As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initiall...As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initially proposed by Jiang et al.(Computational and Applied Mathematics,2021,40:174),through the utilization of a convex combination technique.And this improvement allows for an adaptive search direction by integrating a newly constructed spectral gradient-type restart strategy.Then,we develop a new spectral CGM by employing an inexact line search to determine the step size.With the application of the weak Wolfe line search,we establish the sufficient descent property of the proposed search direction.Moreover,under general assumptions,including the employment of the strong Wolfe line search for step size calculation,we demonstrate the global convergence of our new algorithm.Finally,the given unconstrained optimization test results show that the new algorithm is effective.展开更多
The degree of numerical linear independence is proposed and discussed. Based on this linear independence theory, a modified limited memory BFGS method is deve loped. Similar to the standard limited memory method, thi...The degree of numerical linear independence is proposed and discussed. Based on this linear independence theory, a modified limited memory BFGS method is deve loped. Similar to the standard limited memory method, this new method determines the new update by applying the updating formula m times to an initial positive diagonal matrix using the m previous pairs of the change in iteration and gradient. Besides the most recent pair of the change, which guarantees the quadratic termination, the choice of the other ( m -1) pairs of the change in the new method is dependent on the degree of numerical linear independence of previous search directions. In addition, the numerical linear independence theory is further discussed and the computation of the degree of linear independence is simplified. Theoretical and numerical results show that this new modified method improves efficiently the standard limited memory method.展开更多
Blending is an important unit operation in process industry. Blending scheduling is nonlinear optimiza- tion problem with constraints. It is difficult to obtain optimum solution by other general optimization methods. ...Blending is an important unit operation in process industry. Blending scheduling is nonlinear optimiza- tion problem with constraints. It is difficult to obtain optimum solution by other general optimization methods. Particle swarm optimization (PSO) algorithm is developed for nonlinear optimization problems with both contin- uous and discrete variables. In order to obtain a global optimum solution quickly, PSO algorithm is applied to solve the problem of blending scheduling under uncertainty. The calculation results based on an example of gasoline blending agree satisfactory with the ideal values, which illustrates that the PSO algorithm is valid and effective in solving the blending scheduling problem.展开更多
A methodology for topology optimization based on element independent nodal density(EIND) is developed.Nodal densities are implemented as the design variables and interpolated onto element space to determine the densit...A methodology for topology optimization based on element independent nodal density(EIND) is developed.Nodal densities are implemented as the design variables and interpolated onto element space to determine the density of any point with Shepard interpolation function.The influence of the diameter of interpolation is discussed which shows good robustness.The new approach is demonstrated on the minimum volume problem subjected to a displacement constraint.The rational approximation for material properties(RAMP) method and a dual programming optimization algorithm are used to penalize the intermediate density point to achieve nearly 0-1 solutions.Solutions are shown to meet stability,mesh dependence or non-checkerboard patterns of topology optimization without additional constraints.Finally,the computational efficiency is greatly improved by multithread parallel computing with OpenMP.展开更多
The application of multiple UAVs in complicated tasks has been widely explored in recent years.Due to the advantages of flexibility,cheapness and consistence,the performance of heterogeneous multi-UAVs with proper coo...The application of multiple UAVs in complicated tasks has been widely explored in recent years.Due to the advantages of flexibility,cheapness and consistence,the performance of heterogeneous multi-UAVs with proper cooperative task allocation is superior to over the single UAV.Accordingly,several constraints should be satisfied to realize the efficient cooperation,such as special time-window,variant equipment,specified execution sequence.Hence,a proper task allocation in UAVs is the crucial point for the final success.The task allocation problem of the heterogeneous UAVs can be formulated as a multi-objective optimization problem coupled with the UAV dynamics.To this end,a multi-layer encoding strategy and a constraint scheduling method are designed to handle the critical logical and physical constraints.In addition,four optimization objectives:completion time,target reward,UAV damage,and total range,are introduced to evaluate various allocation plans.Subsequently,to efficiently solve the multi-objective optimization problem,an improved multi-objective quantum-behaved particle swarm optimization(IMOQPSO)algorithm is proposed.During this algorithm,a modified solution evaluation method is designed to guide algorithmic evolution;both the convergence and distribution of particles are considered comprehensively;and boundary solutions which may produce some special allocation plans are preserved.Moreover,adaptive parameter control and mixed update mechanism are also introduced in this algorithm.Finally,both the proposed model and algorithm are verified by simulation experiments.展开更多
