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Principal-subordinate hierarchical multi-objective programming model of initial water rights allocation 被引量:5
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作者 Dan WU Feng-ping WU Yan-ping CHEN 《Water Science and Engineering》 EI CAS 2009年第2期105-116,共12页
The principal-subordinate hierarchical multi-objective programming model of initial water rights allocation was developed based on the principle of coordinated and sustainable development of different regions and wate... The principal-subordinate hierarchical multi-objective programming model of initial water rights allocation was developed based on the principle of coordinated and sustainable development of different regions and water sectors within a basin. With the precondition of strictly controlling maximum emissions rights, initial water rights were allocated between the first and the second levels of the hierarchy in order to promote fair and coordinated development across different regions of the basin and coordinated and efficient water use across different water sectors, realize the maximum comprehensive benefits to the basin, promote the unity of quantity and quality of initial water rights allocation, and eliminate water conflict across different regions and water sectors. According to interactive decision-making theory, a principal-subordinate hierarchical interactive iterative algorithm based on the satisfaction degree was developed and used to solve the initial water rights allocation model. A case study verified the validity of the model. 展开更多
关键词 initial water rights allocation principal-subordinate hierarchy multi-objective programming model satisfaction degree
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Bi-level programming model for reconstruction of urban branch road network 被引量:6
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作者 史峰 黄恩厚 +1 位作者 陈群 王英姿 《Journal of Central South University》 SCIE EI CAS 2009年第1期172-176,共5页
Considering the decision-making variables of the capacities of branch roads and the optimization targets of lowering the saturation of arterial roads and the reconstruction expense of branch roads, the bi-level progra... Considering the decision-making variables of the capacities of branch roads and the optimization targets of lowering the saturation of arterial roads and the reconstruction expense of branch roads, the bi-level programming model for reconstructing the branch roads was set up. The upper level model was for determining the enlarged capacities of the branch roads, and the lower level model was for calculating the flows of road sections via the user equilibrium traffic assignment method. The genetic algorithm for solving the bi-level model was designed to obtain the reconstruction capacities of the branch roads. The results show that by the bi-level model and its algorithm, the optimum scheme of urban branch roads reconstruction can be gained, which reduces the saturation of arterial roads apparently, and alleviates traffic congestion. In the data analysis the arterial saturation decreases from 1.100 to 0.996, which verifies the micro-circulation transportation's function of urban branch road network. 展开更多
关键词 branch road RECONSTRUCTION bi-level programming model micro-circulation traffic
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Multi-objective planning model for simultaneous reconfiguration of power distribution network and allocation of renewable energy resources and capacitors with considering uncertainties 被引量:10
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作者 Sajad Najafi Ravadanegh Mohammad Reza Jannati Oskuee Masoumeh Karimi 《Journal of Central South University》 SCIE EI CAS CSCD 2017年第8期1837-1849,共13页
This research develops a comprehensive method to solve a combinatorial problem consisting of distribution system reconfiguration, capacitor allocation, and renewable energy resources sizing and siting simultaneously a... This research develops a comprehensive method to solve a combinatorial problem consisting of distribution system reconfiguration, capacitor allocation, and renewable energy resources sizing and siting simultaneously and to improve power system's accountability and system performance parameters. Due to finding solution which is closer to realistic characteristics, load forecasting, market price errors and the uncertainties related to the variable output power of wind based DG units are put in consideration. This work employs NSGA-II accompanied by the fuzzy set theory to solve the aforementioned multi-objective problem. The proposed scheme finally leads to a solution with a minimum voltage deviation, a maximum voltage stability, lower amount of pollutant and lower cost. The cost includes the installation costs of new equipment, reconfiguration costs, power loss cost, reliability cost, cost of energy purchased from power market, upgrade costs of lines and operation and maintenance costs of DGs. Therefore, the proposed methodology improves power quality, reliability and security in lower costs besides its preserve, with the operational indices of power distribution networks in acceptable level. To validate the proposed methodology's usefulness, it was applied on the IEEE 33-bus distribution system then the outcomes were compared with initial configuration. 展开更多
关键词 optimal reconfiguration renewable energy resources sitting and sizing capacitor allocation electric distribution system uncertainty modeling scenario based-stochastic programming multi-objective genetic algorithm
