering Zhejiang University Hangzhou 310027 China Zhejiang University Hangzhou Zhejiang 310027 China.

ISBN: (纸本)9781467327275

This paper presents a security-constrained unit commitment (SCUC) model which takes into account the volatility of wind power generation and load. With the help of interval linear programming theory, this model can guarantee the security of the power system within the forecasting interval of wind power generation and load. The Benders decomposition technique is applied to decompose this model into a master problem and two sub-problems. The master problem solves a unit commitment (UC) without network security constraints. One sub-problem checks whether the commitment and dispatch solution of master problem can satisfy the network security constraints. The other sub-problem, using interval linear programming theory, checks whether the worst-case security constraints can be satisfied with the schedule obtained in the master problem. The iterative process will continue until no violation occurs in both sub-problems. The case studies are analyzed to exhibit the effectiveness of the proposed UC model to guarantee the security of power system and improve the economy of the system.

关键词： security-constrained unit commitment uncertainty benders decomposition interval liner programming Wind energy generation Unit commitment Power system security interval linear programming power systems Benders decomposition Network security

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Optimization of electric-heat-gas model based on interval linear programming

Optimization of electric-heat-gas model based on interval li...

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第33届中国控制与决策会议

作者： Li Mingtong Wang Lidi Zhu Sitong Miao Yilin Wang Xinyao Shenyang Agricultural University

In order to improve the coupling relationship between energy sources and improve the energy utilization rate,this paper controls the parameter variables of energy storage equipment and renewable energy power generation technology,compiles the corresponding optimization program,obtains the optimal combination of different energy types distribution work,and realizes the economic optimization *** program analysis shows that:the existence of renewable energy power generation technology will greatly reduce the wind energy abandonment rate and make the wind energy output regulation within the controllable range;the existence of energy storage equipment will reduce the overall economic consumption of the system;the joint output of different energy sources can not only meet the energy demand,but also improve the efficiency of the whole system,so the system has flexible energy regulation ability,At the same time,the economic budget is within the controllable range and has practical value.

关键词： interval linear programming Combined power heating and gas Renewable energy Optimal design

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On the new solution to interval linear fractional programming problems

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EVOLUTIONARY INTELLIGENCE 2024年第5-6期17卷 4001-4005页

作者： Khastan, A. Jimenez, B. Hernandez Moreno, A. Beato Inst Adv Studies Basic Sci Dept Math Zanjan Iran Univ Pablo Olavide Dept Econ Metodos Cuantitat & Hist Econ Seville Spain Univ Seville Dept Estadist & Invest Operat Seville Spain

In this paper, we study the interval linear fractional programming problems using the concept of g-division. We transform the problem into a new linear fractional programming problem and obtain a nondominated solution to the interval linear fractional programming problem. We show that the new solution dominates the previous nondominated objective value presented in the literature. Finally, some examples are provided to illustrate our results.

关键词： interval linear fractional programming g-division interval linear programming interval arithmetic

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A New Method to Solve Fuzzy interval Flexible linear programming Using a Multi-Objective Approach

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FUZZY INFORMATION AND ENGINEERING 2021年第2期13卷 248-265页

作者： Nasseri, S. H. Verdegay, J. L. Mahmoudi, F. Univ Mazandaran Dept Math Babolsar Iran Univ Granada Dept Comp Sci & AI Granada Spain

Recently fuzzy interval flexible linear programs have attracted many interests. These models are an extension of the classical linear programming which deal with crisp parameters. However, in most of the real-world applications, the nature of the parameters of the decision-making problems are generally imprecise. Such uncertainties can lead to increased complexities in the related optimisation efforts. Simply ignoring these uncertainties is considered undesired as it may result in inferior or wrong decisions. Therefore, inexact linear programming methods are desired under uncertainty. In this paper, we concentrate a fuzzy flexible linear programming model with flexible constraints and the interval objective function and then propose a new solving approach based on solving an associated multi-objective model. Finally, a numerical example is included to illustrate the mentioned solving process.

