Based on the uncertainty theory, this paper is devoted to the redundancy allocation problem in repairable parallel-series systems with uncertain factors, where the failure rate, repair rate and other relative coeffici...Based on the uncertainty theory, this paper is devoted to the redundancy allocation problem in repairable parallel-series systems with uncertain factors, where the failure rate, repair rate and other relative coefficients involved are considered as uncertain variables. The availability of the system and the corresponding designing cost are considered as two optimization objectives. A crisp multiobjective optimization formulation is presented on the basis of uncertainty theory to solve this resultant problem. For solving this problem efficiently, a new multiobjective artificial bee colony algorithm is proposed to search the Pareto efficient set, which introduces rank value and crowding distance in the greedy selection strategy, applies fast non-dominated sort procedure in the exploitation search and inserts tournament selection in the onlooker bee phase. It shows that the proposed algorithm outperforms NSGA-II greatly and can solve multiobjective redundancy allocation problem efficiently. Finally, a numerical example is provided to illustrate this approach.展开更多
E-commerce, as an emerging marketing mode, has attracted more and more attention and gradually changed the way of our life. However, the existing layout of distribution centers can't fulfill the storage and picking d...E-commerce, as an emerging marketing mode, has attracted more and more attention and gradually changed the way of our life. However, the existing layout of distribution centers can't fulfill the storage and picking demands of e-commerce sufficiently. In this paper, a modified miniload automated storageetrieval system is designed to fit these new characteristics of e-commerce in logistics. Meanwhile, a matching problem, concerning with the improvement of picking efficiency in new system, is studied in this paper. The problem is how to reduce the travelling distance of totes between aisles and picking stations. A multi-stage heuristic algorithm is proposed based on statement and model of this problem. The main idea of this algorithm is, with some heuristic strategies based on similarity coefficients, minimizing the transportations of items which can not arrive in the destination picking stations just through direct conveyors. The experimental results based on the cases generated by computers show that the average reduced rate of indirect transport times can reach 14.36% with the application of multi-stage heuristic algorithm. For the cases from a real e-commerce distribution center, the order processing time can be reduced from 11.20 h to 10.06 h with the help of the modified system and the proposed algorithm. In summary, this research proposed a modified system and a multi-stage heuristic algorithm that can reduce the travelling distance of totes effectively and improve the whole performance of e-commerce distribution center.展开更多
An improved genetic algorithm(IGA) based on a novel selection strategy to handle nonlinear programming problems is proposed.Each individual in selection process is represented as a three-dimensional feature vector w...An improved genetic algorithm(IGA) based on a novel selection strategy to handle nonlinear programming problems is proposed.Each individual in selection process is represented as a three-dimensional feature vector which is composed of objective function value,the degree of constraints violations and the number of constraints violations.It is easy to distinguish excellent individuals from general individuals by using an individuals' feature vector.Additionally,a local search(LS) process is incorporated into selection operation so as to find feasible solutions located in the neighboring areas of some infeasible solutions.The combination of IGA and LS should offer the advantage of both the quality of solutions and diversity of solutions.Experimental results over a set of benchmark problems demonstrate that IGA has better performance than other algorithms.展开更多
An integer linear bilevel programming problem is firstly transformed into a binary linear bilevel programming problem, and then converted into a single-level binary implicit programming. An orthogonal genetic algorith...An integer linear bilevel programming problem is firstly transformed into a binary linear bilevel programming problem, and then converted into a single-level binary implicit programming. An orthogonal genetic algorithm is developed for solving the binary linear implicit programming problem based on the orthogonal design. The orthogonal design with the factor analysis, an experimental design method is applied to the genetic algorithm to make the algorithm more robust, statistical y sound and quickly convergent. A crossover operator formed by the orthogonal array and the factor analysis is presented. First, this crossover operator can generate a smal but representative sample of points as offspring. After al of the better genes of these offspring are selected, a best combination among these offspring is then generated. The simulation results show the effectiveness of the proposed algorithm.展开更多
