REST(Rust-based electronic structure toolkit)is a modern open-source electronic structure code entirely written in Rust,combining high performance,memory safety,and expressive concurrency.As a community-driven project...REST(Rust-based electronic structure toolkit)is a modern open-source electronic structure code entirely written in Rust,combining high performance,memory safety,and expressive concurrency.As a community-driven project,its source code is freely available at https://gitee.com/restgroup,fostering open collaboration and transparent development.It supports a wide range of density functional methods-from local density approximation(LDA),generalized gradient approximation(GGA),meta-GGA,and hybrids to doubly hybrids,as well as machine learning-augmented functionals-enabling high-accuracy simulations with low computational overhead.Its“disk-free”RI-based(RI:resolution-of-the-identity)implementation and efficient shared-memory parallelism(via Rayon)ensure rapid calculations even for challenging systems.REST also of-fers unique user support through large language model-assisted input generation and develop-erfriendly tensor libraries for rapid algorithm prototyping.展开更多
This paper presents an adaptive path planner for unmanned aerial vehicles （UAVs） to adapt a real-time path search procedure to variations and fluctuations of UAVs’ relevant performances, with respect to sensory cap...This paper presents an adaptive path planner for unmanned aerial vehicles （UAVs） to adapt a real-time path search procedure to variations and fluctuations of UAVs’ relevant performances, with respect to sensory capability, maneuverability, and flight velocity limit. On the basis of a novel adaptability-involved problem statement, bi-level programming （BLP） and variable planning step techniques are introduced to model the necessary path planning components and then an adaptive path planner is developed for the purpose of adaptation and optimization. Additionally, both probabilistic-risk-based obstacle avoidance and performance limits are described as path search constraints to guarantee path safety and navigability. A discrete-search-based path planning solution, embedded with four optimization strategies, is especially designed for the planner to efficiently generate optimal flight paths in complex operational spaces, within which different surface-to-air missiles （SAMs） are deployed. Simulation results in challenging and stochastic scenarios firstly demonstrate the effectiveness and efficiency of the proposed planner, and then verify its great adaptability and relative stability when planning optimal paths for a UAV with changing or fluctuating performances.展开更多
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
In this article,a novel model-free coordinated optimal regulation design methodology is proposed for the rigidly connected dual permanent magnet synchronous motor(PMSM)system via adaptive dynamic programming(ADP).Firs...In this article,a novel model-free coordinated optimal regulation design methodology is proposed for the rigidly connected dual permanent magnet synchronous motor(PMSM)system via adaptive dynamic programming(ADP).First,we adopt the classical master-slave structure to maintain torque synchronization by virtue of field-oriented control.Then,a reducedorder model of the dual-PMSM system is established through the application of singular perturbation theory(SPT),which is of significance to decrease the learning time and computational complexity in the outer speed loop design.Afterwards,we design a coordinated adaptive optimal regulator in framework of ADP to drive the speed of girth gear asymptotic tracking the reference signal and accommodate the load torque disturbance,which is independent of the knowledge of model parameters of the system.According to SPT,we analyze the suboptimality,closed-loop stability,and robustness properties of the obtained controller under mild conditions.Finally,comprehensive experimental studies are provided to verify that the proposed control strategy can achieve the speed regulation and the torque synchronization,as well as ameliorate the transient response.展开更多
An algorithm is proposed in this paper for solving two-dimensional bi-level linear programming problems without making a graph. Based on the classification of constraints, algorithm removes all redundant constraints, ...An algorithm is proposed in this paper for solving two-dimensional bi-level linear programming problems without making a graph. Based on the classification of constraints, algorithm removes all redundant constraints, which eliminate the possibility of cycling and the solution of the problem is reached in a finite number of steps. Example to illustrate the method is also included in the paper.展开更多
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
Approximate dynamic programming (ADP) is a general and effective approach for solving optimal control and estimation problems by adapting to uncertain and nonconvex environments over time.
