The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcom...The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcome the result mesh-sensitivity problem in the dynamic strain softening or strain localization analysis. The equations for the dynamic elastic-plastic problems are derived in terms of the parametric variational principle, which is valid for associated, non-associated and strain softening plastic constitutive models in the finite element analysis. The precise integration method, which has been widely used for discretization in time domain of the linear problems, is introduced for the solution of dynamic nonlinear equations. The new algorithm proposed is based on the combination of the parametric quadratic programming method and the precise integration method and has all the advantages in both of the algorithms. Results of numerical examples demonstrate not only the validity, but also the advantages of the algorithm proposed for the numerical solution of nonlinear dynamic problems.展开更多
A method of minimizing rankings inconsistency is proposed for a decision-making problem with rankings of alternatives given by multiple decision makers according to multiple criteria. For each criteria, at first, the ...A method of minimizing rankings inconsistency is proposed for a decision-making problem with rankings of alternatives given by multiple decision makers according to multiple criteria. For each criteria, at first, the total inconsistency between the rankings of all alternatives for the group and the ones for every decision maker is defined after the decision maker weights in respect to the criteria are considered. Similarly, the total inconsistency between their final rankings for the group and the ones under every criteria is determined after the criteria weights are taken into account. Then two nonlinear integer programming models minimizing respectively the two total inconsistencies above are developed and then transformed to two dynamic programming models to obtain separately the rankings of all alternatives for the group with respect to each criteria and their final rankings. A supplier selection case illustrated the proposed method, and some discussions on the results verified its effectiveness. This work develops a new measurement of ordinal preferences’ inconsistency in multi-criteria group decision-making （MCGDM） and extends the cook-seiford social selection function to MCGDM considering weights of criteria and decision makers and can obtain unique ranking result.展开更多
An efficient active-set approach is presented for both nonnegative and general linear programming by adding varying numbers of constraints at each iteration. Computational experiments demonstrate that the proposed app...An efficient active-set approach is presented for both nonnegative and general linear programming by adding varying numbers of constraints at each iteration. Computational experiments demonstrate that the proposed approach is significantly faster than previous active-set and standard linear programming algorithms.展开更多
From a perspective of theoretical study, there are some faults in the models of the existing object-oriented programming languages. For example, C# does not support metaclasses, the primitive types of Java and C# are ...From a perspective of theoretical study, there are some faults in the models of the existing object-oriented programming languages. For example, C# does not support metaclasses, the primitive types of Java and C# are not objects, etc. So, this paper designs a programming language, Shrek, which integrates many language features and constructions in a compact and consistent model. The Shrek language is a class-based purely object-oriented language. It has a dynamical strong type system, and adopts a single-inheritance mechanism with Mixin as its complement. It has a consistent class instantiation and inheritance structure, and the ability of intercessive structural computational reflection, which enables it to support safe metaclass programming. It also supports multi-thread programming and automatic garbage collection, and enforces its expressive power by adopting a native method mechanism. The prototype system of the Shrek language is implemented and anticipated design goals are achieved.展开更多
A certain number of considerations should be taken into account in the dynamic control of robot manipulators as highly complex non-linear systems.In this article,we provide a detailed presentation of the mechanical an...A certain number of considerations should be taken into account in the dynamic control of robot manipulators as highly complex non-linear systems.In this article,we provide a detailed presentation of the mechanical and electrical impli- cations of robots equipped with DC motor actuators.This model takes into account all non-linear aspects of the system.Then,we develop computational algorithms for optimal control based on dynamic programming.The robot's trajectory must be predefined,but performance criteria and constraints applying to the system are not limited and we may adapt them freely to the robot and the task being studied.As an example,a manipulator arm with 3 degrees of freedom is analyzed.展开更多
