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Determining the Range of the Power Consumption in linear DC interval Parameter Circuits

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2011年第9期58卷 2182-2188页

作者： Kolev, Lubomir Tech Univ Sofia Dept Elect Theoret Engn Sofia 1000 Bulgaria

The paper considers the following worst-case steady-state tolerance analysis problem: given a linear dc circuit whose resistors and sources have preset tolerances, determine the range of the electrical power consumed in the circuit. It is shown that the power range sought can be computed as the range of an associated interval linear programming problem. A method for solving the latter problem is suggested whose numerical complexity is not a priori exponential. A numerical example illustrating the new method is provided.

关键词： linear dc circuits power consumption range interval methods interval linear programming

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An inexact fuzzy-random-chance-constrained air quality management model

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STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT 2013年第8期27卷 1929-1946页

作者： Xu, Y. Shao, L. G. Huang, G. H. North China Elect Power Univ MOE Key Lab Reg Energy & Environm Syst Optimizat Sino Canada Resources & Environm Res Acad Beijing 102206 Peoples R China China Ctr Informat Ind Dev Beijing 100846 Peoples R China Univ Regina Fac Engn & Appl Sci Regina SK S4S 0A2 Canada

An inexact fuzzy-random-chance-constrained programming model (IFRCCMM) was developed for supporting regional air quality management under uncertainty. IFRCCMM was formulated through integrating interval linear programming within fuzzy-random-chance-constrained programming framework. It could deal with parameter uncertainties expressed as not only fuzzy random variables but also discrete intervals. Based on the stochastic and fuzzy chance-constrained programming algorithms, IFRCCMM was solved when constraints was satisfied under different satisfaction and violation levels of constraints, leading to interval solutions with different risk and cost implications. The proposed model was applied to a regional air quality management problem for demonstration. The obtained results indicated that the proposed model could effectively reflect uncertain components within air quality management system through employing multiple uncertainty-characterization techniques (in random, fuzzy and interval forms), and help decision makers analyze trade-offs between system economy and reliability. In fact, many types of solutions (i.e. conservative solutions with lower risks and optimistic solutions with higher risks) provided by IFRCCMM were suitable for local decision makers to make more applicable decision schemes according to their understanding and preference about the risk and economy. In addition, the modeling philosophy is general and applicable to many other environmental problems that may be complicated with multiple forms of uncertainties.

关键词： Fuzzy-random-chance-constrained programming interval linear programming Air quality management Uncertainty

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A hybrid waste-flow allocation model considering multiple stage and interval-fuzzy chance constraints

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CIVIL ENGINEERING AND ENVIRONMENTAL SYSTEMS 2012年第1期29卷 59-78页

作者： Xu, Y. Huang, G. H. Cao, M. F. Dong, C. Li, Y. F. N China Elect Power Univ MOE Key Lab Reg Energy & Environm Syst Optimizat Resources & Environm Res Acad Beijing 102206 Peoples R China

An inexact two-stage fuzzy chance-constrained programming (ITSFCCP) model was developed in this study for dealing with multiple uncertainties associated with solid waste management systems. The model was formulated by incorporating fuzzy chance-constrained programming and interval linear programming within a two-stage stochastic programming framework. The model could be used to facilitate analysis of the policy scenarios;meanwhile, the uncertainties associated with solid waste management systems could be expressed as probability distributions, possibility distribution and discrete intervals. A long-term waste planning problem was used to demonstrate the applicability of the ITSFCCP model. The study results indicated that ITSFCCP could provide a linkage to pre-defined policies and allowed violation of system constraints at predefined confidence levels. Moreover, it allowed uncertain information presented as discrete intervals to be communicated into the optimisation process. ITSFCCP could help waste managers to identify desired policies and gain insights into the tradeoffs between system economy and reliability.

关键词： fuzzy chance-constrained programming interval linear programming two-stage stochastic programming solid waste management uncertainty

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Inexact Two-Stage Stochastic Robust Optimization Model for Water Resources Management Under Uncertainty

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ENVIRONMENTAL ENGINEERING SCIENCE 2009年第12期26卷 1765-1776页

作者： Xu, Ye Huang, Guohe Qin, Xiaosheng Univ Regina Fac Engn Regina SK S4S 0A2 Canada N China Elect Power Univ Sino Canada Ctr Energy & Environm Res Beijing Peoples R China Nanyang Technol Univ Sch Civil & Environm Engn Singapore Singapore

An inexact two-stage stochastic robust programming model (ITSRP) was developed in this study for dealing with water resources allocation problems under uncertainty. ITSRP was formulated based on integration of interval linear programming (ILP), stochastic robust optimization (SRO), and two-stage stochastic programming (TSP) techniques. It could deal with uncertainties expressed as not only probability distributions but also discrete intervals, and could facilitate analyses of the policy scenarios that are associated with economic penalties when the predefined policies were violated. Moreover, the variability measure about the second-stage penalty costs was incorporated into the objective function, such that the trade-off between system economy and stability could be evaluated. The developed model was applied to a hypothetical case of water resources management system. Results demonstrated that the ITSRP model could help decision makers generate stable and balanced water resources allocation patterns, gain in-depth insights into effects of the uncertainties, and analyze trade-offs between system economy and stability.