This paper studies the problem of optimal parallel tracking control for continuous-time general nonlinear systems.Unlike existing optimal state feedback control,the control input of the optimal parallel control is int...This paper studies the problem of optimal parallel tracking control for continuous-time general nonlinear systems.Unlike existing optimal state feedback control,the control input of the optimal parallel control is introduced into the feedback system.However,due to the introduction of control input into the feedback system,the optimal state feedback control methods can not be applied directly.To address this problem,an augmented system and an augmented performance index function are proposed firstly.Thus,the general nonlinear system is transformed into an affine nonlinear system.The difference between the optimal parallel control and the optimal state feedback control is analyzed theoretically.It is proven that the optimal parallel control with the augmented performance index function can be seen as the suboptimal state feedback control with the traditional performance index function.Moreover,an adaptive dynamic programming(ADP)technique is utilized to implement the optimal parallel tracking control using a critic neural network(NN)to approximate the value function online.The stability analysis of the closed-loop system is performed using the Lyapunov theory,and the tracking error and NN weights errors are uniformly ultimately bounded(UUB).Also,the optimal parallel controller guarantees the continuity of the control input under the circumstance that there are finite jump discontinuities in the reference signals.Finally,the effectiveness of the developed optimal parallel control method is verified in two cases.展开更多
In order to meet the needs of collaborative decision making,considering the different demands of air traffic control units,airlines,airports and passengers in various traffic scenarios,the joint scheduling problem of ...In order to meet the needs of collaborative decision making,considering the different demands of air traffic control units,airlines,airports and passengers in various traffic scenarios,the joint scheduling problem of arrival and departure flights is studied systematically.According to the matching degree of capacity and flow,it is determined that the traffic state of arrival/departure operation in a certain period is peak or off-peak.The demands of all parties in each traffic state are analyzed,and the mathematical models of arrival/departure flight scheduling in each traffic state are established.Aiming at the four kinds of joint operation traffic scenarios of arrival and departure,the corresponding bi-level programming models for joint scheduling of arrival and departure flights are established,respectively,and the elitism genetic algorithm is designed to solve the models.The results show that:Compared with the first-come-firstserved method,in the scenarios of arrival peak&departure off-peak and arrival peak&departure peak,the departure flight equilibrium satisfaction is improved,and the runway occupation time of departure flight flow is reduced by 38.8%.In the scenarios of arrival off-peak&departure off-peak and departure peak&arrival off-peak,the arrival flight equilibrium delay time is significantly reduced,the departure flight equilibrium satisfaction is improved by 77.6%,and the runway occupation time of departure flight flow is reduced by 46.6%.Compared with other four kinds of strategies,the optimal scheduling method can better balance fairness and efficiency,so the scheduling results are more reasonable.展开更多
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
Assembling paradigms programming are based on the reuses in any programming language (PL) with the passport data of their settings in WSDL. The method of assembling is formal and secures co-operation of the different ...Assembling paradigms programming are based on the reuses in any programming language (PL) with the passport data of their settings in WSDL. The method of assembling is formal and secures co-operation of the different reuses (module, object, component, service and so on) being developed. A formal means of these paradigms creation with help of interfaces is presented. Interface IDL (Stub, Skeleton) is containing data and operations for transmission data to other standard elements linked and describes in the standard language IDL. Assembling will be realized by integration of reuses elements in these paradigms on the instrumental-technological complex (ITC).展开更多
For satate form linear gram as Fang and sao deined and approach which would find an optimal solution by solving an anconstrained convex dual programming.Thedual was construcied by applying an emropic peturbation and a...For satate form linear gram as Fang and sao deined and approach which would find an optimal solution by solving an anconstrained convex dual programming.Thedual was construcied by applying an emropic peturbation and a simple Inequality Inz【z-1 for z】0n,In this paper,we suggest than a paperbation functiontake the place of Inx such that the new approdt has good numerical stability andhas all properties of the original展开更多
