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Optimization Techniques for GPU-Based Parallel Programming Models in High-Performance
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作者 Shuntao Tang Wei Chen 《信息工程期刊(中英文版)》 2024年第1期7-11,共5页
This study embarks on a comprehensive examination of optimization techniques within GPU-based parallel programming models,pivotal for advancing high-performance computing(HPC).Emphasizing the transition of GPUs from g... This study embarks on a comprehensive examination of optimization techniques within GPU-based parallel programming models,pivotal for advancing high-performance computing(HPC).Emphasizing the transition of GPUs from graphic-centric processors to versatile computing units,it delves into the nuanced optimization of memory access,thread management,algorithmic design,and data structures.These optimizations are critical for exploiting the parallel processing capabilities of GPUs,addressingboth the theoretical frameworks and practical implementations.By integrating advanced strategies such as memory coalescing,dynamic scheduling,and parallel algorithmic transformations,this research aims to significantly elevate computational efficiency and throughput.The findings underscore the potential of optimized GPU programming to revolutionize computational tasks across various domains,highlighting a pathway towards achieving unparalleled processing power and efficiency in HPC environments.The paper not only contributes to the academic discourse on GPU optimization but also provides actionable insights for developers,fostering advancements in computational sciences and technology. 展开更多
关键词 Optimization Techniques GPU-Based Parallel programming models High-Performance Computing
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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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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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Tri-level programming model for combined urban traffic signal control and traffic flow guidance 被引量:1
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作者 SUN Zhi-yuan LU Hua-pu QU Wen-cong 《Journal of Central South University》 SCIE EI CAS CSCD 2016年第9期2443-2452,共10页
In order to balance the temporal-spatial distribution of urban traffic flow, a model is established for combined urban traffic signal control and traffic flow guidance. With consideration of the wide use of fixed sign... In order to balance the temporal-spatial distribution of urban traffic flow, a model is established for combined urban traffic signal control and traffic flow guidance. With consideration of the wide use of fixed signal control at intersections, traffic assignment under traffic flow guidance, and dynamic characteristics of urban traffic management, a tri-level programming model is presented. To reflect the impact of intersection delay on traffic assignment, the lower level model is set as a modified user equilibrium model. The middle level model, which contains several definitional constraints for different phase modes, is built for the traffic signal control optimization. To solve the problem of tide lane management, the upper level model is built up based on nonlinear 0-1 integer programming. A heuristic iterative optimization algorithm(HIOA) is set up to solve the tri-level programming model. The lower level model is solved by method of successive averages(MSA), the middle level model is solved by non-dominated sorting genetic algorithm II(NSGA II), and the upper level model is solved by genetic algorithm(GA). A case study is raised to show the efficiency and applicability of the proposed modelling and computing method. 展开更多
关键词 traffic engineering traffic signal control traffic flow guidance tri-level programming model
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A Quadratic Programming Model for Blast Scheduling 被引量:1
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作者 Chunyan Meng Samuel Frimpong Mingjian Zuo(Ph. D. Student (correspondent). 606-Chemical-Mineral Building. Dept of Civil and Environmental Engineering. University of Alberta. T6G 2G6.Edmonton, AB. Canada)(Associate protessor, School of Mining and Petrole 《International Journal of Minerals,Metallurgy and Materials》 SCIE EI CAS CSCD 1999年第3期165-167,共3页
A quadratic programming model is established to choose the blocks to be blasted in a given period. The length of this period depends on the production planning requirements. During the given period, the blocks' pa... A quadratic programming model is established to choose the blocks to be blasted in a given period. The length of this period depends on the production planning requirements. During the given period, the blocks' parameters are available from the geological database of the mine. The objective is to minimize the deviation of the average ore grade of blasted blocks from the standard ore grade required by the mill. Transportation ability constraint. production quantity demand constraint. minimum safety bench constraint. block size constraint and block, bench precedence constraints are considered in forming the programming model. This model has more practical objective function and reasonable constraints compared with the existing model for this kind of problems. 展开更多
关键词 quadratic programming open pit mining blast scheduling mine production scheduling mathematical programming model
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Knowledge representation and rule-based solution system for dynamic programming model