Hardware/software partitioning is an important step in the design of embedded systems. In this paper, the hardware/software partitioning problem is modeled as a constrained binary integer programming problem, which is...Hardware/software partitioning is an important step in the design of embedded systems. In this paper, the hardware/software partitioning problem is modeled as a constrained binary integer programming problem, which is further converted equivalently to an unconstrained binary integer programming problem by a penalty method. A local search method, HSFM, is developed to obtain a discrete local minimizer of the unconstrained binary integer programming problem. Next, an auxiliary function, which has the same global optimal solutions as the unconstrained binary integer programming problem, is constructed, and its properties are studied. We show that applying HSFM to minimize the auxiliary function can escape from previous local optima by the increase of the parameter value successfully. Finally, a discrete dynamic convexized method is developed to solve the hardware/software partitioning problem. Computational results and comparisons indicate that the proposed algorithm can get high-quality solutions.展开更多
In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a gene...In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.展开更多
This paper surveys the literature for the optimization problems in both discrete and continuous time models in macroeconomics,and provides an overview over some related computational methods to solve the models linear...This paper surveys the literature for the optimization problems in both discrete and continuous time models in macroeconomics,and provides an overview over some related computational methods to solve the models linearly and nonlinearly,and to compute the transition dynamics and the impulse response functions.Also,the introduction of the financial sectors,the continuous time analysis,and the advanced mathematical tools into the general equilibrium framework expands greatly the scope of the interdisciplinary research to mathematics,statistics and econometrics,and creates further space for exploration and collaboration.Finally,some future research issues related to this topic are highlighted.展开更多
We introduce and analyze a family of linear least-squares Monte Carlo schemesfor backward SDEs, which interpolate between the one-step dynamic programmingscheme of Lemor, Warin, and Gobet (Bernoulli, 2006) and the mul...We introduce and analyze a family of linear least-squares Monte Carlo schemesfor backward SDEs, which interpolate between the one-step dynamic programmingscheme of Lemor, Warin, and Gobet (Bernoulli, 2006) and the multi-step dynamicprogramming scheme of Gobet and Turkedjiev (Mathematics of Computation, 2016). Ouralgorithm approximates conditional expectations over segments of the time grid. Wediscuss the optimal choice of the segment length depending on the 'smoothness' of theproblem and show that, in typical situations, the complexity can be reduced compared tothe state-of-the-art multi-step dynamic programming scheme.展开更多
This paper presents the optimal method of experiment for multidimensional dynamic programming.It becomes possible to solve the general problems of thousanddimensions.
The multi-satellite electromagnetic formation flight system is nonlinear and strongly coupled,which makes modeling and optimization challenging.To simplify electromagnetic force evaluation and dynamics modeling,we int...The multi-satellite electromagnetic formation flight system is nonlinear and strongly coupled,which makes modeling and optimization challenging.To simplify electromagnetic force evaluation and dynamics modeling,we introduce a reference frame consistent with each satellite body frame,in which the electromagnetic dipoles and electromagnetic forces are represented as two-dimensional vectors.Then,the maneuver time is divided into time intervals,and different satellite sets are activated in each interval,converting the multi-satellite formation reconfiguration problem into an optimal trajectory problem of each two-satellite subsystem.To this end,a token-based dynamic programming method with a switching penalty of active satellite sets is proposed to determine the sequence of satellite sets participating in each time interval,thereby enabling all satellites to reach their desired states.For the two-satellite subsystem with the objectives of minimizing maneuver time and energy consumption,the Gauss pseudo-spectral method is employed to generate the optimal reconfiguration trajectory.Numerical simulations verify the effectiveness of the proposed optimization method.展开更多
This paper presents an efficient algorithm for globally solving a generalized linear fractional programming problem.For establishing this algorithm,we firstly construct a two-level linear relaxation method,and by util...This paper presents an efficient algorithm for globally solving a generalized linear fractional programming problem.For establishing this algorithm,we firstly construct a two-level linear relaxation method,and by utilizing the method,we can convert the initial generalized linear fractional programming problem and its subproblems into a series of linear programming relaxation problems.Based on the branch-and-bound framework and linear programming relaxation problems,a branch-and-bound algorithm is presented for globally solving the generalized linear fractional programming problem,and the computational complexity of the algorithm is given.Finally,numerical experimental results demonstrate the feasibility and efficiency of the proposed algorithm.展开更多