The objective of the paper is to deal with a kind of possibilistic linear programming (PLP) problem involving multiple objectives of conflicting nature. In particular, we have considered a multi objective linear progr...The objective of the paper is to deal with a kind of possibilistic linear programming (PLP) problem involving multiple objectives of conflicting nature. In particular, we have considered a multi objective linear programming (MOLP) problem whose objective is to simultaneously minimize cost and maximize profit in a supply chain where cost and profit coefficients, and related parameters such as available supply, forecast demand and budget are fuzzy with trapezoidal fuzzy numbers. An example is given to illustrate the strategy used to solve the aforesaid PLP problem.展开更多
The maximum clique or maximum independent set of graph is a classical problem in graph theory. Com- bined with Boolean algebra and integer programming, two integer programming models for maximum clique problem, which ...The maximum clique or maximum independent set of graph is a classical problem in graph theory. Com- bined with Boolean algebra and integer programming, two integer programming models for maximum clique problem, which improve the old results were designed in this paper. Then, the programming model for maximum independent set is a corollary of the main results. These two models can be easily applied to computer algorithm and software, and suitable for graphs of any scale. Finally the models are presented as Lingo algorithms, verified and compared by sev- eral examples.展开更多
The existence of strongly polynomial algorithm for linear programming (LP) has been widely sought after for decades. Recently, a new approach called Gravity Sliding algorithm [1] has emerged. It is a gradient descendi...The existence of strongly polynomial algorithm for linear programming (LP) has been widely sought after for decades. Recently, a new approach called Gravity Sliding algorithm [1] has emerged. It is a gradient descending method whereby the descending trajectory slides along the inner surfaces of a polyhedron until it reaches the optimal point. In R3, a water droplet pulled by gravitational force traces the shortest path to descend to the lowest point. As the Gravity Sliding algorithm emulates the water droplet trajectory, it exhibits strongly polynomial behavior in R3. We believe that it could be a strongly polynomial algorithm for linear programming in Rn too. In fact, our algorithm can solve the Klee-Minty deformed cube problem in only two iterations, irrespective of the dimension of the cube. The core of gravity sliding algorithm is how to calculate the projection of the gravity vector g onto the intersection of a group of facets, which is disclosed in the same paper [1]. In this paper, we introduce a more efficient method to compute the gradient projections on complementary facets, and rename it the Sliding Gradient algorithm under the new projection calculation.展开更多
We employ uncertain programming to investigate the competitive logistics distribution center location problem in uncertain environment, in which the demands of customers and the setup costs of new distribution centers...We employ uncertain programming to investigate the competitive logistics distribution center location problem in uncertain environment, in which the demands of customers and the setup costs of new distribution centers are uncertain variables. This research was studied with the assumption that customers patronize the nearest distribution center to satisfy their full demands. Within the framework of uncertainty theory, we construct the expected value model to maximize the expected profit of the new distribution center. In order to seek for the optimal solution, this model can be transformed into its deterministic form by taking advantage of the operational law of uncertain variables. Then we can use mathematical software to obtain the optimal location. In addition, a numerical example is presented to illustrate the effectiveness of the presented model.展开更多
Let be an undirected graph. The maximum cycle packing problem in G then is to find a collection of edge-disjoint cycles C<sub>i</sup>in G such that s is maximum. In general, the maximum cycle packing probl...Let be an undirected graph. The maximum cycle packing problem in G then is to find a collection of edge-disjoint cycles C<sub>i</sup>in G such that s is maximum. In general, the maximum cycle packing problem is NP-hard. In this paper, it is shown for even graphs that if such a collection satisfies the condition that it minimizes the quantityon the set of all edge-disjoint cycle collections, then it is a maximum cycle packing. The paper shows that the determination of such a packing can be solved by a dynamic programming approach. For its solution, an-shortest path procedure on an appropriate acyclic networkis presented. It uses a particular monotonous node potential.展开更多