关键词： stochastic robust optimization interval linear programming two-stage stochastic programming water resources management uncertainty

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Mathematical modeling for air quality management under stochastic and interval uncertainties

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STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT 2015年第5期29卷 1485-1498页

作者： Liu, Feng Wen, Zhi Zheng, Li Jun Univ Sci & Technol Beijing Sch Mech Engn Beijing Key Lab Energy Saving & Emiss Reduct Met Beijing 100083 Peoples R China Univ Sci & Technol Liaoning Sch High Temp Mat & Magnesium Resource Engn Anshan 114051 Peoples R China

In this study, an inexact stochastic robust air quality management model (ISRAQMM) was developed for supporting regional air pollution control. The Fengrun district in Tangshan City, China, was used as a study case for demonstration. The ISRAQMM has the advantages of reflecting uncertainty and evaluating trade-offs between system economy and reliability, where the model parameters are provided as discrete intervals and deterministic values under various scenarios. The model's objective function was an integration of the expected cost, cost variability and penalty function of constraints violation rather than the traditional objective function considering only the economic factor;meanwhile, the inexact model parameters were expressed as discrete intervals, which have low data requirements. A variety of solutions were obtained, which could be used to help evaluate the trade-off between system economy and reliability. Using the case study, the applicability of the ISRAQMM was demonstrated. A set of conservative solutions with lower risks and cost-effective solutions with higher risks was provided. The balanced scenario solution was recommended for decision makers, since it respects both system economy and reliability. The successful applications of the ISRAQMM in the studied real world are expected to be a good demonstration for many other areas.

关键词： Stochastic robust optimization interval linear programming Air quality management Fengrun district Uncertainty

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Robust Fully Fuzzy programming with Fuzzy Set Ranking Method for Environmental Systems Planning Under Uncertainty

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ENVIRONMENTAL ENGINEERING SCIENCE 2013年第6期30卷 280-293页

作者： Jin, Lei Huang, Guohe H. Wang, Li Wang, Xiuqian Xiamen Univ Technol Dept Environm Engn Xiamen Peoples R China Xiamen Univ Technol Dept Math & Phys Xiamen Peoples R China Univ Regina Fac Engn Regina SK S4S 0A2 Canada

This article proposes a new robust interactive interval fully fuzzy linear programming (RIIFFLP) method, using the fuzzy ranking method to find a balance between the requirements of constraints and the objective function of a fuzzy set function, as a technique for optimal decision-making under uncertainty. It considerably improved previous interval fuzzy linear programming (FLP) methods by using a new solution method named the robust two-step method (RTSM). The RTSM has a higher membership degree for the fuzzy subset, which allows interval results to stay within the boundaries of constraints. This RIIFFLP model was applied to a case study in municipal solid waste management. Results demonstrated that the solution obtained from the RIIFFLP model had more feasible results by comparison with existing FLP methods. The RIIFFLP also provided optimal interval solutions in different alpha levels that made decision making easier by simply choosing a suitable scenario. Therefore, the RIIFFLP model can be considered a better practical method for problem-solving when uncertainties are present.

关键词： fuzzy programming fuzzy ranking method interval linear programming municipal solid waste robust two-step method

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Optimization-based provincial hybrid renewable and non-renewable energy planning - A case study of Shanxi, China

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ENERGY 2017年 128卷 839-856页

作者： Liu, Yuan He, Li Shen, Jing North China Elect Power Univ Sch Renewable Energy Beijing 102206 Peoples R China North China Elect Power Univ State Key Lab Alternate Elect Power Syst Renewabl Beijing 102206 Peoples R China

Energy planning is crucial to regional sustainable development, it contributes to dealing with electricity demand and supply effectively and tackling air-pollution control in a long-term view. However, the planning is complicated with various factor interrelationships and uncertainties. In this paper, an inexact Bi-level optimization method based on provincial scale hybrid renewable and non-renewable energy planning is developed. This method incorporates Analytic Hierarchy Process based on induced ordered weighted averaging operator and demand side management policies (IOWA-AHP-DSM), interval linear programming (ILP), and bi-level programming method (BLP) into electric power system (EPS) to optimize energy planning and air pollution control. A case study with both environmental and economic objects in Shanxi Province, China, are involved to demonstrate the availability of this method. Seven renewable energy proportion scenarios (0%, 5%, 10%, 15%, 20%, 25% and 30%) are set in this study. Results show that as the proportion increases, the amount of power generation and capacity expansion from natural gas and renewable energy resources increases, while the amount of power from coal and oil, the pollutants emissions and the trading volume of SO2 decreases. According to the satisfaction degrees of these solutions, results show that it meets both goals when the proportion is 20%. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Energy planning Electric power system Bi-level optimization interval linear programming System cost Pollutants emissions

