In order to achieve highly accurate and efficient numerical calculations of structural dynamics, time collocation method is presented. For a given time interval, the numerical solution of the method is approximated by...In order to achieve highly accurate and efficient numerical calculations of structural dynamics, time collocation method is presented. For a given time interval, the numerical solution of the method is approximated by a polynomial. The polynomial coefficients are evaluated by solving algebraic equation. Once the polynomial coefficients are evaluated, the numerical solutions at any time in the interval can be easily calculated. New formulae are derived for the polynomial coefficients,which are more practical and succinct than those previously given. Two structural dynamic equations are calculated by the proposed method. The numerical solutions are compared with the traditional fourth-order Runge-Kutta method. The results show that the method proposed is highly accurate and computationally efficient. In addition, an important advantage of the method is the simplicity in software programming.展开更多
In this paper the author has used the normalized Routh equations[1]to .solve the dynamic problems and establish the general method for. finding out the constraint forces and the variations of the state of motion for t...In this paper the author has used the normalized Routh equations[1]to .solve the dynamic problems and establish the general method for. finding out the constraint forces and the variations of the state of motion for the complicated system.展开更多
In this study,we construct a bi-level optimization model based on the Stackelberg game and propose a robust optimization algorithm for solving the bi-level model,assuming an actual situation with several participants ...In this study,we construct a bi-level optimization model based on the Stackelberg game and propose a robust optimization algorithm for solving the bi-level model,assuming an actual situation with several participants in energy trading.Firstly,the energy trading process is analyzed between each subject based on the establishment of the operation framework of multi-agent participation in energy trading.Secondly,the optimal operation model of each energy trading agent is established to develop a bi-level game model including each energy participant.Finally,a combination algorithm of improved robust optimization over time(ROOT)and CPLEX is proposed to solve the established game model.The experimental results indicate that under different fitness thresholds,the robust optimization results of the proposed algorithm are increased by 56.91%and 68.54%,respectively.The established bi-level game model effectively balances the benefits of different energy trading entities.The proposed algorithm proposed can increase the income of each participant in the game by an average of 8.59%.展开更多
A new scheme of time stepping for solving the dynamic viscoelastic problems are presented. By expanding variables at a discrete time interval, FEM based recurrent formulae are derived. A self-adaptive algorithm for di...A new scheme of time stepping for solving the dynamic viscoelastic problems are presented. By expanding variables at a discrete time interval, FEM based recurrent formulae are derived. A self-adaptive algorithm for different sizes of time steps can be carried out to improve computing accuracy. Numerical validation shows satisfactory performance.展开更多
Numerical error caused by“ghost forces”in a quasicontinuum method is studied in the context of dynamic problems.The error in the discrete W^(1,∞)norm is analyzed for the time scale O(ε)and the time scale O(1)with...Numerical error caused by“ghost forces”in a quasicontinuum method is studied in the context of dynamic problems.The error in the discrete W^(1,∞)norm is analyzed for the time scale O(ε)and the time scale O(1)withεbeing the lattice spacing.展开更多
The difficulty in solving stochastic dynamics problems lies in the need for a large number of repeated computations of deterministic dynamic equations,which has been a challenge in stochastic dynamics analysis and was...The difficulty in solving stochastic dynamics problems lies in the need for a large number of repeated computations of deterministic dynamic equations,which has been a challenge in stochastic dynamics analysis and was discussed in this study.To efficiently and accurately compute the exponential of the dynamics state matrix and the matrix functions due to external loads,an adaptively filtered precise integration method was proposed,which inherits the high precision of the precise integrationmethod,improves the computational efficiency and saves the memory required.Moreover,the perturbation method was introduced to avoid repeated computations of matrix exponential and terms due to external loads.Based on the filtering and perturbation techniques,an adaptively filtered precise integration method considering perturbation for stochastic dynamics problems was developed.Two numerical experiments,including a model of phononic crystal and a bridge model considering random parameters,were performed to test the performance of the proposed method in terms of accuracy and efficiency.Numerical results show that the accuracy and efficiency of the proposed method are better than those of the existing precise integration method,the Newmark-βmethod and the Wilson-θmethod.展开更多