With the prevailing and popular entertainment programs, it brought huge benefits to TV stations, but at the same time caused a variety problems of homogenization. The paper analyzes the causes of the entertainment pro...With the prevailing and popular entertainment programs, it brought huge benefits to TV stations, but at the same time caused a variety problems of homogenization. The paper analyzes the causes of the entertainment programs, the root of homogenization, building game theory models between TV stations, TV station and audience to regulate and control the issue of homogeneity about entertainment programs.展开更多
In this paper we study L-shaped convex programming. An algorithm for it is given. The result of computation shows that the algorithm is effective. The algorithm can be applied to two stage problem of stochastic convex...In this paper we study L-shaped convex programming. An algorithm for it is given. The result of computation shows that the algorithm is effective. The algorithm can be applied to two stage problem of stochastic convex programming.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 22125301, 22393911, 22393912, 22321003, 22233002)the Innovation Program for Quantum Science and Technology (2021ZD0303305)the robotic AI-Scientist platform of the Chinese Academy of Science。
文摘REST(Rust-based electronic structure toolkit)is a modern open-source electronic structure code entirely written in Rust,combining high performance,memory safety,and expressive concurrency.As a community-driven project,its source code is freely available at https://gitee.com/restgroup,fostering open collaboration and transparent development.It supports a wide range of density functional methods-from local density approximation(LDA),generalized gradient approximation(GGA),meta-GGA,and hybrids to doubly hybrids,as well as machine learning-augmented functionals-enabling high-accuracy simulations with low computational overhead.Its“disk-free”RI-based(RI:resolution-of-the-identity)implementation and efficient shared-memory parallelism(via Rayon)ensure rapid calculations even for challenging systems.REST also of-fers unique user support through large language model-assisted input generation and develop-erfriendly tensor libraries for rapid algorithm prototyping.
基金the National Natural Science Foundation of China(No.60904066)
文摘This paper presents an adaptive path planner for unmanned aerial vehicles （UAVs） to adapt a real-time path search procedure to variations and fluctuations of UAVs’ relevant performances, with respect to sensory capability, maneuverability, and flight velocity limit. On the basis of a novel adaptability-involved problem statement, bi-level programming （BLP） and variable planning step techniques are introduced to model the necessary path planning components and then an adaptive path planner is developed for the purpose of adaptation and optimization. Additionally, both probabilistic-risk-based obstacle avoidance and performance limits are described as path search constraints to guarantee path safety and navigability. A discrete-search-based path planning solution, embedded with four optimization strategies, is especially designed for the planner to efficiently generate optimal flight paths in complex operational spaces, within which different surface-to-air missiles （SAMs） are deployed. Simulation results in challenging and stochastic scenarios firstly demonstrate the effectiveness and efficiency of the proposed planner, and then verify its great adaptability and relative stability when planning optimal paths for a UAV with changing or fluctuating performances.
基金Project(2006CB705507) supported by the National Basic Research and Development Program of ChinaProject(20060533036) supported by the Specialized Research Foundation for the Doctoral Program of Higher Education of China
文摘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.
基金supported by the National Natural Science Foundation of China(62073327,62403467,62373090,62273350,62521001)the Natural Science Foundation of Jiangsu Province(BK20241635)+2 种基金the Postdoctoral Fellowship Program of China Postdoctoral Science Foundation(CPSF)(GZB20240827)Jiangsu Funding Program for Excellent Postdoctoral Talent(2024ZB604)the China Postdoctoral Science Foundation(2024M763545,2025T054ZGMK).
文摘In this article,a novel model-free coordinated optimal regulation design methodology is proposed for the rigidly connected dual permanent magnet synchronous motor(PMSM)system via adaptive dynamic programming(ADP).First,we adopt the classical master-slave structure to maintain torque synchronization by virtue of field-oriented control.Then,a reducedorder model of the dual-PMSM system is established through the application of singular perturbation theory(SPT),which is of significance to decrease the learning time and computational complexity in the outer speed loop design.Afterwards,we design a coordinated adaptive optimal regulator in framework of ADP to drive the speed of girth gear asymptotic tracking the reference signal and accommodate the load torque disturbance,which is independent of the knowledge of model parameters of the system.According to SPT,we analyze the suboptimality,closed-loop stability,and robustness properties of the obtained controller under mild conditions.Finally,comprehensive experimental studies are provided to verify that the proposed control strategy can achieve the speed regulation and the torque synchronization,as well as ameliorate the transient response.