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Bi-Level Programming for the Optimal Nonlinear Distance-Based Transit Fare Structure Incorporating Principal-Agent Game
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作者 Xin Sun Shuyan Chen Yongfeng Ma 《Journal of Harbin Institute of Technology(New Series)》 CAS 2022年第5期69-77,共9页
The urban transit fare structure and level can largely affect passengers’travel behavior and route choices.The commonly used transit fare policies in the present transit network would lead to the unbalanced transit a... The urban transit fare structure and level can largely affect passengers’travel behavior and route choices.The commonly used transit fare policies in the present transit network would lead to the unbalanced transit assignment and improper transit resources distribution.In order to distribute transit passenger flow evenly and efficiently,this paper introduces a new distance-based fare pattern with Euclidean distance.A bi-level programming model is developed for determining the optimal distance-based fare pattern,with the path-based stochastic transit assignment(STA)problem with elastic demand being proposed at the lower level.The upper-level intends to address a principal-agent game between transport authorities and transit enterprises pursing maximization of social welfare and financial interest,respectively.A genetic algorithm(GA)is implemented to solve the bi-level model,which is verified by a numerical example to illustrate that the proposed nonlinear distance-based fare pattern presents a better financial performance and distribution effect than other fare structures. 展开更多
关键词 bi-level programming model principal-agent game nonlinear distance-based fare path-based stochastic transit assignment
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Analysis of Energy Storage Operation Configuration of Power System Based on Multi-Objective Optimization 被引量:1
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作者 Linyao Zhou Tengfei Ma 《Journal of Electronic Research and Application》 2022年第4期13-37,共25页
Driven by the goal of“carbon neutrality,”the increase in use of renewable energy power systems will be inevitable in the future.Uncontrolled output power and random volatility make it difficult to balance power in r... Driven by the goal of“carbon neutrality,”the increase in use of renewable energy power systems will be inevitable in the future.Uncontrolled output power and random volatility make it difficult to balance power in real time during system operation.Therefore,energy storage is considered to be an effective way to ensure the real-time balance of system power.However,cost of energy storage is relatively expensive.As a solution,energy storage can be used to balance the system power in order to reduce system operating costs.Taking the high proportion of wind power systems as an example,the impact of the“supply side”low-carbon transformation on the economics and reliability of power system operation is explored.In order to solve the problem of power system operation configuration optimization under the background of“carbon neutrality,”this paper establishes a multi-objective programming model. 展开更多
关键词 multi-objective planning Energy storage analysis Carbon-neutral Carbon neutrality multi-objective programming model
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Model and algorithm of optimizing alternate traffic restriction scheme in urban traffic network 被引量:1
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作者 徐光明 史峰 +1 位作者 刘冰 黄合来 《Journal of Central South University》 SCIE EI CAS 2014年第12期4742-4752,共11页
An optimization model and its solution algorithm for alternate traffic restriction(ATR) schemes were introduced in terms of both the restriction districts and the proportion of restricted automobiles. A bi-level progr... An optimization model and its solution algorithm for alternate traffic restriction(ATR) schemes were introduced in terms of both the restriction districts and the proportion of restricted automobiles. A bi-level programming model was proposed to model the ATR scheme optimization problem by aiming at consumer surplus maximization and overload flow minimization at the upper-level model. At the lower-level model, elastic demand, mode choice and multi-class user equilibrium assignment were synthetically optimized. A genetic algorithm involving prolonging codes was constructed, demonstrating high computing efficiency in that it dynamically includes newly-appearing overload links in the codes so as to reduce the subsequent searching range. Moreover,practical processing approaches were suggested, which may improve the operability of the model-based solutions. 展开更多
关键词 urban traffic congestion alternate traffic restriction equilibrium analysis bi-level programming model
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Evaluation and advancement of the integrated circular economy model of farming and stock raising
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作者 Qingsong Wang Mingqiang Liu +2 位作者 Yuzhou Tang Xueliang Yuan Qiao Ma 《Chinese Journal of Population,Resources and Environment》 2020年第4期350-360,共11页