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作者 胡祥培 王旭茵 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2003年第2期190-194,共5页
A knowledge representation has been proposed using the state space theory of Artificial Intelligence for Dynamic Programming Model, in which a model can be defined as a six tuple M=(I,G,O,T,D,S). A building block mode... A knowledge representation has been proposed using the state space theory of Artificial Intelligence for Dynamic Programming Model, in which a model can be defined as a six tuple M=(I,G,O,T,D,S). A building block modeling method uses the modules of a six tuple to form a rule based solution model. Moreover, a rule based system has been designed and set up to solve the Dynamic Programming Model. This knowledge based representation can be easily used to express symbolical knowledge and dynamic characteristics for Dynamic Programming Model, and the inference based on the knowledge in the process of solving Dynamic Programming Model can also be conveniently realized in computer. 展开更多
关键词 knowledge representation operations research Dynamic programming model intelligent modeling support
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Application of Linear Programming Model to Refugee Migrating Problem
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作者 Chongyu Jiang Xiaorong Li Yandong Li 《Journal of Applied Mathematics and Physics》 2016年第5期967-977,共11页
The refugee immigration problem can be considered as a special “transportation problem”. Linear Programming Model is built, where two objectives with weight in the objective function, for the shortest routes that th... The refugee immigration problem can be considered as a special “transportation problem”. Linear Programming Model is built, where two objectives with weight in the objective function, for the shortest routes that the refugees go along and the minimum number of refugees stayed in each country. An example of EU is introduced and calculated on Lingo software. The results show that the model is available to solve the refugee immigration problem in different scale. 展开更多
关键词 REFUGEE Linear programming model Optimal Solution
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Managing Tourism Development in the Dutch City of Utrecht using a Linear Programming Model of the Tourist Carrying Capacity
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作者 让·范·德·博格 《全球城市研究(中英文)》 2021年第3期13-26,F0002,186,187,共17页
As one part of the Landstad International Metropolitan Area,Utrecht has become known as one of the best tourist destinations in recent years,with the rapid growth of worldwide travel trends.In this paper,through the a... As one part of the Landstad International Metropolitan Area,Utrecht has become known as one of the best tourist destinations in recent years,with the rapid growth of worldwide travel trends.In this paper,through the adaption of the linear programming model,the paper intends to not only quantify the optimum number of visitors to Utrecht but also formulate a number of policy recommendations based on the reconstruction of this optimum.The paper draws the following conclusions:(1) tourist carrying capacity of Utrecht is not yet exceeded;(2) restrictive accommodation policy does not currently seem necessary;(3) the cultural-historical attractions are not yet optimally used;(4) investing in strategic provisions is currently not necessary.And from the conclusion,the paper further puts forward the following suggestions on the city’s tourism development strategy:(1) to identify "tourist flood plains";(2) to encourage the tourist disclosure of these alternatives;(3) to invest even more explicitly in residential tourism and,where possible,curb day tourism;(4) to introduce a new business model. 展开更多
关键词 Utrecht Tourism Carrying Capacity Linear programming model Sustainable Development of Tourism
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Unified Programming Models for Heterogeneous High-Performance Computers 被引量:1
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作者 马子轩 金煜阳 +4 位作者 唐适之 王豪杰 薛伟诚 翟季冬 郑纬民 《Journal of Computer Science & Technology》 SCIE EI CSCD 2023年第1期211-218,共8页
Unified programming models can effectively improve program portability on various heterogeneous high-performance computers.Existing unified programming models put a lot of effort to code portability but are still far ... Unified programming models can effectively improve program portability on various heterogeneous high-performance computers.Existing unified programming models put a lot of effort to code portability but are still far from achieving good performance portability.In this paper,we present a preliminary design of a performance-portable unified programming model including four aspects:programming language,programming abstraction,compilation optimization,and scheduling system.Specifically,domain-specific languages introduce domain knowledge to decouple the optimizations for different applications and architectures.The unified programming abstraction unifies the common features of different architectures to support common optimizations.Multi-level compilation optimization enables comprehensive performance optimization based on multi-level intermediate representations.Resource-aware lightweight runtime scheduling system improves the resource utilization of heterogeneous computers.This is a perspective paper to show our viewpoints on programming models for emerging heterogeneous systems. 展开更多
关键词 performance portability programming model heterogeneous supercomputer
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Automatic Algorithm Programming Model Based on the Improved Morgan's Refinement Calculus 被引量:2