A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker(KKT) conditions.To cope with the complementarity constraints,a binary encod...A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker(KKT) conditions.To cope with the complementarity constraints,a binary encoding scheme is adopted for KKT multipliers,and then the complementarity slackness problem is simplified to successive quadratic programming problems,which can be solved by many algorithms available.Based on 0-1 binary encoding,an orthogonal genetic algorithm,in which the orthogonal experimental design with both two-level orthogonal array and factor analysis is used as crossover operator,is proposed.Numerical experiments on 10 benchmark examples show that the orthogonal genetic algorithm can find global optimal solutions of quadratic bilevel programming problems with high accuracy in a small number of iterations.展开更多
Three dimensional frictional contact problems are formulated as linear complementarity problems based on the parametric variational principle. Two aggregate-functionbased algorithms for solving complementarity problem...Three dimensional frictional contact problems are formulated as linear complementarity problems based on the parametric variational principle. Two aggregate-functionbased algorithms for solving complementarity problems are proposed. One is called the self-adjusting interior point algorithm, the other is called the aggregate function smoothing algorithm. Numerical experiment shows the efficiency of the proposed two algorithms.展开更多
In order to overcome the shortcoming of the classical Hungarian algorithm that it can only solve the problems where the total cost is the sum of that of each job, an improved Hungarian algorithm is proposed and used t...In order to overcome the shortcoming of the classical Hungarian algorithm that it can only solve the problems where the total cost is the sum of that of each job, an improved Hungarian algorithm is proposed and used to solve the assignment problem of serial-parallel systems. First of all, by replacing parallel jobs with virtual jobs, the proposed algorithm converts the serial-parallel system into a pure serial system, where the classical Hungarian algorithm can be used to generate a temporal assignment plan via optimization. Afterwards, the assignment plan is validated by checking whether the virtual jobs can be realized by real jobs through local searching. If the assignment plan is not valid, the converted system will be adapted by adjusting the parameters of virtual jobs, and then be optimized again. Through iterative searching, the valid optimal assignment plan can eventually be obtained.To evaluate the proposed algorithm, the valid optimal assignment plan is applied to labor allocation of a manufacturing system which is a typical serial-parallel system.展开更多
A modified sequential linear programming algorithm is presented, whose subproblem is always solvable, for the extended linear complementarity problem (XLCP), the global convergence of the algorithm under assumption of...A modified sequential linear programming algorithm is presented, whose subproblem is always solvable, for the extended linear complementarity problem (XLCP), the global convergence of the algorithm under assumption of X-row sufficiency or X-colunm monotonicity is proved. As a result, a sufficient condition for existence and boundedness of solution to the XLCP are obtained.展开更多
A novel genetic algorithm with multiple species in dynamic region is proposed,each of which occupies a dynamic region determined by the weight vector of a fuzzy adaptive Hamming neural network. Through learning and cl...A novel genetic algorithm with multiple species in dynamic region is proposed,each of which occupies a dynamic region determined by the weight vector of a fuzzy adaptive Hamming neural network. Through learning and classification of genetic individuals in the evolutionary procedure,the neural network distributes multiple species into different regions of the search space. Furthermore,the neural network dynamically expands each search region or establishes new region for good offspring individuals to continuously keep the diversification of the genetic population. As a result,the premature problem inherent in genetic algorithm is alleviated and better tradeoff between the ability of exploration and exploitation can be obtained. The experimental results on the vehicle routing problem with time windows also show the good performance of the proposed genetic algorithm.展开更多
To solve single-objective constrained optimization problems,a new population-based evolutionary algorithm with elite strategy(PEAES) is proposed with the concept of single and multi-objective optimization.Constrained ...To solve single-objective constrained optimization problems,a new population-based evolutionary algorithm with elite strategy(PEAES) is proposed with the concept of single and multi-objective optimization.Constrained functions are combined to be an objective function.During the evolutionary process,the current optimal solution is found and treated as the reference point to divide the population into three sub-populations:one feasible and two infeasible ones.Different evolutionary operations of single or multi-objective optimization are respectively performed in each sub-population with elite strategy.Thirteen famous benchmark functions are selected to evaluate the performance of PEAES in comparison of other three optimization methods.The results show the proposed method is valid in efficiency,precision and probability for solving single-objective constrained optimization problems.展开更多