The integrated circular economy model of farming and stock raising(ICEMFSR)has attracted increased attention as an effective model for solving the current irrational allocation of agricultural resources and realizing ... The integrated circular economy model of farming and stock raising(ICEMFSR)has attracted increased attention as an effective model for solving the current irrational allocation of agricultural resources and realizing the agricultural value-added industrial chain.This study uses emergy analysis to comprehensively examine and evaluate the economic benefits,environmental pressures,and sustainable development levels of ICEMFSR in Shucheng County,China.The results show that the ICEMFSR possesses the value of popularization with optimally allocated resources in the studied region,in which the emergy yield ratio(EYR),emergy loading ratio(ELR),and emergy sustainable index(ESI)in this model accounted for 3.59,1.25,and 2.89,respectively.This result indicates a leading position in the national agricultural system.Hence,this study constructs a new model based on the coupling of emergy evaluation and multi-objective linear programming to study ICEMFSR.Consequently,the EYR,ELR,and ESI respectively varied by +24.23%,10.40%,and +38.06%after replanning of ICEMFSR.This variation implies a significant improvement in the sustainable development level of the model.In addition,the optimized scenario design for key substances is proposed based on traceability and the reduce-reuse-recycle principle,including biogasification of crop straw and enhancement of crop scientific planting capacity. 展开更多
关键词 Circular economy model Emergy evaluation multi-objective linear programming Optimization suggestions
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OPTIMIZING CHINA'S EXPORT STRUCTURE COMBINING GOAL PROGRAMMING AND NON-COMPETITIVE INPUT-OUTPUT MODEL 被引量:2
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作者 MU Zhirui YANG Cuihong 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2014年第4期712-728,共17页
supported by the Taishan Scholar Construction Engineering by Shandong Government the National Natural Science Foundation of China under Grant Nos.61120106011 and 61203029
关键词 Export structure goal programming multi-objective model non-competitive input-outputmodel processing export.
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Coordination of Multi-leaders and Multi-followers in Supply Chain of Value-Added Telecom Services 被引量:5
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作者 戴建华 白秀广 舒华英 《China Communications》 SCIE CSCD 2011年第5期157-164,共8页
In order to study supply chain of the telecom value-added service,a multi-leaders and multi-followers Stackelberg game model with multiple telecom operators and multiple service providers whose income is composed of i... In order to study supply chain of the telecom value-added service,a multi-leaders and multi-followers Stackelberg game model with multiple telecom operators and multiple service providers whose income is composed of information fee division and advertisement was constructed.Then a demonstration was simulated,and the results were compared with the situation of service providers' income only from information fee division.The simulated and compared results indicate that,the enterprises in the supply chain have the nature of pursuing the maximum profits in capital markets;meanwhile,first-mover advantages and some enterprise can get more profits with the information asymmetry. 展开更多
关键词 telecom service supply chain coordination multi-leaders multi-followers Stackelberg model bi-level programming
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The Impact on the Environment and Economy Due to the Introduction of Electric Cars: Based on the Fuzzy Synthetical Evaluation Method 被引量:1
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作者 Heli Gao 《Journal of Applied Mathematics and Physics》 2016年第12期2172-2185,共14页
In this paper, we establish a model to analyze the influence of widespread use of electric vehicle on environment, society and economist based on Fuzzy Comprehensive Evaluation method. We set the fuzzy objects are int... In this paper, we establish a model to analyze the influence of widespread use of electric vehicle on environment, society and economist based on Fuzzy Comprehensive Evaluation method. We set the fuzzy objects are internal combustion engine vehicles, pure electric vehicles and hybrid electric vehicles. Considering the difference of environment, society and economics, we use of three different kinds to define the fuzzy evaluation factor sets. According to the data and calculating results, we finally obtain fuzzy synthetical evaluation matrix. Through comparing and analysis, we draw such conclusion that the widespread using of electric vehicle is benefit for both environment and economics, while has disadvantageous influence for some aspects on society. In Section 3, we establish a model to estimate the influence of widespread use of electric vehicles on energy saving. According to the proportion of coal resources in the whole energies, we use Linear Regression Model to forecast the development situation in the following several years. Contrasting energy consumptions of electric vehicles and internal combustion engine vehicles, we calculate the whole energies saved by widespread use of electric vehicles. In Section 4, we establish a multi-objective programming model to plan the number and type of power station. Considering the thermal power, hydropower, nuclear power and solar power as four ways, combined with the funds of setting up power station, running funds and the cost of dealing with the pollutants, we find the objective function and four constraints, and finally we reach optimal solution using lingo software. 展开更多