文摘An algorithm is proposed in this paper for solving two-dimensional bi-level linear programming problems without making a graph. Based on the classification of constraints, algorithm removes all redundant constraints, which eliminate the possibility of cycling and the solution of the problem is reached in a finite number of steps. Example to illustrate the method is also included in the paper.
基金the Humanities and Social Science Foundation of the Ministry of Education of China(Grant No.20YJCZH121).
文摘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.
文摘Approximate dynamic programming (ADP) is a general and effective approach for solving optimal control and estimation problems by adapting to uncertain and nonconvex environments over time.
基金supported in part by the National Key Reseanch and Development Program of China(2018AAA0101502,2018YFB1702300)in part by the National Natural Science Foundation of China(61722312,61533019,U1811463,61533017)in part by the Intel Collaborative Research Institute for Intelligent and Automated Connected Vehicles。
文摘This paper studies the problem of optimal parallel tracking control for continuous-time general nonlinear systems.Unlike existing optimal state feedback control,the control input of the optimal parallel control is introduced into the feedback system.However,due to the introduction of control input into the feedback system,the optimal state feedback control methods can not be applied directly.To address this problem,an augmented system and an augmented performance index function are proposed firstly.Thus,the general nonlinear system is transformed into an affine nonlinear system.The difference between the optimal parallel control and the optimal state feedback control is analyzed theoretically.It is proven that the optimal parallel control with the augmented performance index function can be seen as the suboptimal state feedback control with the traditional performance index function.Moreover,an adaptive dynamic programming(ADP)technique is utilized to implement the optimal parallel tracking control using a critic neural network(NN)to approximate the value function online.The stability analysis of the closed-loop system is performed using the Lyapunov theory,and the tracking error and NN weights errors are uniformly ultimately bounded(UUB).Also,the optimal parallel controller guarantees the continuity of the control input under the circumstance that there are finite jump discontinuities in the reference signals.Finally,the effectiveness of the developed optimal parallel control method is verified in two cases.
基金supported by Nanjing University of Aeronautics and Astronautics Graduate Innovation Base(Laboratory)Open Fund(No.kfjj20200717).
文摘In order to meet the needs of collaborative decision making,considering the different demands of air traffic control units,airlines,airports and passengers in various traffic scenarios,the joint scheduling problem of arrival and departure flights is studied systematically.According to the matching degree of capacity and flow,it is determined that the traffic state of arrival/departure operation in a certain period is peak or off-peak.The demands of all parties in each traffic state are analyzed,and the mathematical models of arrival/departure flight scheduling in each traffic state are established.Aiming at the four kinds of joint operation traffic scenarios of arrival and departure,the corresponding bi-level programming models for joint scheduling of arrival and departure flights are established,respectively,and the elitism genetic algorithm is designed to solve the models.The results show that:Compared with the first-come-firstserved method,in the scenarios of arrival peak&departure off-peak and arrival peak&departure peak,the departure flight equilibrium satisfaction is improved,and the runway occupation time of departure flight flow is reduced by 38.8%.In the scenarios of arrival off-peak&departure off-peak and departure peak&arrival off-peak,the arrival flight equilibrium delay time is significantly reduced,the departure flight equilibrium satisfaction is improved by 77.6%,and the runway occupation time of departure flight flow is reduced by 46.6%.Compared with other four kinds of strategies,the optimal scheduling method can better balance fairness and efficiency,so the scheduling results are more reasonable.
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Assembling paradigms programming are based on the reuses in any programming language (PL) with the passport data of their settings in WSDL. The method of assembling is formal and secures co-operation of the different reuses (module, object, component, service and so on) being developed. A formal means of these paradigms creation with help of interfaces is presented. Interface IDL (Stub, Skeleton) is containing data and operations for transmission data to other standard elements linked and describes in the standard language IDL. Assembling will be realized by integration of reuses elements in these paradigms on the instrumental-technological complex (ITC).
