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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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MULTI-OBJECTIVE PROGRAMMING MODEL OF TROPICAL CROPS IN HAINAN ISLAND
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作者 Zhou Zhaode(Department of Cultivation,South China College of Tropical Crops, Chanxian, Hainan 571700People’s Republic of China)Zheng Jianfei(Department of Agrometeorology,Bejing Agricultural University, Bejing 100094People’s Repulblic of China) 《Journal of Geographical Sciences》 SCIE CSCD 1994年第Z1期48-60,共13页
According to Hainan Island's biological characteristics, and existing structure of productivity of tropical crops and local climatic conditions, this paper carries on regional division of tropical crops by fuzzy m... According to Hainan Island's biological characteristics, and existing structure of productivity of tropical crops and local climatic conditions, this paper carries on regional division of tropical crops by fuzzy mathematics. Based on calculation of basic parameters for tl1e formation of production, near-tem optimum models of tropical crops structure of each region was established by means of multi-objective programming, and a far-term grey programming model was set up through the above-mentioned near-term model and prediction of future parameters. Conclusion shows that the near-term programming may raise the profit by 5. 1-55.7 percent and far-tem programming by 54-90 percent, both gainingobvious economic benefits. 展开更多
关键词 Hainan Island tropical crops multi-objective programming
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Selecting China's strategic petroleum reserve sites by multi-objective programming model
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作者 Hui Li Ren-Jin Sun +3 位作者 Kang-Yin Dong Xiu-Cheng Dong Zhong-Bin Zhou Xia Leng 《Petroleum Science》 SCIE CAS CSCD 2017年第3期622-635,共14页
An important decision for policy makers is selecting strategic petroleum reserve sites. However, policy makers may not choose the most suitable and efficient locations for strategic petroleum reserve(SPR) due to the... An important decision for policy makers is selecting strategic petroleum reserve sites. However, policy makers may not choose the most suitable and efficient locations for strategic petroleum reserve(SPR) due to the complexity in the choice of sites. This paper proposes a multi-objective programming model to determine the optimal locations for China's SPR storage sites. This model considers not only the minimum response time but also the minimum transportation cost based on a series of reasonable assumptions and constraint conditions. The factors influencing SPR sites are identified to determine potential demand points and candidate storage sites. Estimation and suggestions are made for the selection of China's future SPR storage sites based on the results of this model. When the number of petroleum storage sites is less than or equals 25 and the maximum capacity of storage sites is restricted to 10 million tonnes, the model's result best fit for the current layout scheme selected thirteen storage sites in four scenarios. Considering the current status of SPR in China,Tianjin, Qingdao, Dalian, Daqing and Zhanjiang, Chengdu,Xi'an, and Yueyang are suggested to be the candidate locations for the third phase of the construction plan. The locations of petroleum storage sites suggested in this work could be used as a reference for decision makers. 展开更多
关键词 Strategic petroleum reserve Storage siteselection multi-objective modeling China
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Uncertain and multi-objective programming models for crop planting structure optimization
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作者 Mo LI Ping GUO +1 位作者 Liudong ZHANG Chenglong ZHANG 《Frontiers of Agricultural Science and Engineering》 2016年第1期34-45,共12页
Crop planting structure optimization is a signi ficant way to increase agricultural economic bene fits and improve agricultural water management. The complexities of fluctuating stream conditions, varying economic pro... Crop planting structure optimization is a signi ficant way to increase agricultural economic bene fits and improve agricultural water management. The complexities of fluctuating stream conditions, varying economic pro fits, and uncertainties and errors in estimated modeling parameters, as well as the complexities among economic, social, natural resources and environmental aspects, have led to the necessity of developing optimization models for crop planting structure which consider uncertainty and multi-objectives elements. In this study,three single-objective programming models under uncertainty for crop planting structure optimization were developed, including an interval linear programming model, an inexact fuzzy chance-constrained programming(IFCCP) model and an inexact fuzzy linear programming(IFLP) model. Each of the three models takes grayness into account. Moreover, the IFCCP model considers fuzzy uncertainty of parameters/variables and stochastic characteristics of constraints, while the IFLP model takes into account the fuzzy uncertainty of both constraints and objective functions. To satisfy the sustainable development of crop planting structure planning, a fuzzy-optimizationtheory-based fuzzy