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作者 ZUO Zhengkang HU Ying +2 位作者 HUANG Qing WANG Yuan WANG Changjing 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2022年第5期405-414,共10页
The automatic algorithm programming model can increase the dependability and efficiency of algorithm program development,including specification generation,program refinement,and formal verification.However,the existi... The automatic algorithm programming model can increase the dependability and efficiency of algorithm program development,including specification generation,program refinement,and formal verification.However,the existing model has two flaws:incompleteness of program refinement and inadequate automation of formal verification.This paper proposes an automatic algorithm programming model based on the improved Morgan’s refinement calculus.It extends the Morgan’s refinement calculus rules and designs the C++generation system for realizing the complete process of refinement.Meanwhile,the automation tools VCG(Verification Condition Generator)and Isabelle are used to improve the automation of formal verification.An example of a stock’s maximum income demonstrates the effectiveness of the proposed model.Furthermore,the proposed model has some relevance for automatic software generation. 展开更多
关键词 automatic algorithm programming model program refinement VCG ISABELLE Morgan’s refinement calculus
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Genetic programming-based chaotic time series modeling 被引量:1
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作者 张伟 吴智铭 杨根科 《Journal of Zhejiang University Science》 EI CSCD 2004年第11期1432-1439,共8页
This paper proposes a Genetic Programming-Based Modeling (GPM) algorithm on chaotic time series. GP is used here to search for appropriate model structures in function space, and the Particle Swarm Optimization (PSO) ... This paper proposes a Genetic Programming-Based Modeling (GPM) algorithm on chaotic time series. GP is used here to search for appropriate model structures in function space, and the Particle Swarm Optimization (PSO) algorithm is used for Nonlinear Parameter Estimation (NPE) of dynamic model structures. In addition, GPM integrates the results of Nonlinear Time Series Analysis (NTSA) to adjust the parameters and takes them as the criteria of established models. Experiments showed the effectiveness of such improvements on chaotic time series modeling. 展开更多
关键词 Chaotic time series analysis Genetic programming modeling Nonlinear Parameter Estimation (NPE) Particle Swarm Optimization (PSO) Nonlinear system identification
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Cutting CO_(2)emissions through demand side regulation:Implications from multi-regional input-output linear programming model
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作者 Nan LIU Jidong KANG +1 位作者 Tsan Sheng NG Bin SU 《Frontiers of Engineering Management》 2022年第3期452-461,共10页
This study combines multi-regional inputoutput(MRIO)model with linear programming(LP)model to explore economic structure adjustment strategies for the reduction of carbon dioxide(CO_(2))emissions.A particular feature ... This study combines multi-regional inputoutput(MRIO)model with linear programming(LP)model to explore economic structure adjustment strategies for the reduction of carbon dioxide(CO_(2))emissions.A particular feature of this study is the identification of the optimal regulation sequence of final products in various regions to reduce CO_(2)emissions with the minimum loss in gross domestic product(GDP).By using China's MRIO tables 2017 with 28 regions and 42 economic sectors,results show that reduction in final demand leads to simultaneous reductions in GDP and CO_(2)emissions.Nevertheless,certain demand side regulation strategy can be adopted to lower CO_(2)emissions at the smallest loss of economic growth.Several key final products,such as metallurgy,nonmetal,metal,and chemical products,should first be regulated to reduce CO_(2)emissions at the minimum loss in GDP.Most of these key products concentrate in the coastal developed regions in China.The proposed MRIO-LP model considers the inter-relationship among various sectors and regions,and can aid policy makers in designing effective policy for industrial structure adjustment at the regional level to achieve the national environmental and economic targets. 展开更多
关键词 CO_(2)emissions demand side regulation multi-regional input-output model linear programming model
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HEURISTIC MODELING FOR A DYNAMIC AND GOAL PROGRAMMING IN PRODUCTION PLANNING OF CONTINUOUS MANUFACTURING SYSTEMS 被引量:2
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作者 JAHAN A ABDOLSHAH M 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2007年第5期110-113,共4页