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The optimal value range problem for the interval (immune) Transportation Problem

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2020年 95卷 102059-102059页

作者： D'Ambrosio, C. Gentili, M. Cerulli, R. Univ Salerno Dept Math Via Giovanni Paolo II 132 I-84084 Fisciano SA Italy Univ Louisville JB Speed Sch Engn Ind Engn Dept 132 Eastern Pkwy Louisville KY 40292 USA

We address the problem of finding the range of the optimal cost of a transportation problem when supply and demand vary over an interval. We consider the specific version of a transportation problem with supply inequality constraints and demand equality constraints under the assumption that the transportation costs are immune against the transportation paradox. We investigate some theoretical properties of the problem which constitute the basis of a novel solution algorithm. Our results show that the proposed algorithm hugely outperforms the best existing solution approaches. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Transportation problem Uncertain supply and demand interval linear programming

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An inexact irrigation water allocation optimization model under future climate change

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STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT 2019年第1期33卷 271-285页

作者： Wang, Youzhi Liu, Liu Guo, Ping Zhang, Chenglong Zhang, Fan Guo, Shanshan China Agr Univ Coll Water Resources & Civil Engn Ctr Agr Water Res China Beijing 100083 Peoples R China

Due to the widespread uncertainties in agricultural water resources systems and climate change projections, the traditional optimization methods for agricultural water management may have difficulties in generating rational and effective optimal decisions. In order to get optimal future agricultural water allocation schemes for arid areas with consideration of climate change conditions, the model framework established in this paper integrates a statistical downscaling model, back propagation neural networks, and an evapotranspiration model (the Hargreaves model) with inexact irrigation water allocation optimization model under future climate change scenarios. The model framework, which integrates simulation models and optimization models, considers the interactions and uncertainties of parameters, thereby reflecting the realities more accurately. It is applied to the Yingke Irrigation Area in the midstream area of the Heihe River Basin in Zhangye city, Gansu Province, northwest China. Then, water allocation schemes in planning year (2047) under multiple future Representative Concentration Pathways (RCP) scenarios and the status quo (2016) are compared, in order to evaluate the practicability of generated water allocation schemes. The results show that the water shortages of economic crops are improved compared with the status quo under all RCP scenarios while those of the grain crops present opposite results. Meanwhile, the economic benefits decrease from the status quo to planning year under all future scenarios. This phenomenon is directly related to the amount of irrigation water allocation and is indirectly related to the changes of meteorological conditions. The model framework can reveal the regular pattern of hydro-meteorological elements with the impact of climate change. Meanwhile, it can generate irrigation water allocation schemes under various RCPs scenarios which could provide valuable decision support for water resources managers.

关键词： Climate change interval linear programming Statistical downscaling Back propagation neural network Hargreaves model Irrigation water allocation Uncertainty

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Analyzing urban water supply through an acceptability-index-based interval approach

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ADVANCES IN WATER RESOURCES 2011年第7期34卷 873-886页

作者： Qin, X. S. Xu, Y. Nanyang Technol Univ Sch Civil & Environm Engn Singapore 639798 Singapore Nanyang Technol Univ DHI NTU Water & Environm Res Ctr Singapore 639798 Singapore N China Elect Power Univ SC Res Acad Energy & Environm Studies MOE Key Lab Reg Energy Syst Optimizat Beijing 102206 Peoples R China

Incorporation of uncertainties within an urban water supply management system has been a challenging topic for many years. In this study, an acceptability-index-based two-step interval programming (AITIP) model was developed for supporting urban water supply analysis under uncertainty. AITIP improved upon the traditional two-step interval programming (TIP) through incorporating the acceptability level of constraints violation into the optimization framework. A four-layer urban water supply system, including water sources, treatment facilities, reservoirs, and consuming zones, was used to demonstrate the applicability of proposed method. The results indicated that an AITIP model was valuable to help understand the effects of uncertainties related to cost, constraints and decision maker's judgment in the water supply network, and capable of assisting urban water managers gain an in-depth insight into the trade-offs between system cost and constraints-violation risk. Compared with TIP, the solutions from AITIP were of lower degree of uncertainty, making it more reliable to identify effective water supply patterns by adjusting decision variable values within their solution intervals. The study is useful in helping urban water managers to identify cost-effective management schemes in light of uncertainties in hydrology, environment, and decisions. The proposed optimization approach is expected to be applicable for a wide variety of water resources management problems. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Urban water supply analysis Uncertainty interval linear programming Grey degree Optimization

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