linear multi-objective programming model was developed, which is capable of re flecting both uncertainties and multi-objective. In addition, a multiobjective fractional programming model for crop structure optimization was also developed to quantitatively express the multi-objective in one optimization model with the numerator representing maximum economic bene fits and the denominator representing minimum crop planting area allocation. These models better re flect actual situations,considering the uncertainties and multi-objectives of crop planting structure optimization systems. The five models developed were then applied to a real case study in MinqinCounty, north-west China. The advantages, the applicable conditions and the solution methods of each model are expounded. Detailed analysis of results of each model and their comparisons demonstrate the feasibility and applicability of the models developed, therefore decision makers can choose the appropriate model when making decisions. 展开更多
关键词 crop planting structure optimization model UNCERTAINTY multi-objective
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Kinetic modeling and multi-objective optimization of an industrial hydrocracking process with an improved SPEA2-PE algorithm
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作者 Chen Fan Xindong Wang +1 位作者 Gaochao Li Jian Long 《Chinese Journal of Chemical Engineering》 2025年第4期130-146,共17页
Hydrocracking is one of the most important petroleum refining processes that converts heavy oils into gases,naphtha,diesel,and other products through cracking reactions.Multi-objective optimization algorithms can help... Hydrocracking is one of the most important petroleum refining processes that converts heavy oils into gases,naphtha,diesel,and other products through cracking reactions.Multi-objective optimization algorithms can help refining enterprises determine the optimal operating parameters to maximize product quality while ensuring product yield,or to increase product yield while reducing energy consumption.This paper presents a multi-objective optimization scheme for hydrocracking based on an improved SPEA2-PE algorithm,which combines path evolution operator and adaptive step strategy to accelerate the convergence speed and improve the computational accuracy of the algorithm.The reactor model used in this article is simulated based on a twenty-five lumped kinetic model.Through model and test function verification,the proposed optimization scheme exhibits significant advantages in the multiobjective optimization process of hydrocracking. 展开更多
关键词 HYDROCRACKING multi-objective optimization Improved SPEA2 Kinetic modeling
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Multi-Objective Optimization of Marine Winch Based on Surrogate Model and MOGA
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作者 Chunhuan Jin Linsen Zhu +1 位作者 Quanliang Liu Ji Lin 《Computer Modeling in Engineering & Sciences》 2025年第5期1689-1711,共23页
This study proposes a multi-objective optimization framework for electric winches in fiber-reinforced plastic(FRP)fishing vessels to address critical limitations of conventional designs,including excessive weight,mate... This study proposes a multi-objective optimization framework for electric winches in fiber-reinforced plastic(FRP)fishing vessels to address critical limitations of conventional designs,including excessive weight,material inefficiency,and performance redundancy.By integrating surrogate modeling techniques with a multi-objective genetic algorithm(MOGA),we have developed a systematic approach that encompasses parametric modeling,finite element analysis under extreme operational conditions,and multi-fidelity performance evaluation.Through a 10-t electric winch case study,the methodology’s effectiveness is demonstrated via parametric characterization of structural integrity,stiffness behavior,and mass distribution.The comparative analysis identified optimal surrogate models for predicting key performance metrics,which enabled the construction of a robust multi-objective optimization model.The MOGA-derived Pareto solutions produced a design configuration achieving 7.86%mass reduction,2.01%safety factor improvement,and 23.97%deformation mitigation.Verification analysis confirmed the optimization scheme’s reliability in balancing conflicting design requirements.This research establishes a generalized framework for marine deck machinery modernization,particularly addressing the structural compatibility challenges in FRP vessel retrofitting.The proposed methodology demonstrates significant potential for facilitating sustainable upgrades of fishing vessel equipment through systematic performance optimization. 展开更多
关键词 Marine winch multi-objective optimization surrogate model
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Adapting High-Level Language Programming(C Language)Education in the Era of Large Language Models
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作者 Baokai Zu Hongyuan Wang +1 位作者 Hongli Chen Yafang Li 《Journal of Contemporary Educational Research》 2025年第5期264-269,共6页