A precedence order is defined based on the release dates of jobs' direct successors. Using the defined precedence order and Heap Sort, a new polynomial algorithm is provided which aims to solve the parallel schedulin...A precedence order is defined based on the release dates of jobs' direct successors. Using the defined precedence order and Heap Sort, a new polynomial algorithm is provided which aims to solve the parallel scheduling problem P|pj = 1, r j, outtree| ∑Cj Cj. The new algorithm is shown to be more compact and easier to implement.展开更多
Capacitated vehicle routing problem (CVRP) is an important combinatorial optimization problem. However, it is quite difficult to achieve an optimal solution with the traditional optimization methods owing to the high ...Capacitated vehicle routing problem (CVRP) is an important combinatorial optimization problem. However, it is quite difficult to achieve an optimal solution with the traditional optimization methods owing to the high computational complexity. A hybrid algorithm was developed to solve the problem, in which an artificial immune clonal algorithm (AICA) makes use of the global search ability to search the optimal results and simulated annealing (SA) algorithm employs certain probability to avoid becoming trapped in a local optimum. The results obtained from the computational study show that the proposed algorithm is a feasible and effective method for capacitated vehicle routing problem.展开更多
Travelling Salesman Problem(TSP) is a classical optimization problem and it is one of a class of NP-Problem.The purposes of this work is to apply data mining methodologies to explore the patterns in data generated by ...Travelling Salesman Problem(TSP) is a classical optimization problem and it is one of a class of NP-Problem.The purposes of this work is to apply data mining methodologies to explore the patterns in data generated by an Ant Colony Algorithm(ACA) performing a searching operation and to develop a rule set searcher which approximates the ACA′s searcher.An attribute-oriented induction methodology was used to explore the relationship between an operations′ sequence and its attributes and a set of rules has been developed.At the end of this paper,the experimental results have shown that the proposed approach has good performance with respect to the quality of solution and the speed of computation.展开更多
A new iterative method,which is called positive interior-point algorithm,is presented for solving the nonlinear complementarity problems.This method is of the desirable feature of robustness.And the convergence theore...A new iterative method,which is called positive interior-point algorithm,is presented for solving the nonlinear complementarity problems.This method is of the desirable feature of robustness.And the convergence theorems of the algorithm is established.In addition,some numerical results are reported.展开更多
By modeling direct transient heat conduction problems via finite element method (FEM) and precise integral algorithm, a new approach is presented to solve transient inverse heat conduction problems with multi-variable...By modeling direct transient heat conduction problems via finite element method (FEM) and precise integral algorithm, a new approach is presented to solve transient inverse heat conduction problems with multi-variables. Firstly, the spatial space and temporal domain are discretized by FEM and precise integral algorithm respectively. Then, the high accuracy semi-analytical solution of direct problem can be got. Finally, based on the solution, the computing model of inverse problem and expression of sensitivity analysis are established. Single variable and variables combined identifications including thermal parameters, boundary conditions and source-related terms etc. are given to validate the approach proposed in 1-D and 2-D cases. The effects of noise data and initial guess on the results are investigated. The numerical examples show the effectiveness of this approach.展开更多
The paper combines a self-adaptive precise algorithm in the time domain with Meshless Element Free Galerkin Method (EFGM) for solving viscoelastic problems with rotationally periodic symmetry. By expanding variables...The paper combines a self-adaptive precise algorithm in the time domain with Meshless Element Free Galerkin Method (EFGM) for solving viscoelastic problems with rotationally periodic symmetry. By expanding variables at a discretized time interval, the variations of variables can be described more precisely, and iteration is not required for non-linear cases. A space-time domain coupled problem with initial and boundary values can be converted into a series of linear recursive boundary value problems, which are solved by a group theory based on EFGM. It has been proved that the coefficient matrix of the global EFG equation for a rotationally periodic system is block-circulant so long as a kind of symmetry-adapted reference coordinate system is adopted, and then a partitioning algorithm for facilitating parallel processing was proposed via a completely orthogonal group transformation. Therefore instead of solving the original system, only a series of independent small sub-problems need to be solved, leading to computational convenience and a higher computing efficiency. Numerical examples are given to illustrate the full advantages of the proposed algorithm.展开更多