In dynamic environments,it is important to track changing optimal solutions over time.Univariate marginal distribution algorithm（UMDA） which is a class algorithm of estimation of distribution algorithms attracts mor...In dynamic environments,it is important to track changing optimal solutions over time.Univariate marginal distribution algorithm（UMDA） which is a class algorithm of estimation of distribution algorithms attracts more and more attention in recent years.In this paper a new multi-population and diffusion UMDA（MDUMDA） is proposed for dynamic multimodal problems.The multi-population approach is used to locate multiple local optima which are useful to find the global optimal solution quickly to dynamic multimodal problems.The diffusion model is used to increase the diversity in a guided fashion,which makes the neighbor individuals of previous optimal solutions move gradually from the previous optimal solutions and enlarge the search space.This approach uses both the information of current population and the part history information of the optimal solutions.Finally experimental studies on the moving peaks benchmark are carried out to evaluate the proposed algorithm and compare the performance of MDUMDA and multi-population quantum swarm optimization（MQSO） from the literature.The experimental results show that the MDUMDA is effective for the function with moving optimum and can adapt to the dynamic environments rapidly.展开更多
We extended an improved version of the discrete particle swarm optimization (DPSO) algorithm proposed by Liao et al.(2007) to solve the dynamic facility layout problem (DFLP). A computational study was performed with ...We extended an improved version of the discrete particle swarm optimization (DPSO) algorithm proposed by Liao et al.(2007) to solve the dynamic facility layout problem (DFLP). A computational study was performed with the existing heuristic algorithms, including the dynamic programming (DP), genetic algorithm (GA), simulated annealing (SA), hybrid ant system (HAS), hybrid simulated annealing (SA-EG), hybrid genetic algorithms (NLGA and CONGA). The proposed DPSO algorithm, SA, HAS, GA, DP, SA-EG, NLGA, and CONGA obtained the best solutions for 33, 24, 20, 10, 12, 20, 5, and 2 of the 48 problems from (Balakrishnan and Cheng, 2000), respectively. These results show that the DPSO is very effective in dealing with the DFLP. The extended DPSO also has very good computational efficiency when the problem size increases.展开更多
Bifurcation of periodic solutions widely existed in nonlinear dynamical systems is a kind oftonstrained one in intrinsic quality because its amplitude is always non-negative Classification of the bifurcations with the...Bifurcation of periodic solutions widely existed in nonlinear dynamical systems is a kind oftonstrained one in intrinsic quality because its amplitude is always non-negative Classification of the bifurcations with the type of constraint was discussed. All its six types of transition sets are derived, in which three types are newly found and a method is proposed for analyzing the constrained bifurcation.展开更多
Based on the theory of Eider-Bernoulli beam and Winkler assumption for elastic foundation, a mathematical model is presented. By using Fourier transformation for space variable, Laplace transformation for time variabl...Based on the theory of Eider-Bernoulli beam and Winkler assumption for elastic foundation, a mathematical model is presented. By using Fourier transformation for space variable, Laplace transformation for time variable and convolution theorem for their inverse transformations, a general solution for dynamical problem of infinite beam on an elastic foundation is obtained. Finally, the cases of free vibration,impulsive response and moving load are also discussed.展开更多
This paper is intended to be a first step towards the continuous dependence of dynamical contact problems on the initial data as well as the uniqueness of a solution. Moreover,it provides the basis for a proof of the ...This paper is intended to be a first step towards the continuous dependence of dynamical contact problems on the initial data as well as the uniqueness of a solution. Moreover,it provides the basis for a proof of the convergence of popular time integration schemes as the Newmark method.We study a frictionless dynamical contact problem between both linearly elastic and viscoelastic bodies which is formulated via the Signorini contact conditions.For viscoelastic materials fulfilling the Kelvin-Voigt constitutive law,we find a characterization of the class of problems which satisfy a perturbation result in a non-trivial mix of norms in function space.This characterization is given in the form of a stability condition on the contact stresses at the contact boundaries.Furthermore,we present perturbation results for two well-established approximations of the classical Signorini condition:The Signorini condition formulated in velocities and the model of normal compliance,both satisfying even a sharper version of our stability condition.展开更多