With the widespread application of large language models(LLMs)in natural language processing and code generation,traditional High-Level Language Programming courses are facing unprecedented challenges and opportunitie... With the widespread application of large language models(LLMs)in natural language processing and code generation,traditional High-Level Language Programming courses are facing unprecedented challenges and opportunities.As a core programming language for computer science majors,C language remains irreplaceable due to its foundational nature and engineering adaptability.This paper,based on the rapid development of large model technologies,proposes a systematic reform design for C language teaching,focusing on teaching objectives,content structure,teaching methods,and evaluation systems.The article suggests a teaching framework centered on“human-computer collaborative programming,”integrating prompt training,AI-assisted debugging,and code generation analysis,aiming to enhance students’problem modeling ability,programming expression skills,and AI collaboration literacy. 展开更多
关键词 Large language models(LLMs) High-level language programming C language Human-computer collaborative programming
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Multi-objective Markov-enhanced adaptive whale optimization cybersecurity model for binary and multi-class malware cyberthreat classification
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作者 Saif Ali Abd Alradha Alsaidi Riyadh Rahef Nuiaa Al Ogaili +3 位作者 Zaid Abdi Alkareem Alyasseri Dhiah Al-Shammary Ayman Ibaida Adam Slowik 《Journal of Electronic Science and Technology》 2025年第4期95-112,共18页
The rapid and increasing growth in the volume and number of cyber threats from malware is not a real danger;the real threat lies in the obfuscation of these cyberattacks,as they constantly change their behavior,making... The rapid and increasing growth in the volume and number of cyber threats from malware is not a real danger;the real threat lies in the obfuscation of these cyberattacks,as they constantly change their behavior,making detection more difficult.Numerous researchers and developers have devoted considerable attention to this topic;however,the research field has not yet been fully saturated with high-quality studies that address these problems.For this reason,this paper presents a novel multi-objective Markov-enhanced adaptive whale optimization(MOMEAWO)cybersecurity model to improve the classification of binary and multi-class malware threats through the proposed MOMEAWO approach.The proposed MOMEAWO cybersecurity model aims to provide an innovative solution for analyzing,detecting,and classifying the behavior of obfuscated malware within their respective families.The proposed model includes three classification types:Binary classification and multi-class classification(e.g.,four families and 16 malware families).To evaluate the performance of this model,we used a recently published dataset called the Canadian Institute for Cybersecurity Malware Memory Analysis(CIC-MalMem-2022)that contains balanced data.The results show near-perfect accuracy in binary classification and high accuracy in multi-class classification compared with related work using the same dataset. 展开更多
关键词 Malware cybersecurity attacks Malware detection and classification Markov chain multi-objective MOMEAWO cybersecurity model
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Mixed integer programming modeling for the satellite three-dimensional component assignment and layout optimization problem
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作者 Yufeng XIA Xianqi CHEN +3 位作者 Zhijia LIU Weien ZHOU Wen YAO Zhongneng ZHANG 《Chinese Journal of Aeronautics》 2025年第6期427-447,共21页
Satellite Component Layout Optimization(SCLO) is crucial in satellite system design.This paper proposes a novel Satellite Three-Dimensional Component Assignment and Layout Optimization(3D-SCALO) problem tailored to en... Satellite Component Layout Optimization(SCLO) is crucial in satellite system design.This paper proposes a novel Satellite Three-Dimensional Component Assignment and Layout Optimization(3D-SCALO) problem tailored to engineering requirements, aiming to optimize satellite heat dissipation while considering constraints on static stability, 3D geometric relationships between components, and special component positions. The 3D-SCALO problem is a challenging bilevel combinatorial optimization task, involving the optimization of discrete component assignment variables in the outer layer and continuous component position variables in the inner layer,with both influencing each other. To address this issue, first, a Mixed Integer Programming(MIP) model is proposed, which reformulates the original bilevel problem into a single-level optimization problem, enabling the exploration of a more comprehensive optimization space while avoiding iterative nested optimization. Then, to model the 3D geometric relationships between components within the MIP framework, a linearized 3D Phi-function method is proposed, which handles non-overlapping and safety distance constraints between cuboid components in an explicit and effective way. Subsequently, the Finite-Rectangle Method(FRM) is proposed to manage 3D geometric constraints for complex-shaped components by approximating them with a finite set of cuboids, extending the applicability of the geometric modeling approach. Finally, the feasibility and effectiveness of the proposed MIP model are demonstrated through two numerical examples"and a real-world engineering case, which confirms its suitability for complex-shaped components and real engineering applications. 展开更多
