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Monte Carlo Simulation for Computing the Worst Value of the Objective Function in the interval linear programming

International Journal of Applied and Computational Mathematics 2016年第4期2卷 509-518页

作者： Allahdadi, M. Golestane, A. Khaje Mathematics Faculty University of Sistan and Baluchestan Zahedan Iran

In this paper, we consider the interval linear programming (ILP) with equality constraints. Computing the best value of the objective function is easy, but obtaining the worst value of the objective function is much more complicated. Firstly, we determine range of optimal values of the objective function. Secondly, by considering some distribution functions, we use Monte Carlo simulation to explore the solutions for the ILP model, and then we compare the results obtained through the simulations. © 2015, Springer India Pvt. Ltd.

关键词： interval linear programming Monte Carlo simulation The worst optimal value

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Optimal Relay Coordination for Microgrids Using Hybrid Modified Particle Swarm Optimization - interval linear programming Approach

Optimal Relay Coordination for Microgrids Using Hybrid Modif...

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North American Power Symposium (NAPS)

作者： Srinivas, S. T. P. Swarup, K. Shanti IIT Madras Dept Elect Engn Madras Tamil Nadu India

ISBN: (纸本)9781538626993

In practical power systems, the fault current sensed by the relay depends on location of the fault and network topological changes. Fault current sensed by the relay for near end fault is greater than that for a far end fault. In meshed distribution systems with Distribution Generation (DG), the fault currents are fed from both ends of the line and consequently the currents sensed by the relays at both ends are different. These variable fault currents may lead to miscoordination of directional overcurrent relays (DOCRs). To overcome this problem, the coordination constraints corresponding to the fault currents at different fault locations should be satisfied. This paper proposes a new approach based on interval linear programming (ILP) which is hybridized with Modified Particle Swarm Optimization (MPSO). The basic idea is to convert the inequality constraints of a standard linear programming (LP) problem to interval constraints using theory of ILP and represent the ILP problem as a standard LP problem. This procedure reduces considerable number of coordination constraints and better sub-optimal solution is obtained compared to conventional optimization. The proposed method is tested on IEEE 14 bus test system in microgrid perspective.

关键词： Optimal relay coordination microgrids modified particle swarm optimization interval linear programming directional overcurrent relays nonlinear optimization

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Learning from Data by interval linear programming

Learning from Data by Interval Linear Programming

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International Conference on Advanced Measurement and Test (AMT 2010)

作者： Li, Wei Hangzhou Dianzi Univ Sch Sci Hangzhou 310018 Zhejiang Peoples R China

ISBN: (纸本)0878492712

The linear programming based method are popular methods for learning from empirical data (observations, samples, examples, records). In this paper, an interval linear programming based method for regression problems is proposed. The explicit representation of the general optimal solution of regression problem is obtained in terms of a generalized inverse of the constraint matrix. This explicit solution has obvious theoretical (and possibly computational) advantages over the well-known iterative methods of linear programming.

关键词： learning interval linear programming regression generalized inverse of matrix

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Overview of solution methods for solving interval linear programming and new method 4

Overview of solution methods for solving interval linear pro...

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4th Iranian Joint Congress on Fuzzy and Intelligent Systems (CFIS)

作者： Ashayerinasab, H. A. Nehi, H. Mishmast Allahdadi, M. Univ Sistan & Baluchestan Dept Math Zahedan Iran

ISBN: (纸本)9781467385459

In this paper, we review previous methods for solving interval linear programming (ILP) problems. In most of these methods such as BWC, ILP, TSM, and SOM-2 methods, part of solution space is absolutely infeasible and non-optimal. To eliminate infeasible part of solution space, several methods such as MILP, and ITSM are proposed. The solution space of these methods is absolutely feasible and is not completely optimal. Also, we introduce new method to improve SOM-2 method that is called ISOM-2 method and its sub-models. The solution space of ISOM-2 method is absolutely feasible and optimal.