In this paper a hybrid algorithm which combines the pattern search method and the genetic algorithm for unconstrained optimization is presented. The algorithm is a deterministic pattern search algorithm,but in the sea...In this paper a hybrid algorithm which combines the pattern search method and the genetic algorithm for unconstrained optimization is presented. The algorithm is a deterministic pattern search algorithm,but in the search step of pattern search algorithm,the trial points are produced by a way like the genetic algorithm. At each iterate, by reduplication,crossover and mutation, a finite set of points can be used. In theory,the algorithm is globally convergent. The most stir is the numerical results showing that it can find the global minimizer for some problems ,which other pattern search algorithms don＇t bear.展开更多
A projected skill is adopted by use of the differential evolution (DE) algorithm to calculate a conditional nonlinear optimal perturbation (CNOP). The CNOP is the maximal value of a constrained optimization problem wi...A projected skill is adopted by use of the differential evolution (DE) algorithm to calculate a conditional nonlinear optimal perturbation (CNOP). The CNOP is the maximal value of a constrained optimization problem with a constraint condition, such as a ball constraint. The success of the DE algorithm lies in its ability to handle a non-differentiable and nonlinear cost function. In this study, the DE algorithm and the traditional optimization algorithms used to obtain the CNOPs are compared by analyzing a theoretical grassland ecosystem model and a dynamic global vegetation model. This study shows that the CNOPs generated by the DE algorithm are similar to those by the sequential quadratic programming (SQP) algorithm and the spectral projected gradients (SPG2) algorithm. If the cost function is non-differentiable, the CNOPs could also be caught with the DE algorithm. The numerical results suggest the DE algorithm can be employed to calculate the CNOP, especially when the cost function is non-differentiable.展开更多
High-speed vehicle dynamic envelope curve is defined as the maximum limit outline affected by a variety of adverse factors while the train is running. Considering the difficulties in the current measurement system suc...High-speed vehicle dynamic envelope curve is defined as the maximum limit outline affected by a variety of adverse factors while the train is running. Considering the difficulties in the current measurement system such as complicated calibration process,cumbersome aided-instruments,strict limitation of working distance, this paper carries out an optical method in which two high-speed cameras with variable-zoom lenses are adopted as binocular stereo sensors of measurement system and a high-ac-curacy 3D target with fast reconstruction is designed. The intrinsic parameters of the sensors and the relative positions between coordinate systems are solved by the method of colinearity constrained optimization algorithm. The calibration process is easy to operate and the device is also of portability. Most importantly, the severe working distance limitation between sensors and measured body is solved, enhancing the adaptability of measurement system to environment. Experimental results show that when the sensors are in the range of 8 -16 m away from the measured body, system accuracy can reach up to ±0. 5 mm, which meets the requirements to measure the dynamic envelope curve of high-speed vehicle.展开更多
In order to facilitate solution, a complex problem is normally decomposed into many small sub-problems during product development process. Teams are formed to resolve each sub-problem. The original problem is resolved...In order to facilitate solution, a complex problem is normally decomposed into many small sub-problems during product development process. Teams are formed to resolve each sub-problem. The original problem is resolved from solutions of sub-problems. Ideally, sub-problems are not only mutually independent but also inherent parameters of original problem. Solution of original problem can be directly derived from the collection of solutions from simplified sub-problems. In practice, the degree of interdependency is indeed reduced, sub-problems are neither totally independent nor all inherent parameters of original problem. This paper discusses team coordination under this condition and design solution from each team, which not only satisfies total requirements but also is an optimal one. The suggested optimized constraint decomposition method will insure workable Pareto solution.展开更多
In recent years, sinmlated annealing algo-rithms have been extensively developed and uti-lized to solve nmlti-objective optimization problems. In order to obtain better optimization perfonmnce, this paper proposes a N...In recent years, sinmlated annealing algo-rithms have been extensively developed and uti-lized to solve nmlti-objective optimization problems. In order to obtain better optimization perfonmnce, this paper proposes a Novel Adaptive Simulated Annealing （NASA） algorithm for constrained multi-objective optimization based on Archived Multi-objective Simulated Annealing （AMOSA）. For han-dling multi-objective, NASA makes improverrents in three aspects： sub-iteration search, sub-archive and adaptive search, which effectively strengthen the stability and efficiency of the algorithnm For handling constraints, NASA introduces corresponding solution acceptance criterion. Furtherrrore, NASA has also been applied to optimize TD-LTE network perform-ance by adjusting antenna paranleters; it can achieve better extension and convergence than AMOSA, NS-GAII and MOPSO. Analytical studies and simulations indicate that the proposed NASA algorithm can play an important role in improving multi-objective optimi-zation performance.展开更多