The dynamic traveling salesman problem(DTSP)is significant in logistics distribution in real-world applications in smart cities,but it is uncertain and difficult to solve.This paper proposes a scheme library-based ant...The dynamic traveling salesman problem(DTSP)is significant in logistics distribution in real-world applications in smart cities,but it is uncertain and difficult to solve.This paper proposes a scheme library-based ant colony optimization(ACO)with a two-optimization(2-opt)strategy to solve the DTSP efficiently.The work is novel and contributes to three aspects:problemmodel,optimization framework,and algorithmdesign.Firstly,in the problem model,traditional DTSP models often consider the change of travel distance between two nodes over time,while this paper focuses on a special DTSP model in that the node locations change dynamically over time.Secondly,in the optimization framework,the ACO algorithm is carried out in an offline optimization and online application framework to efficiently reuse the historical information to help fast respond to the dynamic environment.The framework of offline optimization and online application is proposed due to the fact that the environmental change inDTSPis caused by the change of node location,and therefore the newenvironment is somehowsimilar to certain previous environments.This way,in the offline optimization,the solutions for possible environmental changes are optimized in advance,and are stored in a mode scheme library.In the online application,when an environmental change is detected,the candidate solutions stored in the mode scheme library are reused via ACO to improve search efficiency and reduce computational complexity.Thirdly,in the algorithm design,the ACO cooperates with the 2-opt strategy to enhance search efficiency.To evaluate the performance of ACO with 2-opt,we design two challenging DTSP cases with up to 200 and 1379 nodes and compare them with other ACO and genetic algorithms.The experimental results show that ACO with 2-opt can solve the DTSPs effectively.展开更多
In this paper, we study the initial-boundary value problem with rigid wall for the equations in combustion dynamics with largy parameter. Introducing variable scalar norms and two seminorms, making use of the vorticit...In this paper, we study the initial-boundary value problem with rigid wall for the equations in combustion dynamics with largy parameter. Introducing variable scalar norms and two seminorms, making use of the vorticity operator, overcome the difficulty from the large parameter. By energy estimation, the existence and unique theorems of local smooth solution is proved.展开更多
Dynamic optimization problems are a kind of optimization problems that involve changes over time. They pose a serious challenge to traditional optimization methods as well as conventional genetic algorithms since the ...Dynamic optimization problems are a kind of optimization problems that involve changes over time. They pose a serious challenge to traditional optimization methods as well as conventional genetic algorithms since the goal is no longer to search for the optimal solution（s） of a fixed problem but to track the moving optimum over time. Dynamic optimization problems have attracted a growing interest from the genetic algorithm community in recent years. Several approaches have been developed to enhance the performance of genetic algorithms in dynamic environments. One approach is to maintain the diversity of the population via random immigrants. This paper proposes a hybrid immigrants scheme that combines the concepts of elitism, dualism and random immigrants for genetic algorithms to address dynamic optimization problems. In this hybrid scheme, the best individual, i.e., the elite, from the previous generation and its dual individual are retrieved as the bases to create immigrants via traditional mutation scheme. These elitism-based and dualism-based immigrants together with some random immigrants are substituted into the current population, replacing the worst individuals in the population. These three kinds of immigrants aim to address environmental changes of slight, medium and significant degrees respectively and hence efficiently adapt genetic algorithms to dynamic environments that are subject to different severities of changes. Based on a series of systematically constructed dynamic test problems, experiments are carried out to investigate the performance of genetic algorithms with the hybrid immigrants scheme and traditional random immigrants scheme. Experimental results validate the efficiency of the proposed hybrid immigrants scheme for improving the performance of genetic algorithms in dynamic environments.展开更多
Traditionally, heuristic re-planning algorithms are used to tackle the problem of dynamic task planning for multiple satellites. However, the traditional heuristic strategies depend on the concrete tasks, which often ...Traditionally, heuristic re-planning algorithms are used to tackle the problem of dynamic task planning for multiple satellites. However, the traditional heuristic strategies depend on the concrete tasks, which often affect the result’s optimality. Noticing that the historical information of cooperative task planning will impact the latter planning results, we propose a hybrid learning algorithm for dynamic multi-satellite task planning, which is based on the multi-agent reinforcement learning of policy iteration and the transfer learning. The reinforcement learning strategy of each satellite is described with neural networks. The policy neural network individuals with the best topological structure and weights are found by applying co-evolutionary search iteratively. To avoid the failure of the historical learning caused by the randomly occurring observation requests, a novel approach is proposed to balance the quality and efficiency of the task planning, which converts the historical learning strategy to the current initial learning strategy by applying the transfer learning algorithm. The simulations and analysis show the feasibility and adaptability of the proposed approach especially for the situation with randomly occurring observation requests.展开更多