关键词 Mixed integer programming modeling Three-dimensional component assignment Layout optimization Phi-function Finite-rectangle method
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Developed Time-OptimalModel Predictive Static Programming Method with Fish Swarm Optimization for Near-Space Vehicle
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作者 Yuanzhuo Wang Honghua Dai 《Computer Modeling in Engineering & Sciences》 2025年第5期1463-1484,共22页
To establish the optimal reference trajectory for a near-space vehicle under free terminal time,a time-optimal model predictive static programming method is proposed with adaptive fish swarm optimization.First,the mod... To establish the optimal reference trajectory for a near-space vehicle under free terminal time,a time-optimal model predictive static programming method is proposed with adaptive fish swarm optimization.First,the model predictive static programming method is developed by incorporating neighboring terms and trust region,enabling rapid generation of precise optimal solutions.Next,an adaptive fish swarm optimization technique is employed to identify a sub-optimal solution,while a momentum gradient descent method with learning rate decay ensures the convergence to the global optimal solution.To validate the feasibility and accuracy of the proposed method,a near-space vehicle example is analyzed and simulated during its glide phase.The simulation results demonstrate that the proposed method aligns with theoretical derivations and outperforms existing methods in terms of convergence speed and accuracy.Therefore,the proposed method offers significant practical value for solving the fast trajectory optimization problem in near-space vehicle applications. 展开更多
关键词 Near-space vehicle model predictive static programming neighboring term and trust region optimal control adaptive fish swarm optimization
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Approach for uncertain multi-objective programming problems with correlated objective functions under C_(EV) criterion 被引量:2
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作者 MENG Xiangfei WANG Ying +2 位作者 LI Chao WANG Xiaoyang LYU Maolong 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2018年第6期1197-1208,共12页
An uncertain multi-objective programming problem is a special type of mathematical multi-objective programming involving uncertain variables. This type of problem is important because there are several uncertain varia... An uncertain multi-objective programming problem is a special type of mathematical multi-objective programming involving uncertain variables. This type of problem is important because there are several uncertain variables in real-world problems.Therefore, research on the uncertain multi-objective programming problem is highly relevant, particularly those problems whose objective functions are correlated. In this paper, an approach that solves an uncertain multi-objective programming problem under the expected-variance value criterion is proposed. First, we define the basic framework of the approach and review concepts such as a Pareto efficient solution and expected-variance value criterion using an order relation between various uncertain variables.Second, the uncertain multi-objective problem is converted into an uncertain single-objective programming problem via a linear weighted method or ideal point method. Then the problem is transformed into a deterministic single objective programming problem under the expected-variance value criterion. Third, four lemmas and two theorems are proved to illustrate that the optimal solution of the deterministic single-objective programming problem is an efficient solution to the original uncertainty problem. Finally, two numerical examples are presented to validate the effectiveness of the proposed approach. 展开更多
关键词 uncertainty theory uncertain multi-objective programming expected-variance value criterion
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New approach for uncertain random multi-objective programming problems based on C_(ESD) criterion 被引量:1
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作者 SUN Yun WANG Ying +2 位作者 MENG Xiangfei FU Chaoqi LUO Chengkun 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2021年第3期619-630,共12页
To overcome the defects that the traditional ap-proach for multi-objective programming under uncertain ran-dom environment(URMOP)neglects the randomness and uncer-tainty of the problem and the volatility of the result... To overcome the defects that the traditional ap-proach for multi-objective programming under uncertain ran-dom environment(URMOP)neglects the randomness and uncer-tainty of the problem and the volatility of the results,a new ap-proach is proposed based on expected value-standard devi-ation value criterion(C_(ESD) criterion).Firstly,the effective solution to the URMOP problem is defined;then,by applying sequence relationship between the uncertain random variables,the UR-MOP problem is transformed into a single-objective program-ming(SOP)under uncertain random environment(URSOP),which are transformed into a deterministic counterpart based on the C_(ESD) criterion.Then the validity of the new approach is proved that the optimal solution to the SOP problem is also effi-cient for the URMOP problem;finally,a numerical example and a case application are presented to show the effectiveness of the new approach. 展开更多