关键词 Electric Vehicle Fuzzy Comprehensive Evaluation Linear Regression model multi-objective programming model
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A Multi-Criteria Decision Making for the Unrelated Parallel Machines Scheduling Problem
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作者 Wei-Shung CHANG Chiuh-Cheng CHYU 《Journal of Software Engineering and Applications》 2009年第5期323-329,共7页
In this paper, we propose a multi-criteria machine-schedules decision making method that can be applied to a produc-tion environment involving several unrelated parallel machines and we will focus on three objectives:... In this paper, we propose a multi-criteria machine-schedules decision making method that can be applied to a produc-tion environment involving several unrelated parallel machines and we will focus on three objectives: minimizing makespan, total flow time, and total number of tardy jobs. The decision making method consists of three phases. In the first phase, a mathematical model of a single machine scheduling problem, of which the objective is a weighted sum of the three objectives, is constructed. Such a model will be repeatedly solved by the CPLEX in the proposed Multi-Objective Simulated Annealing (MOSA) algorithm. In the second phase, the MOSA that integrates job clustering method, job group scheduling method, and job group – machine assignment method, is employed to obtain a set of non-dominated group schedules. During this phase, CPLEX software and the bipartite weighted matching algorithm are used repeatedly as parts of the MOSA algorithm. In the last phase, the technique of data envelopment analysis is applied to determine the most preferable schedule. A practical example is then presented in order to demonstrate the applicability of the proposed decision making method. 展开更多
关键词 multi-objective Optimization UNRELATED Parallel Machines Scheduling Simulated ANNEALING Algorithm INTEGER programming models MULTI-CRITERIA DECISION Making
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Bus frequency optimization in a large-scale multi-modal transportation system:integrating 3D-MFD and dynamic traffic assignment
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作者 Kai Yuan Dandan Cui Jiancheng Long 《Digital Transportation and Safety》 2023年第4期241-252,共12页
A properly designed public transport system is expected to improve traffic efficiency.A high-frequency bus service would decrease the waiting time for passengers,but the interaction between buses and cars might result... A properly designed public transport system is expected to improve traffic efficiency.A high-frequency bus service would decrease the waiting time for passengers,but the interaction between buses and cars might result in more serious congestion.On the other hand,a low-frequency bus service would increase the waiting time for passengers and would not reduce the use of private cars.It is important to strike a balance between high and low frequencies in order to minimize the total delays for all road users.It is critical to formulate the impacts of bus frequency on congestion dynamics and mode choices.However,as far as the authors know,most proposed bus frequency optimization formulations are based on static demand and the Bureau of Public Roads function,and do not properly consider the congestion dynamics and their impacts on mode choices.To fill this gap,this paper proposes a bi-level optimization model.A three-dimensional Macroscopic Fundamental Diagram based modeling approach is developed to capture the bi-modal congestion dynamics.A variational inequality model for the user equilibrium in mode choices is presented and solved using a double projection algorithm.A surrogate model-based algorithm is used to solve the bi-level programming problem. 展开更多
关键词 Three-dimensional macroscopic fundamental diagram Dynamic traffic assignment bi-level programming model Double projection algorithm Surrogate model-based algorithm
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A Chaotic Approach for the Bi-level Discrete Equilibrium Network Design Problem
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《Journal of Systems Science and Information》 2006年第2期193-202,共10页
A chaotic algorithm for providing a solution to the bi-level Discrete Equilibrium Network Design Problem (NDP) is discussed following an introduction of the Discrete Network Design Problem (DNDP) model and Chaos O... A chaotic algorithm for providing a solution to the bi-level Discrete Equilibrium Network Design Problem (NDP) is discussed following an introduction of the Discrete Network Design Problem (DNDP) model and Chaos Optimization Algorithms (COA). A description of the chaotic approach for the DNDP model is described in details. Then a numerical example for the DNDP is carried out to investigate the chaotic approach. The results have been encouraging, indicating that the chaotic approach has great potential ability in finding the optimal solution of DNDP models. 展开更多
关键词 discrete equilibrium network design problem bi-level programming model chaos optimization algorithms
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Selecting vehicle dispatching plan for typhoon emergency evacuation based on fault-tolerance analysis
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作者 Zhao-ge Liu Xiang-yang Li 《Journal of Safety Science and Resilience》 2025年第3期465-473,共9页