The paper deals with a development of the discrete-analytical method for the solution of the dynamical problems of a hollow sphere with inhomogeneous initial stresses.The examinations are made with respect to the prob...The paper deals with a development of the discrete-analytical method for the solution of the dynamical problems of a hollow sphere with inhomogeneous initial stresses.The examinations are made with respect to the problem on the natural vibration of the hollow sphere the initial stresses in which is caused by internal and external uniformly distributed pressure.The initial stresses in the sphere are determined within the scope of the exact equations of elastostatics.It is assumed that after appearing this static initial stresses the sphere gets a dynamical excitation and mechanical behavior of the sphere caused by this excitation is described with the so-called three-dimensional linearized equations of elastic wave propagation in initially stressed bodies.For the solution of these equations,which have variable coefficients,the discrete analytical solution method is developed and applied.In particular,it is established that the convergence of the numerical results with respect to the number of discretization is very acceptable and applicable for the considered type dynamical problems.Numerical results on the influence of the initial stresses on the values of the natural frequencies of the hollow sphere are also presented and these results are discussed.展开更多
A mesh-free method based on local Petrov-Galerkin formulation is presented to solve dynamic impact problems of hyperelastic material.In the present method,a simple Heaviside test function is chosen for simplifying dom...A mesh-free method based on local Petrov-Galerkin formulation is presented to solve dynamic impact problems of hyperelastic material.In the present method,a simple Heaviside test function is chosen for simplifying domain integrals.Trial function is constructed by using a radial basis function （RBF） coupled with a polynomial basis function,in which the shape function possesses the kronecker delta function property.So,additional treatment is not required for imposing essential boundary conditions.Governing equations of impact problems are established and solved node by node by using an explicit time integration algorithm in a local domain,which is very similar to that of the collocation method except that numerical integration can be implemented over local domain in the present method.Numerical results for several examples show that the present method performs well in dealing with the dynamic impact problem of hyperelastic material.展开更多
The dynamic weapon target assignment(DWTA)problem is of great significance in modern air combat.However,DWTA is a highly complex constrained multi-objective combinatorial optimization problem.An improved elitist non-d...The dynamic weapon target assignment(DWTA)problem is of great significance in modern air combat.However,DWTA is a highly complex constrained multi-objective combinatorial optimization problem.An improved elitist non-dominated sorting genetic algorithm-II(NSGA-II)called the non-dominated shuffled frog leaping algorithm(NSFLA)is proposed to maximize damage to enemy targets and minimize the self-threat in air combat constraints.In NSFLA,the shuffled frog leaping algorithm(SFLA)is introduced to NSGA-II to replace the inside evolutionary scheme of the genetic algorithm(GA),displaying low optimization speed and heterogeneous space search defects.Two improvements have also been raised to promote the internal optimization performance of SFLA.Firstly,the local evolution scheme,a novel crossover mechanism,ensures that each individual participates in updating instead of only the worst ones,which can expand the diversity of the population.Secondly,a discrete adaptive mutation algorithm based on the function change rate is applied to balance the global and local search.Finally,the scheme is verified in various air combat scenarios.The results show that the proposed NSFLA has apparent advantages in solution quality and efficiency,especially in many aircraft and the dynamic air combat environment.展开更多
This paper studics thc optimal pairs trading stratcgy of the mcan-variance(MV)objective function under a continuous-time cointegration model with a common stochastic factor.Although this common stochastic factor is no...This paper studics thc optimal pairs trading stratcgy of the mcan-variance(MV)objective function under a continuous-time cointegration model with a common stochastic factor.Although this common stochastic factor is not directly tradable,it significantly impacts asset prices.We first provide a semiclosed-form solution under a general model.We then specify the common factor model to be a mean-reverting process with time-varying parameters and provide closed-form optimal strategies for pairs trading with fixed and flexible ratios,respectively.Empirical analysis based on historical data from Chinese sccuritics markcts shows thc cffcctivencss of both optimal stratcgics.The optimal flcxiblc-ratio strategy outperforms the optimal fixed-ratio strategy in terms of both profit and risk.展开更多
This paper derives energy level formula for two moving charged particles with Coulomb coupling by making full use of two mutually conjugate entangled state representations. These newly introduced entangled state repre...This paper derives energy level formula for two moving charged particles with Coulomb coupling by making full use of two mutually conjugate entangled state representations. These newly introduced entangled state representations seem to provide a direct and convenient approach for solving certain dynamical problems for two-body systems.展开更多
基金Supported by Liu Hui Applied Mathematics Center of Nankai University-Tianjin University( No. H10124).