关键词： Multi-objective linear programming fuzzy interval flexible linear programming interval linear programming interval arithmetic flexible constraints

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A New Method to Solve Fuzzy interval Flexible linear programming Using a Multi-Objective Approach

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Fuzzy Information and Engineering 2019年第2期11卷 221-238页

作者： S. H. Nasseri J. L. Verdegay F. Mahmoudi a Department of Mathematics University of Mazandaran Babolsar Iran b Department of Computer Science and A.I. Universidad de Granada Granada Spain

ABSTRACTFormulae display:?Mathematical formulae have been encoded as MathML and are displayed in this HTML version using MathJax in order to improve their display. Uncheck the box to turn MathJax off. This feature requires Javascript. Click on a formula to *** fuzzy interval flexible linear programs have attracted many interests. These models are an extension of the classical linear programming which deal with crisp parameters. However, in most of the real-world applications, the nature of the parameters of the decision-making problems are generally imprecise. Such uncertainties can lead to increased complexities in the related optimisation efforts. Simply ignoring these uncertainties is considered undesired as it may result in inferior or wrong decisions. Therefore, inexact linear programming methods are desired under uncertainty. In this paper, we concentrate a fuzzy flexible linear programming model with flexible constraints and the interval objective function and then propose a new solving approach based on solving an associated multi-objective model. Finally, a numerical example is included to illustrate the mentioned solving process.

关键词： Multi-objective linear programming fuzzy interval flexible linear programming interval linear programming interval arithmetic flexible constraints

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Inverse linear programming with interval coefficients

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2016年 292卷 591-608页

作者： Mostafaee, Amin Hladik, Milan Cerny, Michal Islamic Azad Univ Northern Tehran Branch Dept Math Tehran Iran Charles Univ Prague Fac Math & Phys Dept Appl Math Prague 11800 Czech Republic Univ Econ Fac Informat & Stat Prague 13067 Czech Republic

The paper deals with the inverse linear programming problem over intervals. More precisely, given interval domains for the objective function coefficients and constraint coefficients of a linear program, we ask for which scenario a prescribed optimal value is attained. Using continuity of the optimal value function (under some assumptions), we propose a method based on parametric linear programming techniques. We study special cases when the interval coefficients are situated in the objective function and/or on the right-hand sides of the constraints as well as the generic case when possibly all coefficients are intervals. We also compare our method with the straightforward binary search technique. Finally, we illustrate the theory by an accompanying numerical study, called "Matrix Casino", showing some approaches to designing a matrix game with a prescribed game value. (C) 2015 Elsevier B.V. All rights reserved.

关键词： interval analysis interval linear programming Inverse linear programming Parametric analysis Matrix game

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Checking weak optimality of the solution to linear programming with interval right-hand side

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OPTIMIZATION LETTERS 2014年第4期8卷 1287-1299页

作者： Li, Wei Luo, Jiajia Wang, Qin Li, Ya Hangzhou Dianzi Univ Inst Operat Res & Cybernet Hangzhou 310018 Zhejiang Peoples R China China Jiliang Univ Coll Sci Hangzhou 310018 Zhejiang Peoples R China

The interval linear programming (IvLP) is a method for decision making under uncertainty. A weak feasible solution to IvLP is called weakly optimal if it is optimal for some scenario of the IvLP. One of the basic and difficult tasks in IvLP is to check whether a given point is weak optimal. In this paper, we investigate linear programming problems with interval right-hand side. Some necessary and sufficient conditions for checking weak optimality of given feasible solutions are established, based on the KKT conditions of linear programming. The proposed methods are simple, easy to implement yet very effective, since they run in polynomial time.

关键词： interval linear programming Weak feasible solution Weak optimal solution KKT conditions

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Optimization with uncertain, inexact or unstable data: linear programming and the interval approach

Optimization with uncertain, inexact or unstable data: Linea...