This study proposes an efficient indirect approach for general nonlinear dynamic optimization problems without path constraints. The approach incorporates the virtues both from indirect and direct methods: it solves t...This study proposes an efficient indirect approach for general nonlinear dynamic optimization problems without path constraints. The approach incorporates the virtues both from indirect and direct methods: it solves the optimality conditions like the traditional indirect methods do, but uses a discretization technique inspired from direct methods. Compared with other indirect approaches, the proposed approach has two main advantages: (1) the discretized optimization problem only employs unconstrained nonlinear programming (NLP) algorithms such as BFGS (Broyden-Fletcher-Goldfarb-Shanno), rather than constrained NLP algorithms, therefore the computational efficiency is increased; (2) the relationship between the number of the discretized time intervals and the integration error of the four-step Adams predictor-corrector algorithm is established, thus the minimal number of time intervals that under desired integration tolerance can be estimated. The classic batch reactor problem is tested and compared in detail with literature reports, and the results reveal the effectiveness of the proposed approach. Dealing with path constraints requires extra techniques, and will be studied in the second paper.展开更多
A discrete optimization problem for minimizing the sum of fabrication cost and steel material cost of sf^el frames under constraints based on Japanese seismic code is set up. Enhancements of the genetic algorithm for ...A discrete optimization problem for minimizing the sum of fabrication cost and steel material cost of sf^el frames under constraints based on Japanese seismic code is set up. Enhancements of the genetic algorithm for the above-mentioned problem are proposed, which are combined with a 1D （one-dimensional） search or a 2D （two-dimensional） search. After the proposed methods are described, they are applied to a five-story frame. A comparison with an exact solution obtained by a revised enumeration algorithm demonstrates the effectiveness of the proposed methods.展开更多
基金supported by the National Natural Science Foundation of China(No.72071202)the Key Laboratory of Mathematics and Engineering Applications,Ministry of Education。
文摘As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initially proposed by Jiang et al.(Computational and Applied Mathematics,2021,40:174),through the utilization of a convex combination technique.And this improvement allows for an adaptive search direction by integrating a newly constructed spectral gradient-type restart strategy.Then,we develop a new spectral CGM by employing an inexact line search to determine the step size.With the application of the weak Wolfe line search,we establish the sufficient descent property of the proposed search direction.Moreover,under general assumptions,including the employment of the strong Wolfe line search for step size calculation,we demonstrate the global convergence of our new algorithm.Finally,the given unconstrained optimization test results show that the new algorithm is effective.
文摘The degree of numerical linear independence is proposed and discussed. Based on this linear independence theory, a modified limited memory BFGS method is deve loped. Similar to the standard limited memory method, this new method determines the new update by applying the updating formula m times to an initial positive diagonal matrix using the m previous pairs of the change in iteration and gradient. Besides the most recent pair of the change, which guarantees the quadratic termination, the choice of the other ( m -1) pairs of the change in the new method is dependent on the degree of numerical linear independence of previous search directions. In addition, the numerical linear independence theory is further discussed and the computation of the degree of linear independence is simplified. Theoretical and numerical results show that this new modified method improves efficiently the standard limited memory method.
基金Supported by the National 863 Project (No. 2003AA412010) and the National 973 Program of China (No. 2002CB312201)
文摘Blending is an important unit operation in process industry. Blending scheduling is nonlinear optimiza- tion problem with constraints. It is difficult to obtain optimum solution by other general optimization methods. Particle swarm optimization (PSO) algorithm is developed for nonlinear optimization problems with both contin- uous and discrete variables. In order to obtain a global optimum solution quickly, PSO algorithm is applied to solve the problem of blending scheduling under uncertainty. The calculation results based on an example of gasoline blending agree satisfactory with the ideal values, which illustrates that the PSO algorithm is valid and effective in solving the blending scheduling problem.