文摘In order to achieve highly accurate and efficient numerical calculations of structural dynamics, time collocation method is presented. For a given time interval, the numerical solution of the method is approximated by a polynomial. The polynomial coefficients are evaluated by solving algebraic equation. Once the polynomial coefficients are evaluated, the numerical solutions at any time in the interval can be easily calculated. New formulae are derived for the polynomial coefficients,which are more practical and succinct than those previously given. Two structural dynamic equations are calculated by the proposed method. The numerical solutions are compared with the traditional fourth-order Runge-Kutta method. The results show that the method proposed is highly accurate and computationally efficient. In addition, an important advantage of the method is the simplicity in software programming.
文摘In this paper the author has used the normalized Routh equations[1]to .solve the dynamic problems and establish the general method for. finding out the constraint forces and the variations of the state of motion for the complicated system.
基金supported by the National Nature Science Foundation of China(Nos.62063019)Natural Science Foundation of Gansu Province(22JR5RA241,2023CXZX-465).
文摘In this study,we construct a bi-level optimization model based on the Stackelberg game and propose a robust optimization algorithm for solving the bi-level model,assuming an actual situation with several participants in energy trading.Firstly,the energy trading process is analyzed between each subject based on the establishment of the operation framework of multi-agent participation in energy trading.Secondly,the optimal operation model of each energy trading agent is established to develop a bi-level game model including each energy participant.Finally,a combination algorithm of improved robust optimization over time(ROOT)and CPLEX is proposed to solve the established game model.The experimental results indicate that under different fitness thresholds,the robust optimization results of the proposed algorithm are increased by 56.91%and 68.54%,respectively.The established bi-level game model effectively balances the benefits of different energy trading entities.The proposed algorithm proposed can increase the income of each participant in the game by an average of 8.59%.
文摘A new scheme of time stepping for solving the dynamic viscoelastic problems are presented. By expanding variables at a discrete time interval, FEM based recurrent formulae are derived. A self-adaptive algorithm for different sizes of time steps can be carried out to improve computing accuracy. Numerical validation shows satisfactory performance.
文摘Numerical error caused by“ghost forces”in a quasicontinuum method is studied in the context of dynamic problems.The error in the discrete W^(1,∞)norm is analyzed for the time scale O(ε)and the time scale O(1)withεbeing the lattice spacing.
基金the support of the National Natural Science Foundation of China(Grant Nos.11472067 and 51609034)the Science Foundation of Liaoning Province of China(No.2021-MS-119)+1 种基金the Dalian Youth Science and Technology Star Project(No.2018RQ06)the Fundamental Research Funds for the Central Universities(Grant No.DUT20GJ216).