Based on Arnoldi's method, a version of generalized Arnoldi algorithm has been developed for the reduction of gyroscopic eigenvalue problems. By utilizing the skew symmetry of system matrix, a very simple recurren...Based on Arnoldi's method, a version of generalized Arnoldi algorithm has been developed for the reduction of gyroscopic eigenvalue problems. By utilizing the skew symmetry of system matrix, a very simple recurrence scheme, named gyroscopic Arnoldi reduction algorithm has been obtained, which is even simpler than the Lanczos algorithm for symmetric eigenvalue problems. The complex number computation is completely avoided. A restart technique is used to enable the reduction algorithm to have iterative characteristics. It has been found that the restart technique is not only effective for the convergence of multiple eigenvalues but it also furnishes the reduction algorithm with a technique to check and compute missed eigenvalues. By combining it with the restart technique, the algorithm is made practical for large-scale gyroscopic eigenvalue problems. Numerical examples are given to demonstrate the effectiveness of the method proposed.展开更多
An improved Guo Tao algorithm (IGT algorithm) is proposed for solving complicated dynamic function optimization problems, and a function optimization benchmark problem with constrained condition and two dynamic para...An improved Guo Tao algorithm (IGT algorithm) is proposed for solving complicated dynamic function optimization problems, and a function optimization benchmark problem with constrained condition and two dynamic parameters has been designed. The results achieved by IGT algorithm have been compared with the results from the Guo Tao algorithm (GT algorithm). It is shown that the new algorithm (IGT algorithm) provides better results. This preliminarily demonstrates the efficiency of the new algorithm in complicated dynamic environments.展开更多
In this paper,a novel location inventory routing(LIR)model is proposed to solve cold chain logistics network problem under uncertain demand environment. The goal of the developed model is to optimize costs of location...In this paper,a novel location inventory routing(LIR)model is proposed to solve cold chain logistics network problem under uncertain demand environment. The goal of the developed model is to optimize costs of location,inventory and transportation.Due to the complex of LIR problem( LIRP), a multi-objective genetic algorithm(GA), non-dominated sorting in genetic algorithm Ⅱ( NSGA-Ⅱ) has been introduced. Its performance is tested over a real case for the proposed problems. Results indicate that NSGA-Ⅱ provides a competitive performance than GA,which demonstrates that the proposed model and multi-objective GA are considerably efficient to solve the problem.展开更多
An extended crowding genetic algorithm (ECGA) is introduced for solvingoptimal pump configuration problem, which was presented by T. Westerlund in 1994. This problem hasbeen found to be non-convex, and the objective f...An extended crowding genetic algorithm (ECGA) is introduced for solvingoptimal pump configuration problem, which was presented by T. Westerlund in 1994. This problem hasbeen found to be non-convex, and the objective function contained several local optima and globaloptimality could not be ensured by all the traditional MINLP optimization method. The concepts ofspecies conserving and composite encoding are introduced to crowding genetic algorithm (CGA) formaintain the diversity of population more effectively and coping with the continuous and/or discretevariables in MINLP problem. The solution of three-levels pump configuration got from DICOPT++software (OA algorithm) is also given. By comparing with the solutions obtained from DICOPT++, ECPmethod, and MIN-MIN method, the ECGA algorithm proved to be very effective in finding the globaloptimal solution of multi-levels pump configuration via using the problem-specific information.展开更多
基金supported by National Natural Science Foundation of China (No. 71171199)Natural Science Foundation of Shaanxi Province of China (No. 2013JM1003)
摘要Based on the uncertainty theory, this paper is devoted to the redundancy allocation problem in repairable parallel-series systems with uncertain factors, where the failure rate, repair rate and other relative coefficients involved are considered as uncertain variables. The availability of the system and the corresponding designing cost are considered as two optimization objectives. A crisp multiobjective optimization formulation is presented on the basis of uncertainty theory to solve this resultant problem. For solving this problem efficiently, a new multiobjective artificial bee colony algorithm is proposed to search the Pareto efficient set, which introduces rank value and crowding distance in the greedy selection strategy, applies fast non-dominated sort procedure in the exploitation search and inserts tournament selection in the onlooker bee phase. It shows that the proposed algorithm outperforms NSGA-II greatly and can solve multiobjective redundancy allocation problem efficiently. Finally, a numerical example is provided to illustrate this approach.