关键词 chance theory independent-uncertain random multi-objective programming expected value-standard derivation value criterion(C_(ESD)criterion)
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MULTI-OBJECTIVE PROGRAMMING FOR AIRPORT GATE REASSIGNMENT
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作者 李军会 陈欣 朱金福 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2013年第2期209-215,共7页
To improve the efficiency of gate reassignment and optimize the plan of gate reassignment,the concept of disruption management is introduced,and a multi-objective programming model for airport gate reassignment is pro... To improve the efficiency of gate reassignment and optimize the plan of gate reassignment,the concept of disruption management is introduced,and a multi-objective programming model for airport gate reassignment is proposed.Considering the interests of passengers and the airport,the model minimizes the total flight delay,the total passengers′walking distance and the number of flights reassigned to other gates different from the planned ones.According to the characteristics of the gate reassignment,the model is simplified.As the multi-objective programming model is hard to reach the optimal solutions simultaneously,a threshold of satisfactory solutions of the model is set.Then a simulated annealing algorithm is designed for the model.Case studies show that the model decreases the total flight delay to the satisfactory solutions,and minimizes the total passengers′walking distance.The least change of planned assignment is also reached.The results achieve the goals of disruption management.Therefore,the model is verified to be effective. 展开更多
关键词 gate assignment multi-objective programming simulated annealing algorithm disruption management
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Estimating the Macroeconomic Costs of CO_2 Emission Reduction in China Based on Multi-objective Programming
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作者 Ying Fan Xiaobing Zhang Lei Zhu 《Advances in Climate Change Research》 SCIE 2010年第1期27-33,共7页
This paper estimates the macroeconornic costs of CO2 emission reduction in China employing the input-output analysis with the multi-objective programming approach. The results show that the effect of reducing CO2 emis... This paper estimates the macroeconornic costs of CO2 emission reduction in China employing the input-output analysis with the multi-objective programming approach. The results show that the effect of reducing CO2 emissions on China's economy is significant. Under the present conditions, the estimated macroeconomic costs of CO2 emission reduction in 2010 for China are approximately 3,100-4,024 RMB t-1. The stronger the abatement actions, the higher the macroeconomic costs of per unit emission reduction would be. Excavation industry, oil industry, chemical industry, and metal smelting industry have high potential to abate their CO2 emissions. 展开更多
关键词 CO2 emission reduction macroeconomic cost multi-objective programming input-output analysis
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Compactness, Contractibility and Fixed Point Properties of the Pareto Sets in Multi-Objective Programming
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作者 Zdravko Dimitrov Slavov Christina Slavova Evans 《Applied Mathematics》 2011年第5期556-561,共6页
This paper presents the Pareto solutions in continuous multi-objective mathematical programming. We discuss the role of some assumptions on the objective functions and feasible domain, the relationship between them, a... This paper presents the Pareto solutions in continuous multi-objective mathematical programming. We discuss the role of some assumptions on the objective functions and feasible domain, the relationship between them, and compactness, contractibility and fixed point properties of the Pareto sets. The authors have tried to remove the concavity assumptions on the objective functions which are usually used in multi-objective maximization problems. The results are based on constructing a retraction from the feasible domain onto the Pareto-optimal set. 展开更多
关键词 multi-objective programming PARETO-OPTIMAL Pareto-Front Compact CONTRACTIBLE Fixed Point RETRACTION
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Path Selection of Multimodal Transport Based on Multi-Objective Mixed Integer Programming
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作者 Zhongxin Luo 《Journal of Transportation Technologies》 2019年第4期462-473,共12页
Based on “One Belt and One Road”, this paper studies the path selection of multimodal transport by using the method of multi-objective mixed integer programming. Therefore, this paper studies the factors of transpor... Based on “One Belt and One Road”, this paper studies the path selection of multimodal transport by using the method of multi-objective mixed integer programming. Therefore, this paper studies the factors of transportation time, transportation cost and transportation safety performance, and establishes a mathematical model. In addition, the method of multi-objective mixed integer programming is used to comprehensively consider the different emphasis and differences of customers on cargo transportation. Then we use planning tools of Microsoft Excel to solve path selection and to determine whether the chosen path is economical and reliable. Finally, a relatively complex road network is built as an example to verify the accuracy of this planning method. 展开更多