Autonomous-rail rapid transit(ART)is a new medium-capacity rapid transportation system with punctuality,comfort and convenience,but low-cost construction.Combined velocity planning is a critical approach to meet the r...Autonomous-rail rapid transit(ART)is a new medium-capacity rapid transportation system with punctuality,comfort and convenience,but low-cost construction.Combined velocity planning is a critical approach to meet the requirements of energy-saving and punctuality.An ART velocity pre-planning and re-planning strategy based on the combination of punctuality dynamic programming(PDP)and pseudospectral(PS)method is proposed in this paper.Firstly,the longitudinal dynamics model of ART is established by a multi-particle model.Secondly,the PDP algorithm with global optimal characteristics is adopted as the pre-planning strategy.A model for determining the number of collocation points of the real-time PS method is proposed to improve the energy-saving effect while ensuring computation efficiency.Then the enhanced PS method is utilized to design the velocity re-planning strategy.Finally,simulations are conducted in the typical scenario with sloping roads,traffic lights,and intrusion of the pedestrian.The simulation results indicate that the ART with the proposed velocity trajectory optimization strategy can meet the punctuality requirement,and obtain better economy efficiency compared with the punctuality green light optimal speed advisory(PGLOSA).展开更多
To solve vehicle routing problem with different fleets, two methodologies are developed. The first methodology adopts twophase strategy. In the first phase, the improved savings method is used to assign customers to a...To solve vehicle routing problem with different fleets, two methodologies are developed. The first methodology adopts twophase strategy. In the first phase, the improved savings method is used to assign customers to appropriate vehicles. In the second phase, the iterated dynasearch algorithm is adopted to route each selected vehicle with the assigned customers. The iterated dynasearch algorithm combines dynasearch algorithm with iterated local search algorithm based on random kicks. The second methodplogy adopts the idea of cyclic transfer which is performed by using dynamic programming algorithm, and the iterated dynasearch algorithm is also embedded in it. The test results show that both methodologies generate better solutions than the traditional method, and the second methodology is superior to the first one.展开更多
文摘The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcome the result mesh-sensitivity problem in the dynamic strain softening or strain localization analysis. The equations for the dynamic elastic-plastic problems are derived in terms of the parametric variational principle, which is valid for associated, non-associated and strain softening plastic constitutive models in the finite element analysis. The precise integration method, which has been widely used for discretization in time domain of the linear problems, is introduced for the solution of dynamic nonlinear equations. The new algorithm proposed is based on the combination of the parametric quadratic programming method and the precise integration method and has all the advantages in both of the algorithms. Results of numerical examples demonstrate not only the validity, but also the advantages of the algorithm proposed for the numerical solution of nonlinear dynamic problems.
基金supported by the National Natural Science Foundation of China (60904059 60975049)+1 种基金the Philosophy and Social Science Foundation of Hunan Province (2010YBA104)the National High Technology Research and Development Program of China (863 Program)(2009AA04Z107)
文摘A method of minimizing rankings inconsistency is proposed for a decision-making problem with rankings of alternatives given by multiple decision makers according to multiple criteria. For each criteria, at first, the total inconsistency between the rankings of all alternatives for the group and the ones for every decision maker is defined after the decision maker weights in respect to the criteria are considered. Similarly, the total inconsistency between their final rankings for the group and the ones under every criteria is determined after the criteria weights are taken into account. Then two nonlinear integer programming models minimizing respectively the two total inconsistencies above are developed and then transformed to two dynamic programming models to obtain separately the rankings of all alternatives for the group with respect to each criteria and their final rankings. A supplier selection case illustrated the proposed method, and some discussions on the results verified its effectiveness. This work develops a new measurement of ordinal preferences’ inconsistency in multi-criteria group decision-making （MCGDM） and extends the cook-seiford social selection function to MCGDM considering weights of criteria and decision makers and can obtain unique ranking result.
文摘An efficient active-set approach is presented for both nonnegative and general linear programming by adding varying numbers of constraints at each iteration. Computational experiments demonstrate that the proposed approach is significantly faster than previous active-set and standard linear programming algorithms.