文摘The difficulty in solving stochastic dynamics problems lies in the need for a large number of repeated computations of deterministic dynamic equations,which has been a challenge in stochastic dynamics analysis and was discussed in this study.To efficiently and accurately compute the exponential of the dynamics state matrix and the matrix functions due to external loads,an adaptively filtered precise integration method was proposed,which inherits the high precision of the precise integrationmethod,improves the computational efficiency and saves the memory required.Moreover,the perturbation method was introduced to avoid repeated computations of matrix exponential and terms due to external loads.Based on the filtering and perturbation techniques,an adaptively filtered precise integration method considering perturbation for stochastic dynamics problems was developed.Two numerical experiments,including a model of phononic crystal and a bridge model considering random parameters,were performed to test the performance of the proposed method in terms of accuracy and efficiency.Numerical results show that the accuracy and efficiency of the proposed method are better than those of the existing precise integration method,the Newmark-βmethod and the Wilson-θmethod.
基金supported by the National Natural Science Foundation of China (6087309960775013)
文摘In dynamic environments,it is important to track changing optimal solutions over time.Univariate marginal distribution algorithm（UMDA） which is a class algorithm of estimation of distribution algorithms attracts more and more attention in recent years.In this paper a new multi-population and diffusion UMDA（MDUMDA） is proposed for dynamic multimodal problems.The multi-population approach is used to locate multiple local optima which are useful to find the global optimal solution quickly to dynamic multimodal problems.The diffusion model is used to increase the diversity in a guided fashion,which makes the neighbor individuals of previous optimal solutions move gradually from the previous optimal solutions and enlarge the search space.This approach uses both the information of current population and the part history information of the optimal solutions.Finally experimental studies on the moving peaks benchmark are carried out to evaluate the proposed algorithm and compare the performance of MDUMDA and multi-population quantum swarm optimization（MQSO） from the literature.The experimental results show that the MDUMDA is effective for the function with moving optimum and can adapt to the dynamic environments rapidly.
文摘We extended an improved version of the discrete particle swarm optimization (DPSO) algorithm proposed by Liao et al.(2007) to solve the dynamic facility layout problem (DFLP). A computational study was performed with the existing heuristic algorithms, including the dynamic programming (DP), genetic algorithm (GA), simulated annealing (SA), hybrid ant system (HAS), hybrid simulated annealing (SA-EG), hybrid genetic algorithms (NLGA and CONGA). The proposed DPSO algorithm, SA, HAS, GA, DP, SA-EG, NLGA, and CONGA obtained the best solutions for 33, 24, 20, 10, 12, 20, 5, and 2 of the 48 problems from (Balakrishnan and Cheng, 2000), respectively. These results show that the DPSO is very effective in dealing with the DFLP. The extended DPSO also has very good computational efficiency when the problem size increases.
文摘Bifurcation of periodic solutions widely existed in nonlinear dynamical systems is a kind oftonstrained one in intrinsic quality because its amplitude is always non-negative Classification of the bifurcations with the type of constraint was discussed. All its six types of transition sets are derived, in which three types are newly found and a method is proposed for analyzing the constrained bifurcation.
文摘Based on the theory of Eider-Bernoulli beam and Winkler assumption for elastic foundation, a mathematical model is presented. By using Fourier transformation for space variable, Laplace transformation for time variable and convolution theorem for their inverse transformations, a general solution for dynamical problem of infinite beam on an elastic foundation is obtained. Finally, the cases of free vibration,impulsive response and moving load are also discussed.
基金supported by the DFG Research Center MATHEON,"Mathematicsfor key technologies:Modelling,simulation,and optimization of real-world processes",Berlin
文摘This paper is intended to be a first step towards the continuous dependence of dynamical contact problems on the initial data as well as the uniqueness of a solution. Moreover,it provides the basis for a proof of the convergence of popular time integration schemes as the Newmark method.We study a frictionless dynamical contact problem between both linearly elastic and viscoelastic bodies which is formulated via the Signorini contact conditions.For viscoelastic materials fulfilling the Kelvin-Voigt constitutive law,we find a characterization of the class of problems which satisfy a perturbation result in a non-trivial mix of norms in function space.This characterization is given in the form of a stability condition on the contact stresses at the contact boundaries.Furthermore,we present perturbation results for two well-established approximations of the classical Signorini condition:The Signorini condition formulated in velocities and the model of normal compliance,both satisfying even a sharper version of our stability condition.