基金The project was supported by the National Natural Science Fundation of China
文摘For satate form linear gram as Fang and sao deined and approach which would find an optimal solution by solving an anconstrained convex dual programming.Thedual was construcied by applying an emropic peturbation and a simple Inequality Inz【z-1 for z】0n,In this paper,we suggest than a paperbation functiontake the place of Inx such that the new approdt has good numerical stability andhas all properties of the original
文摘The objective of the paper is to deal with a kind of possibilistic linear programming (PLP) problem involving multiple objectives of conflicting nature. In particular, we have considered a multi objective linear programming (MOLP) problem whose objective is to simultaneously minimize cost and maximize profit in a supply chain where cost and profit coefficients, and related parameters such as available supply, forecast demand and budget are fuzzy with trapezoidal fuzzy numbers. An example is given to illustrate the strategy used to solve the aforesaid PLP problem.
文摘The maximum clique or maximum independent set of graph is a classical problem in graph theory. Com- bined with Boolean algebra and integer programming, two integer programming models for maximum clique problem, which improve the old results were designed in this paper. Then, the programming model for maximum independent set is a corollary of the main results. These two models can be easily applied to computer algorithm and software, and suitable for graphs of any scale. Finally the models are presented as Lingo algorithms, verified and compared by sev- eral examples.
文摘The existence of strongly polynomial algorithm for linear programming (LP) has been widely sought after for decades. Recently, a new approach called Gravity Sliding algorithm [1] has emerged. It is a gradient descending method whereby the descending trajectory slides along the inner surfaces of a polyhedron until it reaches the optimal point. In R3, a water droplet pulled by gravitational force traces the shortest path to descend to the lowest point. As the Gravity Sliding algorithm emulates the water droplet trajectory, it exhibits strongly polynomial behavior in R3. We believe that it could be a strongly polynomial algorithm for linear programming in Rn too. In fact, our algorithm can solve the Klee-Minty deformed cube problem in only two iterations, irrespective of the dimension of the cube. The core of gravity sliding algorithm is how to calculate the projection of the gravity vector g onto the intersection of a group of facets, which is disclosed in the same paper [1]. In this paper, we introduce a more efficient method to compute the gradient projections on complementary facets, and rename it the Sliding Gradient algorithm under the new projection calculation.
文摘We employ uncertain programming to investigate the competitive logistics distribution center location problem in uncertain environment, in which the demands of customers and the setup costs of new distribution centers are uncertain variables. This research was studied with the assumption that customers patronize the nearest distribution center to satisfy their full demands. Within the framework of uncertainty theory, we construct the expected value model to maximize the expected profit of the new distribution center. In order to seek for the optimal solution, this model can be transformed into its deterministic form by taking advantage of the operational law of uncertain variables. Then we can use mathematical software to obtain the optimal location. In addition, a numerical example is presented to illustrate the effectiveness of the presented model.
文摘Let be an undirected graph. The maximum cycle packing problem in G then is to find a collection of edge-disjoint cycles C<sub>i</sup>in G such that s is maximum. In general, the maximum cycle packing problem is NP-hard. In this paper, it is shown for even graphs that if such a collection satisfies the condition that it minimizes the quantityon the set of all edge-disjoint cycle collections, then it is a maximum cycle packing. The paper shows that the determination of such a packing can be solved by a dynamic programming approach. For its solution, an-shortest path procedure on an appropriate acyclic networkis presented. It uses a particular monotonous node potential.
文摘With the prevailing and popular entertainment programs, it brought huge benefits to TV stations, but at the same time caused a variety problems of homogenization. The paper analyzes the causes of the entertainment programs, the root of homogenization, building game theory models between TV stations, TV station and audience to regulate and control the issue of homogeneity about entertainment programs.
基金This work is supported by Science Research Foundation (20262250) of the Education Department of Liaoning Province.
文摘In this paper we study L-shaped convex programming. An algorithm for it is given. The result of computation shows that the algorithm is effective. The algorithm can be applied to two stage problem of stochastic convex programming.