Unexpected scenarios often occur during typhoon response,which is likely to cause the failure of evacuation vehicle dispatching and other preparedness plans.To solve this problem,a vehicle dispatching plan selecting m... Unexpected scenarios often occur during typhoon response,which is likely to cause the failure of evacuation vehicle dispatching and other preparedness plans.To solve this problem,a vehicle dispatching plan selecting method based on fault-tolerance analysis is proposed,which considers the bounded rationality of emergency decision-makers.The method improves the capability of responding to unexpected scenarios by increasing backup resources.First,under the expected scenarios,a bi-level programming model for arranging the quantities of each type of vehicle and their routes is established,with the goal of minimizing the expected total evacuation time.A corresponding solving algorithm is designed.Second,possible unexpected scenarios are preset by integrating local and non-local historical experiences,and the scenario influences on vehicle dispatching constraints are analyzed.Third,under unexpected scenarios,a fault-tolerance plan set is established considering the failure risk of vehicle dispatching and fault-tolerant cost.The optimal plan is selected by calculating and ranking fault-tolerant rates.Finally,a case study in Shenzhen,China is provided to verify the reasonability and effectiveness of the method.The results show that the proposed method can help discover and address the‘fault’of vehicle dispatching plans during emergency preparedness and thus improve evacuation capabilities in emergency response.The proposed method can be used to develop evacuation vehicle dispatching planning methods with comprehensive scenario adaptability and a precisely improved capability. 展开更多
关键词 Emergency preparedness Fault-tolerance analysis Typhoon emergency evacuation Vehicle dispatching bi-level programming model Case study
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Optimizing Emergency Logistics for the Offsite Hazardous Waste Management 被引量:8
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作者 Jiahong Zhao Ginger Y.Ke 《Journal of Systems Science and Systems Engineering》 SCIE EI CSCD 2019年第6期747-765,共19页
Hazardous wastes pose increasing threats to people and environment during the processes of offsite collection,storage,treatment,and disposal.A novel game theoretic model,including two levels,is developed for the corre... Hazardous wastes pose increasing threats to people and environment during the processes of offsite collection,storage,treatment,and disposal.A novel game theoretic model,including two levels,is developed for the corresponding optimization of emergency logistics,where the upper level indicates the location and capacity problem for the regulator,and the lower level reflects the allocation problem for the emergency commander.Different from other works in the literature,we focus on the issue of multi-quality coverages (full and partial coverages) in the optimization of facility location and allocation.To be specific,the regulator decides the location plan and the corresponding capacity of storing emergency groups for multiple types of hazmats,so to minimizes the total potential environmental risk posed by incident sites;while the commander minimizes the total costs to provide an efficient allocation policy.To solve the bi-level programming model,two solution techniques,namely a KKT condition approach and a heuristic model,are designed and compared.The proposed model and solution techniques are then applied to a hypothetical case and a real-world case to demonstrate the practicality and provide managerial insights. 展开更多
关键词 bi-level programming hazardous MATERIAL time-based RISK assessment multi-quality COVERING model KKT HEURISTIC technique
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Incident-based traffic congestion control strategy 被引量:4
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作者 ZHANG AoMuHan GAO ZiYou REN HuaLing 《Science China(Technological Sciences)》 SCIE EI CAS 2011年第5期1338-1344,共7页
Traffic incident happens frequently in urban traffic network and it affects normal operation of traffic system seriously so that study on incident-based congestion control strategies is very important. This study addr... Traffic incident happens frequently in urban traffic network and it affects normal operation of traffic system seriously so that study on incident-based congestion control strategies is very important. This study addresses the problem of the temporary vehicle movement bans design under incident-based traffic congestion situation. A bi-level programming model is proposed to formulate this problem. The upper level problem is to minimize the total travel cost in the view of traffic management agencies, and the lower level problem is to present travelers’ dynamic route choice behavior under temporary vehicle movement bans using the simulation of cell transmission model, then a genetic algorithm is employed to solve the proposed bi-level programming model. Computational results show that the temporary vehicle movement bans measure is able to alleviate the traffic network incident-based congestion effectively and improve system performance of traffic network. 展开更多
关键词 vehicle movement bans design bi-level program genetic algorithm cell transmission model
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Water Resource Allocation under Consideration of the National NIY Plan in Harbin, China