基金The National Science Fund for Distinguished Young Scholars (No.60425206)the National Natural Science Foundation of China (No.60633010)the Natural Science Foundation of Jiangsu Province(No.BK2006094)
文摘From a perspective of theoretical study, there are some faults in the models of the existing object-oriented programming languages. For example, C# does not support metaclasses, the primitive types of Java and C# are not objects, etc. So, this paper designs a programming language, Shrek, which integrates many language features and constructions in a compact and consistent model. The Shrek language is a class-based purely object-oriented language. It has a dynamical strong type system, and adopts a single-inheritance mechanism with Mixin as its complement. It has a consistent class instantiation and inheritance structure, and the ability of intercessive structural computational reflection, which enables it to support safe metaclass programming. It also supports multi-thread programming and automatic garbage collection, and enforces its expressive power by adopting a native method mechanism. The prototype system of the Shrek language is implemented and anticipated design goals are achieved.
文摘A certain number of considerations should be taken into account in the dynamic control of robot manipulators as highly complex non-linear systems.In this article,we provide a detailed presentation of the mechanical and electrical impli- cations of robots equipped with DC motor actuators.This model takes into account all non-linear aspects of the system.Then,we develop computational algorithms for optimal control based on dynamic programming.The robot's trajectory must be predefined,but performance criteria and constraints applying to the system are not limited and we may adapt them freely to the robot and the task being studied.As an example,a manipulator arm with 3 degrees of freedom is analyzed.
基金Supported by the National Natural Science Foundation of China(11301255)the Fund by Collaborative Innovation Center of IoT Industrialization and Intelligent Production,Minjiang University(IIC1703)+1 种基金Foundation of Minjiang University(MYK17032)the Program for New Century Excellent Talents in Fujian Province University
文摘Hardware/software partitioning is an important step in the design of embedded systems. In this paper, the hardware/software partitioning problem is modeled as a constrained binary integer programming problem, which is further converted equivalently to an unconstrained binary integer programming problem by a penalty method. A local search method, HSFM, is developed to obtain a discrete local minimizer of the unconstrained binary integer programming problem. Next, an auxiliary function, which has the same global optimal solutions as the unconstrained binary integer programming problem, is constructed, and its properties are studied. We show that applying HSFM to minimize the auxiliary function can escape from previous local optima by the increase of the parameter value successfully. Finally, a discrete dynamic convexized method is developed to solve the hardware/software partitioning problem. Computational results and comparisons indicate that the proposed algorithm can get high-quality solutions.
基金supported by the Swiss National Science Foundation(Grant No.189882)the National Natural Science Foundation of China(Grant No.41961134032)support provided by the New Investigator Award grant from the UK Engineering and Physical Sciences Research Council(Grant No.EP/V012169/1).
文摘In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.
基金Supported by the National Natural Science Foundation of China(72033008,72133002)。
文摘This paper surveys the literature for the optimization problems in both discrete and continuous time models in macroeconomics,and provides an overview over some related computational methods to solve the models linearly and nonlinearly,and to compute the transition dynamics and the impulse response functions.Also,the introduction of the financial sectors,the continuous time analysis,and the advanced mathematical tools into the general equilibrium framework expands greatly the scope of the interdisciplinary research to mathematics,statistics and econometrics,and creates further space for exploration and collaboration.Finally,some future research issues related to this topic are highlighted.
文摘We introduce and analyze a family of linear least-squares Monte Carlo schemesfor backward SDEs, which interpolate between the one-step dynamic programmingscheme of Lemor, Warin, and Gobet (Bernoulli, 2006) and the multi-step dynamicprogramming scheme of Gobet and Turkedjiev (Mathematics of Computation, 2016). Ouralgorithm approximates conditional expectations over segments of the time grid. Wediscuss the optimal choice of the segment length depending on the 'smoothness' of theproblem and show that, in typical situations, the complexity can be reduced compared tothe state-of-the-art multi-step dynamic programming scheme.