基金Projects(11372055,11302033)supported by the National Natural Science Foundation of ChinaProject supported by the Huxiang Scholar Foundation from Changsha University of Science and Technology,ChinaProject(2012KFJJ02)supported by the Key Labortory of Lightweight and Reliability Technology for Engineering Velicle,Education Department of Hunan Province,China
文摘A methodology for topology optimization based on element independent nodal density(EIND) is developed.Nodal densities are implemented as the design variables and interpolated onto element space to determine the density of any point with Shepard interpolation function.The influence of the diameter of interpolation is discussed which shows good robustness.The new approach is demonstrated on the minimum volume problem subjected to a displacement constraint.The rational approximation for material properties(RAMP) method and a dual programming optimization algorithm are used to penalize the intermediate density point to achieve nearly 0-1 solutions.Solutions are shown to meet stability,mesh dependence or non-checkerboard patterns of topology optimization without additional constraints.Finally,the computational efficiency is greatly improved by multithread parallel computing with OpenMP.
基金Project(61801495)supported by the National Natural Science Foundation of China
文摘The application of multiple UAVs in complicated tasks has been widely explored in recent years.Due to the advantages of flexibility,cheapness and consistence,the performance of heterogeneous multi-UAVs with proper cooperative task allocation is superior to over the single UAV.Accordingly,several constraints should be satisfied to realize the efficient cooperation,such as special time-window,variant equipment,specified execution sequence.Hence,a proper task allocation in UAVs is the crucial point for the final success.The task allocation problem of the heterogeneous UAVs can be formulated as a multi-objective optimization problem coupled with the UAV dynamics.To this end,a multi-layer encoding strategy and a constraint scheduling method are designed to handle the critical logical and physical constraints.In addition,four optimization objectives:completion time,target reward,UAV damage,and total range,are introduced to evaluate various allocation plans.Subsequently,to efficiently solve the multi-objective optimization problem,an improved multi-objective quantum-behaved particle swarm optimization(IMOQPSO)algorithm is proposed.During this algorithm,a modified solution evaluation method is designed to guide algorithmic evolution;both the convergence and distribution of particles are considered comprehensively;and boundary solutions which may produce some special allocation plans are preserved.Moreover,adaptive parameter control and mixed update mechanism are also introduced in this algorithm.Finally,both the proposed model and algorithm are verified by simulation experiments.
文摘In this paper a hybrid algorithm which combines the pattern search method and the genetic algorithm for unconstrained optimization is presented. The algorithm is a deterministic pattern search algorithm,but in the search step of pattern search algorithm,the trial points are produced by a way like the genetic algorithm. At each iterate, by reduplication,crossover and mutation, a finite set of points can be used. In theory,the algorithm is globally convergent. The most stir is the numerical results showing that it can find the global minimizer for some problems ,which other pattern search algorithms don＇t bear.
基金provided by grants from the National Basic Research Program of China (Grant No. 2006CB400503)LASG Free Exploration Fund+1 种基金LASG State Key Laboratory Special Fundthe KZCX3-SW-230 of the Chinese Academy of Sciences
文摘A projected skill is adopted by use of the differential evolution (DE) algorithm to calculate a conditional nonlinear optimal perturbation (CNOP). The CNOP is the maximal value of a constrained optimization problem with a constraint condition, such as a ball constraint. The success of the DE algorithm lies in its ability to handle a non-differentiable and nonlinear cost function. In this study, the DE algorithm and the traditional optimization algorithms used to obtain the CNOPs are compared by analyzing a theoretical grassland ecosystem model and a dynamic global vegetation model. This study shows that the CNOPs generated by the DE algorithm are similar to those by the sequential quadratic programming (SQP) algorithm and the spectral projected gradients (SPG2) algorithm. If the cost function is non-differentiable, the CNOPs could also be caught with the DE algorithm. The numerical results suggest the DE algorithm can be employed to calculate the CNOP, especially when the cost function is non-differentiable.