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作者 张焱 刘苏峡 陈军锋 《Journal of Resources and Ecology》 CSCD 2012年第2期161-168,共8页
Water resource allocation (WRA) is a useful but complicated topic in water resource management. With the targets set out in the Plan of Newly Increasing Yield (NIY) of 10×1011 Jin (1 kg=2 Jin) from 2009 to ... Water resource allocation (WRA) is a useful but complicated topic in water resource management. With the targets set out in the Plan of Newly Increasing Yield (NIY) of 10×1011 Jin (1 kg=2 Jin) from 2009 to 2020, the immediate question for the Songhua River Region (SHRR) is whether water is sufficient to support the required yield increase. Very few studies have considered to what degree this plan influences the solution of WRA and how to adapt. This paper used a multi-objective programming model for WRA across the Harbin region located in the SHRR in 2020 and 2030 (p=75%). The Harbin region can be classified into four types of sub-regions according to WRA: Type I is Harbin city zone. With rapid urbanization, Harbin city zone has the highest risk of agricultural water shortage. Considering the severe situation, there is little space for Harbin city zone to reach the NIY goal. Type II is sub-regions including Wuchang, Shangzhi and Binxian. There are some agricultural water shortage risks in this type region. Because the water shortage is relatively small, it is possible to increase agricultural production through strengthening agricultural water-saving countermeasures and constructing water conservation facilities. Type III is sub-regions including Acheng, Hulan, Mulan and Fangzheng. In this type region, there may be a water shortage if the rate of urbanization accelerates. According to local conditions, it is needed to enhance water-saving countermeasures to increase agricultural production to a certain degree. Type IV is sub-regions including Shuangcheng, Bayan, Yilan, Yanshou and Tonghe. There are good water conditions for the extensive development of agriculture. Nevertheless, in order to ensure an increase in agricultural production, it is necessary to enhance the way in which water is utilized and consider soil resources. These results will help decision makers make a scientific NIY plan for the Harbin region for sustainable utilization of regional water resources and an increase in agricultural production. 展开更多
关键词 the Harbin region supply and demand prediction multi-objective programming model genetic algorithm water resource allocation (WRA)
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An Optimization-Based Rezoning for ALE Methods 被引量:3
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作者 Yibing Chen Song Jiang 《Communications in Computational Physics》 SCIE 2008年第10期1216-1244,共29页
Based on the theory of optimization,we use edges and angles of cells to represent the geometric quality of computational grids,employ the local gradients of the flow variables to describe the variation of flow field,a... Based on the theory of optimization,we use edges and angles of cells to represent the geometric quality of computational grids,employ the local gradients of the flow variables to describe the variation of flow field,and construct a multi-objective programming model.The solution of this optimization problem gives appropriate balance between the geometric quality and adaptation of grids.By solving the optimization problem,we propose a new grid rezoning method,which not only keeps good geometric quality of grids,but also can track rapid changes in the flow field.In particular,it performs well for some complex concave domains with corners.We also incorporate the rezoningmethod into anArbitrary Lagrangian-Eulerian(ALE)method which is widely used in the simulation of high-speed multi-material flows.The proposed rezoning and ALE methods of this paper are tested by a number of numerical examples with complex concave domains and compared with some other rezoning methods.The numerical results validate the robustness of the proposed methods. 展开更多
关键词 Grid rezoning multi-objective programming models ALE methods
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Conic Optimal Energy Flow of Integrated Electricity and Natural Gas Systems 被引量:1
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作者 Rufeng Zhang Tao Jiang +3 位作者 Fangxing Li Guoqing Li Xue Li Houhe Chen 《Journal of Modern Power Systems and Clean Energy》 SCIE EI CSCD 2021年第4期963-967,共5页
In this letter, we propose a market-based bi-level conic optimal energy flow (OEF) model of integrated electricity and natural gas systems (IENGSs). Conic alternating current optimal power flow (ACOPF) is formulated i... In this letter, we propose a market-based bi-level conic optimal energy flow (OEF) model of integrated electricity and natural gas systems (IENGSs). Conic alternating current optimal power flow (ACOPF) is formulated in the upper-level model, and the generation cost of natural gas fired generation units (NGFGUs) is calculated based on natural gas locational marginal prices (NG-LMPs). The market clearing process of natural gas system is modeled in the lower-level model. The bi-level model is then transferred into a mixed-integer second-order cone programming (MISOCP) problem. Simulation results demonstrate the effectiveness of the proposed conic OEF model. 展开更多
关键词 Optimal energy flow(OEF) bi-level model second-order cone programming(SOCP) integrated energy system
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