文摘This paper presents the optimal method of experiment for multidimensional dynamic programming.It becomes possible to solve the general problems of thousanddimensions.
文摘The multi-satellite electromagnetic formation flight system is nonlinear and strongly coupled,which makes modeling and optimization challenging.To simplify electromagnetic force evaluation and dynamics modeling,we introduce a reference frame consistent with each satellite body frame,in which the electromagnetic dipoles and electromagnetic forces are represented as two-dimensional vectors.Then,the maneuver time is divided into time intervals,and different satellite sets are activated in each interval,converting the multi-satellite formation reconfiguration problem into an optimal trajectory problem of each two-satellite subsystem.To this end,a token-based dynamic programming method with a switching penalty of active satellite sets is proposed to determine the sequence of satellite sets participating in each time interval,thereby enabling all satellites to reach their desired states.For the two-satellite subsystem with the objectives of minimizing maneuver time and energy consumption,the Gauss pseudo-spectral method is employed to generate the optimal reconfiguration trajectory.Numerical simulations verify the effectiveness of the proposed optimization method.
基金the National Natural Science Foundation of China(Nos.11871196,12071133 and 12071112)the China Postdoctoral Science Foundation(No.2017M622340)+1 种基金the Key Scientific and Technological Research Projects of Henan Province(Nos.202102210147 and 192102210114)the Science and Technology Climbing Program of Henan Institute of Science and Technology(No.2018JY01).
文摘This paper presents an efficient algorithm for globally solving a generalized linear fractional programming problem.For establishing this algorithm,we firstly construct a two-level linear relaxation method,and by utilizing the method,we can convert the initial generalized linear fractional programming problem and its subproblems into a series of linear programming relaxation problems.Based on the branch-and-bound framework and linear programming relaxation problems,a branch-and-bound algorithm is presented for globally solving the generalized linear fractional programming problem,and the computational complexity of the algorithm is given.Finally,numerical experimental results demonstrate the feasibility and efficiency of the proposed algorithm.
基金Supported by National Natural Science Foundation of China(Grant Nos.52072073 and 52025121)National Key R&D Program of China(Grant No.2018YFB1201602).
文摘Autonomous-rail rapid transit(ART)is a new medium-capacity rapid transportation system with punctuality,comfort and convenience,but low-cost construction.Combined velocity planning is a critical approach to meet the requirements of energy-saving and punctuality.An ART velocity pre-planning and re-planning strategy based on the combination of punctuality dynamic programming(PDP)and pseudospectral(PS)method is proposed in this paper.Firstly,the longitudinal dynamics model of ART is established by a multi-particle model.Secondly,the PDP algorithm with global optimal characteristics is adopted as the pre-planning strategy.A model for determining the number of collocation points of the real-time PS method is proposed to improve the energy-saving effect while ensuring computation efficiency.Then the enhanced PS method is utilized to design the velocity re-planning strategy.Finally,simulations are conducted in the typical scenario with sloping roads,traffic lights,and intrusion of the pedestrian.The simulation results indicate that the ART with the proposed velocity trajectory optimization strategy can meet the punctuality requirement,and obtain better economy efficiency compared with the punctuality green light optimal speed advisory(PGLOSA).
基金The National Natural Science Founda-tion of China ( No.70471039)the National Social Science Foundation of China (No.07BJY038)the Program for New Century Excellent Talents in University (No.NCET-04-0886)
文摘To solve vehicle routing problem with different fleets, two methodologies are developed. The first methodology adopts twophase strategy. In the first phase, the improved savings method is used to assign customers to appropriate vehicles. In the second phase, the iterated dynasearch algorithm is adopted to route each selected vehicle with the assigned customers. The iterated dynasearch algorithm combines dynasearch algorithm with iterated local search algorithm based on random kicks. The second methodplogy adopts the idea of cyclic transfer which is performed by using dynamic programming algorithm, and the iterated dynasearch algorithm is also embedded in it. The test results show that both methodologies generate better solutions than the traditional method, and the second methodology is superior to the first one.