基金National Science and Technology Major Project(No.2016ZX04003001)
文摘High-speed vehicle dynamic envelope curve is defined as the maximum limit outline affected by a variety of adverse factors while the train is running. Considering the difficulties in the current measurement system such as complicated calibration process,cumbersome aided-instruments,strict limitation of working distance, this paper carries out an optical method in which two high-speed cameras with variable-zoom lenses are adopted as binocular stereo sensors of measurement system and a high-ac-curacy 3D target with fast reconstruction is designed. The intrinsic parameters of the sensors and the relative positions between coordinate systems are solved by the method of colinearity constrained optimization algorithm. The calibration process is easy to operate and the device is also of portability. Most importantly, the severe working distance limitation between sensors and measured body is solved, enhancing the adaptability of measurement system to environment. Experimental results show that when the sensors are in the range of 8 -16 m away from the measured body, system accuracy can reach up to ±0. 5 mm, which meets the requirements to measure the dynamic envelope curve of high-speed vehicle.
基金Supportedby 86 3/CIMS (No .2 0 0 1AA4 1114 0 )andtheNationalNaturalScienceFoundationofChina (No .6 0 10 4 0 0 8)
文摘In order to facilitate solution, a complex problem is normally decomposed into many small sub-problems during product development process. Teams are formed to resolve each sub-problem. The original problem is resolved from solutions of sub-problems. Ideally, sub-problems are not only mutually independent but also inherent parameters of original problem. Solution of original problem can be directly derived from the collection of solutions from simplified sub-problems. In practice, the degree of interdependency is indeed reduced, sub-problems are neither totally independent nor all inherent parameters of original problem. This paper discusses team coordination under this condition and design solution from each team, which not only satisfies total requirements but also is an optimal one. The suggested optimized constraint decomposition method will insure workable Pareto solution.
基金supported by the Major National Science & Technology Specific Project of China under Grants No.2010ZX03002-007-02,No.2009ZX03002-002,No.2010ZX03002-002-03
文摘In recent years, sinmlated annealing algo-rithms have been extensively developed and uti-lized to solve nmlti-objective optimization problems. In order to obtain better optimization perfonmnce, this paper proposes a Novel Adaptive Simulated Annealing （NASA） algorithm for constrained multi-objective optimization based on Archived Multi-objective Simulated Annealing （AMOSA）. For han-dling multi-objective, NASA makes improverrents in three aspects： sub-iteration search, sub-archive and adaptive search, which effectively strengthen the stability and efficiency of the algorithnm For handling constraints, NASA introduces corresponding solution acceptance criterion. Furtherrrore, NASA has also been applied to optimize TD-LTE network perform-ance by adjusting antenna paranleters; it can achieve better extension and convergence than AMOSA, NS-GAII and MOPSO. Analytical studies and simulations indicate that the proposed NASA algorithm can play an important role in improving multi-objective optimi-zation performance.
基金Supported by the National Natural Science Foundation of China (U1162130)the National High Technology Research and Development Program of China (2006AA05Z226)the Outstanding Youth Science Foundation,Zhejiang Province (R4100133)
文摘This study proposes an efficient indirect approach for general nonlinear dynamic optimization problems without path constraints. The approach incorporates the virtues both from indirect and direct methods: it solves the optimality conditions like the traditional indirect methods do, but uses a discretization technique inspired from direct methods. Compared with other indirect approaches, the proposed approach has two main advantages: (1) the discretized optimization problem only employs unconstrained nonlinear programming (NLP) algorithms such as BFGS (Broyden-Fletcher-Goldfarb-Shanno), rather than constrained NLP algorithms, therefore the computational efficiency is increased; (2) the relationship between the number of the discretized time intervals and the integration error of the four-step Adams predictor-corrector algorithm is established, thus the minimal number of time intervals that under desired integration tolerance can be estimated. The classic batch reactor problem is tested and compared in detail with literature reports, and the results reveal the effectiveness of the proposed approach. Dealing with path constraints requires extra techniques, and will be studied in the second paper.
文摘A discrete optimization problem for minimizing the sum of fabrication cost and steel material cost of sf^el frames under constraints based on Japanese seismic code is set up. Enhancements of the genetic algorithm for the above-mentioned problem are proposed, which are combined with a 1D （one-dimensional） search or a 2D （two-dimensional） search. After the proposed methods are described, they are applied to a five-story frame. A comparison with an exact solution obtained by a revised enumeration algorithm demonstrates the effectiveness of the proposed methods.