摘要E-commerce, as an emerging marketing mode, has attracted more and more attention and gradually changed the way of our life. However, the existing layout of distribution centers can't fulfill the storage and picking demands of e-commerce sufficiently. In this paper, a modified miniload automated storageetrieval system is designed to fit these new characteristics of e-commerce in logistics. Meanwhile, a matching problem, concerning with the improvement of picking efficiency in new system, is studied in this paper. The problem is how to reduce the travelling distance of totes between aisles and picking stations. A multi-stage heuristic algorithm is proposed based on statement and model of this problem. The main idea of this algorithm is, with some heuristic strategies based on similarity coefficients, minimizing the transportations of items which can not arrive in the destination picking stations just through direct conveyors. The experimental results based on the cases generated by computers show that the average reduced rate of indirect transport times can reach 14.36% with the application of multi-stage heuristic algorithm. For the cases from a real e-commerce distribution center, the order processing time can be reduced from 11.20 h to 10.06 h with the help of the modified system and the proposed algorithm. In summary, this research proposed a modified system and a multi-stage heuristic algorithm that can reduce the travelling distance of totes effectively and improve the whole performance of e-commerce distribution center.
基金supported by the National Natural Science Foundation of China (60632050)National Basic Research Program of Jiangsu Province University (08KJB520003)
摘要An improved genetic algorithm(IGA) based on a novel selection strategy to handle nonlinear programming problems is proposed.Each individual in selection process is represented as a three-dimensional feature vector which is composed of objective function value,the degree of constraints violations and the number of constraints violations.It is easy to distinguish excellent individuals from general individuals by using an individuals' feature vector.Additionally,a local search(LS) process is incorporated into selection operation so as to find feasible solutions located in the neighboring areas of some infeasible solutions.The combination of IGA and LS should offer the advantage of both the quality of solutions and diversity of solutions.Experimental results over a set of benchmark problems demonstrate that IGA has better performance than other algorithms.
基金supported by the Fundamental Research Funds for the Central Universities(K50511700004)the Natural Science Basic Research Plan in Shaanxi Province of China(2013JM1022)
摘要An integer linear bilevel programming problem is firstly transformed into a binary linear bilevel programming problem, and then converted into a single-level binary implicit programming. An orthogonal genetic algorithm is developed for solving the binary linear implicit programming problem based on the orthogonal design. The orthogonal design with the factor analysis, an experimental design method is applied to the genetic algorithm to make the algorithm more robust, statistical y sound and quickly convergent. A crossover operator formed by the orthogonal array and the factor analysis is presented. First, this crossover operator can generate a smal but representative sample of points as offspring. After al of the better genes of these offspring are selected, a best combination among these offspring is then generated. The simulation results show the effectiveness of the proposed algorithm.
基金supported by the National Natural Science Foundation of China (60873099)
摘要A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker(KKT) conditions.To cope with the complementarity constraints,a binary encoding scheme is adopted for KKT multipliers,and then the complementarity slackness problem is simplified to successive quadratic programming problems,which can be solved by many algorithms available.Based on 0-1 binary encoding,an orthogonal genetic algorithm,in which the orthogonal experimental design with both two-level orthogonal array and factor analysis is used as crossover operator,is proposed.Numerical experiments on 10 benchmark examples show that the orthogonal genetic algorithm can find global optimal solutions of quadratic bilevel programming problems with high accuracy in a small number of iterations.
基金The project supported by the National Natural Science foundation of china(10225212,50178016.10302007)the National Kev Basic Research Special Foundation and the Ministry of Education of China
摘要Three dimensional frictional contact problems are formulated as linear complementarity problems based on the parametric variational principle. Two aggregate-functionbased algorithms for solving complementarity problems are proposed. One is called the self-adjusting interior point algorithm, the other is called the aggregate function smoothing algorithm. Numerical experiment shows the efficiency of the proposed two algorithms.
摘要In order to overcome the shortcoming of the classical Hungarian algorithm that it can only solve the problems where the total cost is the sum of that of each job, an improved Hungarian algorithm is proposed and used to solve the assignment problem of serial-parallel systems. First of all, by replacing parallel jobs with virtual jobs, the proposed algorithm converts the serial-parallel system into a pure serial system, where the classical Hungarian algorithm can be used to generate a temporal assignment plan via optimization. Afterwards, the assignment plan is validated by checking whether the virtual jobs can be realized by real jobs through local searching. If the assignment plan is not valid, the converted system will be adapted by adjusting the parameters of virtual jobs, and then be optimized again. Through iterative searching, the valid optimal assignment plan can eventually be obtained.To evaluate the proposed algorithm, the valid optimal assignment plan is applied to labor allocation of a manufacturing system which is a typical serial-parallel system.