基金supported in part by the National Research Foundation of Korea (NRF-2021H1D3A2A01082705).
文摘The dynamic traveling salesman problem(DTSP)is significant in logistics distribution in real-world applications in smart cities,but it is uncertain and difficult to solve.This paper proposes a scheme library-based ant colony optimization(ACO)with a two-optimization(2-opt)strategy to solve the DTSP efficiently.The work is novel and contributes to three aspects:problemmodel,optimization framework,and algorithmdesign.Firstly,in the problem model,traditional DTSP models often consider the change of travel distance between two nodes over time,while this paper focuses on a special DTSP model in that the node locations change dynamically over time.Secondly,in the optimization framework,the ACO algorithm is carried out in an offline optimization and online application framework to efficiently reuse the historical information to help fast respond to the dynamic environment.The framework of offline optimization and online application is proposed due to the fact that the environmental change inDTSPis caused by the change of node location,and therefore the newenvironment is somehowsimilar to certain previous environments.This way,in the offline optimization,the solutions for possible environmental changes are optimized in advance,and are stored in a mode scheme library.In the online application,when an environmental change is detected,the candidate solutions stored in the mode scheme library are reused via ACO to improve search efficiency and reduce computational complexity.Thirdly,in the algorithm design,the ACO cooperates with the 2-opt strategy to enhance search efficiency.To evaluate the performance of ACO with 2-opt,we design two challenging DTSP cases with up to 200 and 1379 nodes and compare them with other ACO and genetic algorithms.The experimental results show that ACO with 2-opt can solve the DTSPs effectively.
文摘In this paper, we study the initial-boundary value problem with rigid wall for the equations in combustion dynamics with largy parameter. Introducing variable scalar norms and two seminorms, making use of the vorticity operator, overcome the difficulty from the large parameter. By energy estimation, the existence and unique theorems of local smooth solution is proved.
基金This work was supported by UK EPSRC(No.EP/E060722/01)Broil FAPESP(Proc.04/04289-6).
文摘Dynamic optimization problems are a kind of optimization problems that involve changes over time. They pose a serious challenge to traditional optimization methods as well as conventional genetic algorithms since the goal is no longer to search for the optimal solution（s） of a fixed problem but to track the moving optimum over time. Dynamic optimization problems have attracted a growing interest from the genetic algorithm community in recent years. Several approaches have been developed to enhance the performance of genetic algorithms in dynamic environments. One approach is to maintain the diversity of the population via random immigrants. This paper proposes a hybrid immigrants scheme that combines the concepts of elitism, dualism and random immigrants for genetic algorithms to address dynamic optimization problems. In this hybrid scheme, the best individual, i.e., the elite, from the previous generation and its dual individual are retrieved as the bases to create immigrants via traditional mutation scheme. These elitism-based and dualism-based immigrants together with some random immigrants are substituted into the current population, replacing the worst individuals in the population. These three kinds of immigrants aim to address environmental changes of slight, medium and significant degrees respectively and hence efficiently adapt genetic algorithms to dynamic environments that are subject to different severities of changes. Based on a series of systematically constructed dynamic test problems, experiments are carried out to investigate the performance of genetic algorithms with the hybrid immigrants scheme and traditional random immigrants scheme. Experimental results validate the efficiency of the proposed hybrid immigrants scheme for improving the performance of genetic algorithms in dynamic environments.
文摘Traditionally, heuristic re-planning algorithms are used to tackle the problem of dynamic task planning for multiple satellites. However, the traditional heuristic strategies depend on the concrete tasks, which often affect the result’s optimality. Noticing that the historical information of cooperative task planning will impact the latter planning results, we propose a hybrid learning algorithm for dynamic multi-satellite task planning, which is based on the multi-agent reinforcement learning of policy iteration and the transfer learning. The reinforcement learning strategy of each satellite is described with neural networks. The policy neural network individuals with the best topological structure and weights are found by applying co-evolutionary search iteratively. To avoid the failure of the historical learning caused by the randomly occurring observation requests, a novel approach is proposed to balance the quality and efficiency of the task planning, which converts the historical learning strategy to the current initial learning strategy by applying the transfer learning algorithm. The simulations and analysis show the feasibility and adaptability of the proposed approach especially for the situation with randomly occurring observation requests.