关键词： Feasibility Optimality interval linear programming

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Optimization of electric-heat-gas model based on interval linear programming 33

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

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33rd Chinese Control and Decision Conference (CCDC)

作者： Li Mingtong Wang Lidi Zhu Sitong Miao Yilin Wang Xinyao Shenyang Agr Univ Shenyang 110866 Peoples R China

ISBN: (纸本)9781665440899

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 goal. The 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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The optimal solution set of interval linear programming problems

The optimal solution set of interval linear programming prob...

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作者： Garajová, Elif Charles University of Prague

Determining the set of all optimal solutions of a linear program with interval data is one of the main problems discussed in interval optimization. We review two methods based on duality in linear programming, which are used to approximate the optimal set. Additionally, another decomposition method based on complementary slackness is proposed. This method provides the exact description of the optimal set for problems with a fixed coefficient matrix. The second part of the thesis is focused on studying the topological and geometric properties of the optimal set. We examine sufficient conditions for closedness, boundedness, connectedness and convexity. We also prove that testing boundedness is co- NP-hard for inequality-constrained problems with free variables. Stronger results are derived for some special classes of interval linear programs, such as problems with a fixed coefficient matrix. Furthermore, we study the effect of transformations commonly used in linear programming on interval problems, which allows for a direct generalization of some results to different types of interval linear programs. Powered by TCPDF (***)

关键词： interval linear programming optimal set topological properties

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A Copula-based interval linear programming model for water resources allocation under uncertainty

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JOURNAL OF ENVIRONMENTAL MANAGEMENT 2022年 317卷 115318页

作者： Yue, Wencong Yu, Shujie Xu, Meng Rong, Qiangqiang Xu, Chao Su, Meirong Dongguan Univ Technol Res Ctr Ecoenvironm Engn Dongguan 523808 Peoples R China Guangdong Prov Key Lab Water Qual Improvement & Ec Guangzhou 510006 Peoples R China Zhejiang Univ Finance & Econ Sch Publ Adm Hangzhou 310018 Peoples R China

Water scarcity tends to be aggravated by increase in water demand with the trend of socio-economic development. Thus, non-stationary characteristics of water demand should be identified in water resources allocation (WRA) to alleviate the potential influences from water shortages. In this study, a Copula-based interval linear programming model was established for regional WRA. Through combining correlation analysis and an interval linear programming model, this model can: 1) identify interactions between water demand and socio-economic development levels based on Copula functions, 2) explore variations in water shortage with consideration of multiple risk tolerance levels of decision-makers based on Copula sampling, and 3) obtain desired strategies for WRA through an interval linear programming model. Also, Dalian City in China was selected as a case study area to verify the effectiveness of the model for WRA to five water users (i.e., agricultural sector, industrial sector, public service sector, domestic residents, and ecological environment). Considering multiple tolerance levels of decision-makers to water shortage risk, three scenarios (i.e., S1 to S3), indicating 20%, 40%, and 60% of their low, medium, and high tolerance levels, were proposed. The results showed that the correlation between the amount of water demand and indicators of socio-economic development can be described by Clayton and Gaussian Copula functions. The total water supply of Dalian in 2030 would increase by 2.06%-2.65%, compared with the one in 2025. The allocation of water resources across districts was influenced by varied water demand, energy consumption, and risk tolerance levels. Compared with the amount of water allocation in 2025, the contribution of transferred water sources would increase by 6.71% and 7.04% under S1 and S2 in 2030, respectively, and decrease by 14.31% under S3. With the increase of risk tolerance levels of decision-makers, the amount of water supply in Dalian City

关键词： Water resources allocation Copula functions interval linear programming Water shortage risk Dalian city

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Optimal allocation of photovoltaic energy storage in DC distribution network based on interval linear programming

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JOURNAL OF ENERGY STORAGE 2024年 85卷