摘要A modified sequential linear programming algorithm is presented, whose subproblem is always solvable, for the extended linear complementarity problem (XLCP), the global convergence of the algorithm under assumption of X-row sufficiency or X-colunm monotonicity is proved. As a result, a sufficient condition for existence and boundedness of solution to the XLCP are obtained.
摘要A novel genetic algorithm with multiple species in dynamic region is proposed,each of which occupies a dynamic region determined by the weight vector of a fuzzy adaptive Hamming neural network. Through learning and classification of genetic individuals in the evolutionary procedure,the neural network distributes multiple species into different regions of the search space. Furthermore,the neural network dynamically expands each search region or establishes new region for good offspring individuals to continuously keep the diversification of the genetic population. As a result,the premature problem inherent in genetic algorithm is alleviated and better tradeoff between the ability of exploration and exploitation can be obtained. The experimental results on the vehicle routing problem with time windows also show the good performance of the proposed genetic algorithm.
摘要To solve single-objective constrained optimization problems,a new population-based evolutionary algorithm with elite strategy(PEAES) is proposed with the concept of single and multi-objective optimization.Constrained functions are combined to be an objective function.During the evolutionary process,the current optimal solution is found and treated as the reference point to divide the population into three sub-populations:one feasible and two infeasible ones.Different evolutionary operations of single or multi-objective optimization are respectively performed in each sub-population with elite strategy.Thirteen famous benchmark functions are selected to evaluate the performance of PEAES in comparison of other three optimization methods.The results show the proposed method is valid in efficiency,precision and probability for solving single-objective constrained optimization problems.
基金This work was supported by the National Natural Science Foundation of China(No.60474023)Science and Technology Key Project Fund of theMinistry of Education(No.03184)the Major State Basic Research Development Program of China(No.2002CB312200).
摘要A precedence order is defined based on the release dates of jobs' direct successors. Using the defined precedence order and Heap Sort, a new polynomial algorithm is provided which aims to solve the parallel scheduling problem P|pj = 1, r j, outtree| ∑Cj Cj. The new algorithm is shown to be more compact and easier to implement.
摘要Capacitated vehicle routing problem (CVRP) is an important combinatorial optimization problem. However, it is quite difficult to achieve an optimal solution with the traditional optimization methods owing to the high computational complexity. A hybrid algorithm was developed to solve the problem, in which an artificial immune clonal algorithm (AICA) makes use of the global search ability to search the optimal results and simulated annealing (SA) algorithm employs certain probability to avoid becoming trapped in a local optimum. The results obtained from the computational study show that the proposed algorithm is a feasible and effective method for capacitated vehicle routing problem.
摘要Travelling Salesman Problem(TSP) is a classical optimization problem and it is one of a class of NP-Problem.The purposes of this work is to apply data mining methodologies to explore the patterns in data generated by an Ant Colony Algorithm(ACA) performing a searching operation and to develop a rule set searcher which approximates the ACA′s searcher.An attribute-oriented induction methodology was used to explore the relationship between an operations′ sequence and its attributes and a set of rules has been developed.At the end of this paper,the experimental results have shown that the proposed approach has good performance with respect to the quality of solution and the speed of computation.
摘要A new iterative method,which is called positive interior-point algorithm,is presented for solving the nonlinear complementarity problems.This method is of the desirable feature of robustness.And the convergence theorems of the algorithm is established.In addition,some numerical results are reported.
摘要By modeling direct transient heat conduction problems via finite element method (FEM) and precise integral algorithm, a new approach is presented to solve transient inverse heat conduction problems with multi-variables. Firstly, the spatial space and temporal domain are discretized by FEM and precise integral algorithm respectively. Then, the high accuracy semi-analytical solution of direct problem can be got. Finally, based on the solution, the computing model of inverse problem and expression of sensitivity analysis are established. Single variable and variables combined identifications including thermal parameters, boundary conditions and source-related terms etc. are given to validate the approach proposed in 1-D and 2-D cases. The effects of noise data and initial guess on the results are investigated. The numerical examples show the effectiveness of this approach.