文摘The paper deals with a development of the discrete-analytical method for the solution of the dynamical problems of a hollow sphere with inhomogeneous initial stresses.The examinations are made with respect to the problem on the natural vibration of the hollow sphere the initial stresses in which is caused by internal and external uniformly distributed pressure.The initial stresses in the sphere are determined within the scope of the exact equations of elastostatics.It is assumed that after appearing this static initial stresses the sphere gets a dynamical excitation and mechanical behavior of the sphere caused by this excitation is described with the so-called three-dimensional linearized equations of elastic wave propagation in initially stressed bodies.For the solution of these equations,which have variable coefficients,the discrete analytical solution method is developed and applied.In particular,it is established that the convergence of the numerical results with respect to the number of discretization is very acceptable and applicable for the considered type dynamical problems.Numerical results on the influence of the initial stresses on the values of the natural frequencies of the hollow sphere are also presented and these results are discussed.
基金supported by the National Natural Science Foundation of China(No.10902038)
文摘A mesh-free method based on local Petrov-Galerkin formulation is presented to solve dynamic impact problems of hyperelastic material.In the present method,a simple Heaviside test function is chosen for simplifying domain integrals.Trial function is constructed by using a radial basis function （RBF） coupled with a polynomial basis function,in which the shape function possesses the kronecker delta function property.So,additional treatment is not required for imposing essential boundary conditions.Governing equations of impact problems are established and solved node by node by using an explicit time integration algorithm in a local domain,which is very similar to that of the collocation method except that numerical integration can be implemented over local domain in the present method.Numerical results for several examples show that the present method performs well in dealing with the dynamic impact problem of hyperelastic material.
基金supported by the National Natural Science Foundation of China(61673209,71971115)。
文摘The dynamic weapon target assignment(DWTA)problem is of great significance in modern air combat.However,DWTA is a highly complex constrained multi-objective combinatorial optimization problem.An improved elitist non-dominated sorting genetic algorithm-II(NSGA-II)called the non-dominated shuffled frog leaping algorithm(NSFLA)is proposed to maximize damage to enemy targets and minimize the self-threat in air combat constraints.In NSFLA,the shuffled frog leaping algorithm(SFLA)is introduced to NSGA-II to replace the inside evolutionary scheme of the genetic algorithm(GA),displaying low optimization speed and heterogeneous space search defects.Two improvements have also been raised to promote the internal optimization performance of SFLA.Firstly,the local evolution scheme,a novel crossover mechanism,ensures that each individual participates in updating instead of only the worst ones,which can expand the diversity of the population.Secondly,a discrete adaptive mutation algorithm based on the function change rate is applied to balance the global and local search.Finally,the scheme is verified in various air combat scenarios.The results show that the proposed NSFLA has apparent advantages in solution quality and efficiency,especially in many aircraft and the dynamic air combat environment.
文摘This paper studics thc optimal pairs trading stratcgy of the mcan-variance(MV)objective function under a continuous-time cointegration model with a common stochastic factor.Although this common stochastic factor is not directly tradable,it significantly impacts asset prices.We first provide a semiclosed-form solution under a general model.We then specify the common factor model to be a mean-reverting process with time-varying parameters and provide closed-form optimal strategies for pairs trading with fixed and flexible ratios,respectively.Empirical analysis based on historical data from Chinese sccuritics markcts shows thc cffcctivencss of both optimal stratcgics.The optimal flcxiblc-ratio strategy outperforms the optimal fixed-ratio strategy in terms of both profit and risk.
基金Project supported by the Natural Science Foundation of Shandong Province of China (Grant No. Y2008A23)the Natural Science Foundation of Liaocheng University (Grant No. X071049)
文摘This paper derives energy level formula for two moving charged particles with Coulomb coupling by making full use of two mutually conjugate entangled state representations. These newly introduced entangled state representations seem to provide a direct and convenient approach for solving certain dynamical problems for two-body systems.