作者： Yu, Dan Tang, Ren Pan, Lezhen Zhejiang Huayun Elect Power Engn Design Consulting Hangzhou 310000 Zhejiang Peoples R China State Grid Wenzhou Power Supply Co Wenzhou 325000 Zhejiang Peoples R China

In order to improve the capacity of optimal allocation of photovoltaic energy storage in DC (Direct Current) distribution network, an optimal allocation method of photovoltaic energy storage in DC distribution network based on interval linear programming is proposed. Taking into account the operational life loss of energy storage and aiming at the minimum operating income of energy storage investment, the fluctuation relationship and constraint variable relationship model are built in the storage and allocation of photovoltaic energy in the DC distribution network, and the comprehensive cost concept distribution set is established based on the network loss cost and the cost of energy storage and allocation, and the optimization detection in the process of energy storage and allocation of photovoltaic energy in the DC distribution network is realized through interval linear programming scheduling. The configuration model is built taking into account the voltage offset index, and the balanced dispatching and fast response model analysis of photovoltaic energy storage in the DC distribution network are realized through the zoning dispatching and power density spectrum analysis. According to the analysis of suppressing the fluctuation of distributed energy, the hybrid energy storage is used to suppress. A twolevel configuration model is constructed. The upper layer is the hybrid energy storage capacity and power planning layer, while the lower layer is the power distribution layer, which is to reduce the battery charging and discharging power to reduce the life loss of photovoltaic power supply in the DC distribution network, and realize the configuration of photovoltaic energy storage in the DC distribution network through interval planning. The test shows that this method has good balance and large gain in the configuration of photovoltaic energy storage in the DC distribution network, which improves the output efficiency of the distribution network. The maximum outpu

关键词： interval linear programming DC distribution network Including photovoltaic energy Energy storage configuration

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The outcome range problem in interval linear programming

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COMPUTERS & OPERATIONS RESEARCH 2021年 129卷 105160-105160页

作者： Mohammadi, Mohsen Gentili, Monica Univ Louisville Dept Ind Engn JB Speed Bldg2301 S 3rd St Louisville KY 40292 USA

Quantifying extra functions, herein referred to as outcome functions, over optimal solutions of an optimization problem can provide decision makers with additional information on a system. This bears more importance when the optimization problem is subject to uncertainty in input parameters. In this paper, we consider linear programming problems where input parameters are described by real-valued intervals, and we address the outcome range problem which is the problem of finding the range of an outcome function over all possible optimal solutions of a linear program with interval data. We give a general definition of the problem and then focus on a special class of it where uncertainty occurs only in the right-hand side of the underlying linear program. We show that our problem is computationally hard to solve and also study some of its theoretical properties. We then develop two approximation methods to solve it: a local search algorithm and a super set based method. We test the methods on a set of randomly generated instances. We also provide a real case study on healthcare access measurement to show the relevance of our problem for reliable decision making. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： interval linear programming interval analysis linear programming Heuristics Healthcare Inexact data

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Satisficing solutions and duality in interval and fuzzy linear programming

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FUZZY SETS AND SYSTEMS 2003年第1期135卷 151-177页

作者： Inuiguchi, M Ramik, J Tanino, T Vlach, M Univ Ostrava Inst Res & Applicat Fuzzy Modeling Ostrava 70103 1 Czech Republic Osaka Univ Grad Sch Engn Suita Osaka 5650871 Japan Japan Adv Inst Sci & Technol Grad Sch Informat Sci Tatsunokuchi 9231292 Japan

In this paper, we introduce a class of fuzzy linear programming problems and define the concepts of feasible and satisficing solutions-the necessary tools for dealing with such problems. In this way, we show that the class of crisp (classical) LP problems can be embedded into the class of FLP ones. Moreover, for FLP problems we define the concept of duality and prove the weak and strong duality theorems. Further, we define a class of interval linear programming problems as a special subclass of FLP problems and apply the previous results to this special case. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： fuzzy relations fuzzy linear programming duality satisficing solution interval linear programming

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