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10th International Conference on Strategic Management and its Support by Information Systems

作者： Cerny, Michal Hladik, Milan Univ Econ Prague Czech Republic

ISBN: (纸本)9788024830964

This paper accompanies our invited lecture on interval methods in optimization. First, we put the interval approach in context with other approaches to modeling inexactness, instability or imprecision of input data;in particular, we discuss the stochastic and fuzzy approach. Then we turn to interval linear programming. We show some important aspects in which the interval-valued linear programs differ from traditional linear programs. We emphasize how various formulations of the auxiliary linear program, which are equivalent in the traditional setting, differ in the interval setting from the computational point of view. We also consider some natural questions, e.g. weak and strong feasibility and the problem of finding the range of possible optimal values and the catastrophic scenario. We also point out some (subjectively selected) interesting open problems in the field.

关键词： interval optimization interval linear programming inexact data interval data open problems

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Optimal synchronization of overcurrent relays in active distribution networks using a hybrid genetic-differential optimization algorithm

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ELECTRICAL ENGINEERING 2025年 1-16页

作者： Shendi, Ahad Jahandideh Mohammadian, Leila Ghanizadeh, Reza Pouladi, Jaber Beiza, Jamal Islamic Azad Univ Dept Elect Engn Shabestar Branch Shabestar Iran Islamic Azad Univ Dept Elect Engn Urmia Branch Orumiyeh Iran

Any failure in the distribution network, a crucial component of a power system, must be swiftly recognized by relays. The presence of distributed generation resources in the distribution network poses a new challenge for the correct performance of overcurrent relays. These sources, by injecting fault current and changing the network structure, can lead to the maloperation of overcurrent relays and alter their performance. Overcurrent relays adhere to various standards, each with a specific characteristic curve. The aim of this paper is to optimize the coordination of overcurrent relay and its characteristic curve, in addition to refining other relay settings. This is achieved with the goal of reducing the operation times of both main and supporting relays and eliminating the inconsistencies between them. To address this issue, we employ a combination of genetic and differential optimization algorithms. The effectiveness of this method is proven through the implementation of different scenarios, demonstrating a reduction in the operation time of the relays.

关键词： Optimal relay coordination Microgrids Fire hawk optimization interval linear programming Directional overcurrent relays Nonlinear optimization

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Synchronic interval Gaussian mixed-integer programming for air quality management

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SCIENCE OF THE TOTAL ENVIRONMENT 2015年 538卷 986-996页

作者： Cheng, Guanhui Huang, Guohe (Gordon) Dong, Cong Univ Regina Fac Engn & Appl Sci Regina SK S4S 0A2 Canada Univ Regina Inst Energy Environm & Sustainabil Res Regina SK S4S 0A2 Canada

To reveal the synchronism of interval uncertainties, the tradeoff between system optimality and security, the discreteness of facility-expansion options, the uncertainty of pollutant dispersion processes, and the seasonality of wind features in air quality management (AQM) systems, a synchronic interval Gaussian mixed-integer programming (SIGMIP) approach is proposed in this study. A robust interval Gaussian dispersion model is developed for approaching the pollutant dispersion process under interval uncertainties and seasonal variations. The reflection of synchronic effects of interval uncertainties in the programming objective is enabled through introducing interval functions. The proposition of constraint violation degrees helps quantify the tradeoff between system optimality and constraint violation under interval uncertainties. The overall optimality of system profits of an SIGMIP model is achieved based on the definition of an integrally optimal solution. Integer variables in the SIGMIP model are resolved by the existing cutting-plane method. Combining these efforts leads to an effective algorithm for the SIGMIP model. An application to an AQM problem in a region in Shandong Province, China, reveals that the proposed SIGMIP model can facilitate identifying the desired scheme for AQM. The enhancement of the robustness of optimization exercises may be helpful for increasing the reliability of suggested schemes for AQM under these complexities. The interrelated tradeoffs among control measures, emission sources, flow processes, receptors, influencing factors, and economic and environmental goals are effectively balanced. Interests of many stakeholders are reasonably coordinated. The harmony between economic development and air quality control is enabled. Results also indicate that the constraint violation degree is effective at reflecting the compromise relationship between constraint-violation risks and system optimality under interval uncertainties. This can he

关键词： interval linear programming Synchronism Constraint violation Global optimality Gaussian model Dispersion process Mixed-integer Air quality management

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