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
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
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
文章以BY公司新建的数字化车间中自动化立体仓库(automated storage and retrieval system,AS/RS)货位分配为研究对象,通过实际调研和咨询,针对BY公司立体仓库提出了较合理货位分配策略和优化原则,据此建立了多目标优化模型(multi-objec...文章以BY公司新建的数字化车间中自动化立体仓库(automated storage and retrieval system,AS/RS)货位分配为研究对象,通过实际调研和咨询,针对BY公司立体仓库提出了较合理货位分配策略和优化原则,据此建立了多目标优化模型(multi-objective optimization,MOP)。基于遗传算法进行算子设计,结合Sheffield遗传算法工具箱,用Matlab进行编程实现,并用实例求解计算得出货位分配方案。研究结果表明,无论是在提高货架稳定性、使货架横向受力均匀,还是提高出库效率方面都有了较大的改善,能满足公司安全生产和高效作业的要求。展开更多
为了提升一种先进的新型机载传感器——嵌入式大气数据传感器(flush air data sensing,FADS)的测量精度,以正态云模型和多目标规划(multi-objective programming,MOP)为出发点,在原有的“三点法”基础上提出一种新的改进方法。基于CFD...为了提升一种先进的新型机载传感器——嵌入式大气数据传感器(flush air data sensing,FADS)的测量精度,以正态云模型和多目标规划(multi-objective programming,MOP)为出发点,在原有的“三点法”基础上提出一种新的改进方法。基于CFD软件得到的数据库和亚音速及超音速情况下的空气动力学知识建立高精度FADS系统模型,利用正态云模型对测量信号的不确定性和随机性进行量化分析,在对系统冗余信号的融合过程中,基于多目标规划中的松弛变量法和拉格朗日乘子法提出一种新的计算客观权重方法。仿真结果表明,与传统方法相比,新提出的基于云模型和多目标规划的方法可将测量精度提升3.2%,测量数据的离散程度降低68.88%。展开更多
Data envelopment analysis（DEA） is a mathematical programming approach to appraise the relative efficiencies of peer decision-making unit（DMU）,which is widely used in ranking DMUs.However,almost all DEA-related ran...Data envelopment analysis（DEA） is a mathematical programming approach to appraise the relative efficiencies of peer decision-making unit（DMU）,which is widely used in ranking DMUs.However,almost all DEA-related ranking approaches are based on the self-evaluation efficiencies.In other words,each DMU chooses the weights it prefers to most,so the resulted efficiencies are not suitable to be used as ranking criteria.Therefore this paper proposes a new approach to determine a bundle of common weights in DEA efficiency evaluation model by introducing a multi-objective integer programming.The paper also gives the solving process of this multi-objective integer programming,and the solution is proven a Pareto efficient solution.The solving process ensures that the obtained common weight bundle is acceptable by a great number of DMUs.Finally a numeral example is given to demonstrate the approach.展开更多
Weapon system portfolio selection is an important combinatorial problem that arises in various applications,such as weapons development planning and equipment procurement,which are of concern to military decision make...Weapon system portfolio selection is an important combinatorial problem that arises in various applications,such as weapons development planning and equipment procurement,which are of concern to military decision makers.However,the existing weapon system-of-systems(SoS)is tightly coupled.Because of the diversity and connectivity of mission requirements,it is difficult to describe the direct mapping relationship from the mission to the weapon system.In the latest service-oriented research,the introduction of service modules to build a service-oriented,flexible,and combinable structure is an important trend.This paper proposes a service-oriented weapon system portfolio selection method,by introducing service to serve as an intermediary to connect missions and system selection,and transferring the weapon system selection into the service portfolio selection.Specifically,the relation between the service and the task is described through the service-task mapping matrix;and the relation between the service and the weapon system is constructed through the servicesystem mapping matrix.The service collaboration network to calculate the flexibility and connectivity of each service portfolio is then established.Through multi-objective programming,the optimal service portfolios are generated,which are further decoded into weapon system portfolios.展开更多
基金supported by the National Natural Science Foundation of China(71601183 71571190)
文摘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.
基金supported by the National Natural Science Foundation of China(72001213)the basic research program of Natural Science of Shaanxi Province,China(2021JQ-369).
文摘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.
文摘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.
文摘为了提升一种先进的新型机载传感器——嵌入式大气数据传感器(flush air data sensing,FADS)的测量精度,以正态云模型和多目标规划(multi-objective programming,MOP)为出发点,在原有的“三点法”基础上提出一种新的改进方法。基于CFD软件得到的数据库和亚音速及超音速情况下的空气动力学知识建立高精度FADS系统模型,利用正态云模型对测量信号的不确定性和随机性进行量化分析,在对系统冗余信号的融合过程中,基于多目标规划中的松弛变量法和拉格朗日乘子法提出一种新的计算客观权重方法。仿真结果表明,与传统方法相比,新提出的基于云模型和多目标规划的方法可将测量精度提升3.2%,测量数据的离散程度降低68.88%。
基金supported by the National Natural Science Foundation of China for Innovative Research Groups(70821001)and the National Natural Science Foundation of China(70801056)
文摘Data envelopment analysis（DEA） is a mathematical programming approach to appraise the relative efficiencies of peer decision-making unit（DMU）,which is widely used in ranking DMUs.However,almost all DEA-related ranking approaches are based on the self-evaluation efficiencies.In other words,each DMU chooses the weights it prefers to most,so the resulted efficiencies are not suitable to be used as ranking criteria.Therefore this paper proposes a new approach to determine a bundle of common weights in DEA efficiency evaluation model by introducing a multi-objective integer programming.The paper also gives the solving process of this multi-objective integer programming,and the solution is proven a Pareto efficient solution.The solving process ensures that the obtained common weight bundle is acceptable by a great number of DMUs.Finally a numeral example is given to demonstrate the approach.
基金the National Key R&D Program of China(2017YFC1405005)the National Natural Science Foundation of China(71901214,71690233).
文摘Weapon system portfolio selection is an important combinatorial problem that arises in various applications,such as weapons development planning and equipment procurement,which are of concern to military decision makers.However,the existing weapon system-of-systems(SoS)is tightly coupled.Because of the diversity and connectivity of mission requirements,it is difficult to describe the direct mapping relationship from the mission to the weapon system.In the latest service-oriented research,the introduction of service modules to build a service-oriented,flexible,and combinable structure is an important trend.This paper proposes a service-oriented weapon system portfolio selection method,by introducing service to serve as an intermediary to connect missions and system selection,and transferring the weapon system selection into the service portfolio selection.Specifically,the relation between the service and the task is described through the service-task mapping matrix;and the relation between the service and the weapon system is constructed through the servicesystem mapping matrix.The service collaboration network to calculate the flexibility and connectivity of each service portfolio is then established.Through multi-objective programming,the optimal service portfolios are generated,which are further decoded into weapon system portfolios.