At the first sight it seems that advanced operation research is not used enough in continuous production systems as comparison with mass production, batch production and job shop systems, but really in a comprehensive... At the first sight it seems that advanced operation research is not used enough in continuous production systems as comparison with mass production, batch production and job shop systems, but really in a comprehensive evaluation the advanced operation research techniques can be used in continuous production systems in developing countries very widely, because of initial inadequate plant layout, stage by stage development of production lines, the purchase of second hand machineries from various countries, plurality of customers. A case of production system planning is proposed for a chemical company in which the above mentioned conditions are almost presented. The goals and constraints in this issue are as follows: (1) Minimizing deviation of customer's requirements. (2) Maximizing the profit. (3) Minimizing the frequencies of changes in formula production. (4) Minimizing the inventory of final products. (5) Balancing the production sections with regard to rate in production. (6) Limitation in inventory of raw material. The present situation is in such a way that various techniques such as goal programming, linear programming and dynamic programming can be used. But dynamic production programming issues are divided into two categories, at first one with limitation in production capacity and another with unlimited production capacity. For the first category, a systematic and acceptable solution has not been presented yet. Therefore an innovative method is used to convert the dynamic situation to a zero- one model. At last this issue is changed to a goal programming model with non-linear limitations with the use of GRG algorithm and that's how it is solved. 展开更多
关键词 Heuristic model Dynamic programming Goal programming production planning
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Dynamic Behavior Modeling in Multi-Agent System By Evolutionary Programming
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作者 Jun Wei Zhenaiun Pan Lishang Kang(State Key Lab of Software Engincering, Wuhan UniversityWuhan 430072, P.R. China) 《Wuhan University Journal of Natural Sciences》 CAS 1996年第Z1期651-657,共7页
In a multi-agent system, each agent must adapt itself to the environment and coordinate with other agents dynamically. TO predict or cooperate with the behavior of oiller agents. An agent should dynamically establish ... In a multi-agent system, each agent must adapt itself to the environment and coordinate with other agents dynamically. TO predict or cooperate with the behavior of oiller agents. An agent should dynamically establish and evolve the cooperative behavior model of itself. In this paper, we represent the behavior model of an agent as a f-mite state machine and propose a new method of dynamically evolving the behavior model of an agent by evolutionary programming. 展开更多
关键词 Dynamic Behavior modeling in Multi-Agent System By Evolutionary programming
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Unmanned Aerial Vehicle Inspection Routing and Scheduling for Engineering Management
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作者 Lu Zhen Zhiyuan Yang +2 位作者 Gilbert Laporte Wen Yi Tianyi Fan 《Engineering》 SCIE EI CAS CSCD 2024年第5期223-239,共17页
Technological advancements in unmanned aerial vehicles(UAVs)have revolutionized various industries,enabling the widespread adoption of UAV-based solutions.In engineering management,UAV-based inspection has emerged as ... Technological advancements in unmanned aerial vehicles(UAVs)have revolutionized various industries,enabling the widespread adoption of UAV-based solutions.In engineering management,UAV-based inspection has emerged as a highly efficient method for identifying hidden risks in high-risk construction environments,surpassing traditional inspection techniques.Building on this foundation,this paper delves into the optimization of UAV inspection routing and scheduling,addressing the complexity introduced by factors such as no-fly zones,monitoring-interval time windows,and multiple monitoring rounds.To tackle this challenging problem,we propose a mixed-integer linear programming(MILP)model that optimizes inspection task assignments,monitoring sequence schedules,and charging decisions.The comprehensive consideration of these factors differentiates our problem from conventional vehicle routing problem(VRP),leading to a mathematically intractable model for commercial solvers in the case of large-scale instances.To overcome this limitation,we design a tailored variable neighborhood search(VNS)metaheuristic,customizing the algorithm to efficiently solve our model.Extensive numerical experiments are conducted to validate the efficacy of our proposed algorithm,demonstrating its scalability for both large-scale and real-scale instances.Sensitivity experiments and a case study based on an actual engineering project are also conducted,providing valuable insights for engineering managers to enhance inspection work efficiency. 展开更多
关键词 Engineering management Unmanned aerial vehicle Inspection routing and scheduling OPTIMIZATION Mixed-integer linear programming model Variable neighborhood search metaheuristic
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Mathematical Model and Simulation of Harmful Invasive Plant Control
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作者 马庆功 杨波 《Agricultural Science & Technology》 CAS 2014年第12期2057-2063,共7页
Plant invasion refers to the phenomenon that some plants grow too fast due to they are far away from the original living environment or predators, affecting the local environment. With the development of tourism and t... Plant invasion refers to the phenomenon that some plants grow too fast due to they are far away from the original living environment or predators, affecting the local environment. With the development of tourism and trade, the harm caused by invasive plants will be more and more serious. Therefore, it is necessary to ex- plore an effective method for controlling plant invasion through qualitative and quan- titative research. In this paper, the models were established for the early and late harmful plant invasion control. The huge computation was completed by the com- puter programming to obtain the optimal solutions of the models. The real meaning of the optimal solution was further discussed. Through numerical simulations and discussion, it could be concluded that the quantitative research on the invasive plant control had a certain application value. 展开更多