关键词 ONE BELT and ONE Road multi-objective MULTIMODAL Transport Mixed INTEGER programming Path Selection
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Determining Efficient Solutions of Multi-Objective Linear Fractional Programming Problems and Application
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作者 Farhana Akond Pramy Md. Ainul Islam 《Open Journal of Optimization》 2017年第4期164-175,共12页
In this paper, a modified method to find the efficient solutions of multi-objective linear fractional programming (MOLFP) problems is presented. While some of the previously proposed methods provide only one efficient... In this paper, a modified method to find the efficient solutions of multi-objective linear fractional programming (MOLFP) problems is presented. While some of the previously proposed methods provide only one efficient solution to the MOLFP problem, this modified method provides multiple efficient solutions to the problem. As a result, it provides the decision makers flexibility to choose a better option from alternatives according to their financial position and their level of satisfaction of objectives. A numerical example is provided to illustrate the modified method and also a real life oriented production problem is modeled and solved. 展开更多
关键词 LINEAR programming (LP) LINEAR FRACTIONAL programming (LFP) multi-objective LINEAR programming (MOLP) multi-objective LINEAR FRACTIONAL programming (MOLFP)
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Roughly <i>B</i>-invex Multi-Objective Programming Problems
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作者 Tarek Emam 《Open Journal of Optimization》 2012年第1期1-7,共7页
In this paper, we shall be interested in characterization of efficient solutions for special classes of problems. These classes consider roughly B-invexity of involved functions. Sufficient and necessary conditions fo... In this paper, we shall be interested in characterization of efficient solutions for special classes of problems. These classes consider roughly B-invexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained. 展开更多
关键词 multi-objective programming Problems Roughly B-invex EFFICIENT SOLUTIONS Properly EFFICIENT SOLUTIONS
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Generating Efficient Solutions in Bilevel Multi-Objective Programming Problems
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作者 Calice Olivier Pieume Patrice Marcotte +1 位作者 Laure Pauline Fotso Patrick Siarry 《American Journal of Operations Research》 2013年第2期289-298,共10页
In this paper, we address bilevel multi-objective programming problems (BMPP) in which the decision maker at each level has multiple objective functions conflicting with each other. Given a BMPP, we show how to constr... In this paper, we address bilevel multi-objective programming problems (BMPP) in which the decision maker at each level has multiple objective functions conflicting with each other. Given a BMPP, we show how to construct two artificial multiobjective programming problems such that any point that is efficient for both the two problems is an efficient solution of the BMPP. Some necessary and sufficient conditions for which the obtained result is applicable are provided. A complete procedure of the implementation of an algorithm for generating efficient solutions for the linear case of BMPP is presented. A numerical example is provided to illustrate how the algorithm operates. 展开更多
关键词 multi-objective programming Bilevel programming EFFICIENT Solution EFFICIENT EDGE HIERARCHICAL Systems
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A Penalty Function Algorithm with Objective Parameters and Constraint Penalty Parameter for Multi-Objective Programming
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作者 Zhiqing Meng Rui Shen Min Jiang 《American Journal of Operations Research》 2014年第6期331-339,共9页
In this paper, we present an algorithm to solve the inequality constrained multi-objective programming (MP) by using a penalty function with objective parameters and constraint penalty parameter. First, the penalty fu... In this paper, we present an algorithm to solve the inequality constrained multi-objective programming (MP) by using a penalty function with objective parameters and constraint penalty parameter. First, the penalty function with objective parameters and constraint penalty parameter for MP and the corresponding unconstraint penalty optimization problem (UPOP) is defined. Under some conditions, a Pareto efficient solution (or a weakly-efficient solution) to UPOP is proved to be a Pareto efficient solution (or a weakly-efficient solution) to MP. The penalty function is proved to be exact under a stable condition. Then, we design an algorithm to solve MP and prove its convergence. Finally, numerical examples show that the algorithm may help decision makers to find a satisfactory solution to MP. 展开更多
关键词 multi-objective programming PENALTY Function Objective PARAMETERS CONSTRAINT PENALTY Parameter PARETO Weakly-Efficient Solution
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