关键词 Invasive plant Linear programming model Logistic model Pontryagin minimum principle Numerical simulation
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Estimation of the Maximum Allowable Loading Amount of COD in Luoyuan Bay by a 3-D COD Transport and Transformation Model 被引量:1
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作者 WU Jialin LI Keqiang +4 位作者 SHI Xiaoyong LIANG Shengkang HAN Xiurong MA Qimin WANG Xiulin 《Journal of Ocean University of China》 SCIE CAS 2014年第4期604-612,共9页
The rapid economic and social developments in the Luoyuan and Lianjiang counties of Fujian Province,China,raise certain environment and ecosystem issues.The unusual phytoplankton bloom and eutrophication,for example,h... The rapid economic and social developments in the Luoyuan and Lianjiang counties of Fujian Province,China,raise certain environment and ecosystem issues.The unusual phytoplankton bloom and eutrophication,for example,have increased in severity in Luoyuan Bay (LB).The constant increase of nutrient loads has largely caused the environmental degradation in LB.Several countermeasures have been implemented to solve these environmental problems.The most effective of these strategies is the reduction of pollutant loadings into the sea in accordance with total pollutant load control (TPLC) plans.A combined three-dimensional hydrodynamic transport-transformation model was constructed to estimate the marine environmental capacity of chemical oxygen demand (COD).The allowed maximum loadings for each discharge unit in LB were calculated with applicable simulation results.The simulation results indicated that the environmental capacity of COD is approximately 11×l0^4tyear^-1 when the water quality complies with the marine functional zoning standards for LB.A pollutant reduction scheme to diminish the present levels of mariculture-and domestic-based COD loadings is based on the estimated marine COD environmental capacity.The obtained values imply that the LB waters could comply with the targeted water quality criteria.To meet the revised marine functional zoning standards,discharge loadings from discharge units 1 and 11 should be reduced to 996 and 3236t year^-1,respectively. 展开更多
关键词 TPLC environmental capacity COD Luoyuan Bay linear programming model
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Weekly Fleet Assignment Model and Algorithm 被引量:1
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作者 朱星辉 朱金福 巩在武 《Journal of Southwest Jiaotong University(English Edition)》 2007年第3期231-235,共5页
A 0-1 integer programming model for weekly fleet assignment was put forward based on linear network and weekly flight scheduling in China. In this model, the objective function is to maximize the total profit of fleet... A 0-1 integer programming model for weekly fleet assignment was put forward based on linear network and weekly flight scheduling in China. In this model, the objective function is to maximize the total profit of fleet assignment, subject to the constraints of coverage, aircraft flow balance, fleet size, aircraft availability, aircraft usage, flight restriction, aircraft seat capacity, and stopover. Then the branch-and-bound algorithm based on special ordered set was applied to solve the model. At last, a real- wofld case study on an airline with 5 fleets, 48 aircrafts and 1 786 flight legs indicated that the profit increase was ¥ 1 591276 one week and the running time was no more than 4 rain, which shows that the model and algorithm are fairly good for domestic airline. 展开更多
关键词 Flight scheduling Fleet assignment problem 0-1 Integer programming model Branch-and-bound algorithm
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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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Parallel Machine Scheduling Models with Fuzzy Parameters and Precedence Constraints: A Credibility Approach
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作者 侯福均 吴祈宗 《Journal of Beijing Institute of Technology》 EI CAS 2007年第2期231-236,共6页
A method for modeling the parallel machine scheduling problems with fuzzy parameters and precedence constraints based on credibility measure is provided. For the given n jobs to be processed on m machines, it is assum... A method for modeling the parallel machine scheduling problems with fuzzy parameters and precedence constraints based on credibility measure is provided. For the given n jobs to be processed on m machines, it is assumed that the processing times and the due dates are nonnegative fuzzy numbers and all the weights are positive, crisp numbers. Based on credibility measure, three parallel machine scheduling problems and a goal-programming model are formulated. Feasible schedules are evaluated not only by their objective values but also by the credibility degree of satisfaction with their precedence constraints. The genetic algorithm is utilized to find the best solutions in a short period of time. An illustrative numerical example is also given. Simulation results show that the proposed models are effective, which can deal with the parallel machine scheduling problems with fuzzy parameters and precedence constraints based on credibility measure. 展开更多
关键词 parallel machine scheduling programming model possibility measure credibility measure fuzzy number genetic algorithm
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