基金The project supported by the National Natural Science Foundation of China (10421002. 10472019 and 10172024) NKBRSF (2005CB321704) and the Fund of Disciplines Leaders of Young and Middle Age Faculty in Colleges of Liaoning Province. The English text was polished by Yunming Chen.
摘要The paper combines a self-adaptive precise algorithm in the time domain with Meshless Element Free Galerkin Method (EFGM) for solving viscoelastic problems with rotationally periodic symmetry. By expanding variables at a discretized time interval, the variations of variables can be described more precisely, and iteration is not required for non-linear cases. A space-time domain coupled problem with initial and boundary values can be converted into a series of linear recursive boundary value problems, which are solved by a group theory based on EFGM. It has been proved that the coefficient matrix of the global EFG equation for a rotationally periodic system is block-circulant so long as a kind of symmetry-adapted reference coordinate system is adopted, and then a partitioning algorithm for facilitating parallel processing was proposed via a completely orthogonal group transformation. Therefore instead of solving the original system, only a series of independent small sub-problems need to be solved, leading to computational convenience and a higher computing efficiency. Numerical examples are given to illustrate the full advantages of the proposed algorithm.
基金This research is supported by The National Science FoundationThe Doctoral Training Foundation
摘要Based on Arnoldi's method, a version of generalized Arnoldi algorithm has been developed for the reduction of gyroscopic eigenvalue problems. By utilizing the skew symmetry of system matrix, a very simple recurrence scheme, named gyroscopic Arnoldi reduction algorithm has been obtained, which is even simpler than the Lanczos algorithm for symmetric eigenvalue problems. The complex number computation is completely avoided. A restart technique is used to enable the reduction algorithm to have iterative characteristics. It has been found that the restart technique is not only effective for the convergence of multiple eigenvalues but it also furnishes the reduction algorithm with a technique to check and compute missed eigenvalues. By combining it with the restart technique, the algorithm is made practical for large-scale gyroscopic eigenvalue problems. Numerical examples are given to demonstrate the effectiveness of the method proposed.
基金Supported by the National Natural Science Foundation of China(60473081,60133010)
摘要An improved Guo Tao algorithm (IGT algorithm) is proposed for solving complicated dynamic function optimization problems, and a function optimization benchmark problem with constrained condition and two dynamic parameters has been designed. The results achieved by IGT algorithm have been compared with the results from the Guo Tao algorithm (GT algorithm). It is shown that the new algorithm (IGT algorithm) provides better results. This preliminarily demonstrates the efficiency of the new algorithm in complicated dynamic environments.
基金Natural Science Foundation of Shanghai,China(No.15ZR1401600)the Fundamental Research Funds for the Central Universities,China(No.CUSF-DH-D-2015096)
摘要In this paper,a novel location inventory routing(LIR)model is proposed to solve cold chain logistics network problem under uncertain demand environment. The goal of the developed model is to optimize costs of location,inventory and transportation.Due to the complex of LIR problem( LIRP), a multi-objective genetic algorithm(GA), non-dominated sorting in genetic algorithm Ⅱ( NSGA-Ⅱ) has been introduced. Its performance is tested over a real case for the proposed problems. Results indicate that NSGA-Ⅱ provides a competitive performance than GA,which demonstrates that the proposed model and multi-objective GA are considerably efficient to solve the problem.
基金This project is supported by Provincial Science Foundation of Hebei (No.01213553).
摘要An extended crowding genetic algorithm (ECGA) is introduced for solvingoptimal pump configuration problem, which was presented by T. Westerlund in 1994. This problem hasbeen found to be non-convex, and the objective function contained several local optima and globaloptimality could not be ensured by all the traditional MINLP optimization method. The concepts ofspecies conserving and composite encoding are introduced to crowding genetic algorithm (CGA) formaintain the diversity of population more effectively and coping with the continuous and/or discretevariables in MINLP problem. The solution of three-levels pump configuration got from DICOPT++software (OA algorithm) is also given. By comparing with the solutions obtained from DICOPT++, ECPmethod, and MIN-MIN method, the ECGA algorithm proved to be very effective in finding the globaloptimal solution of multi-levels pump configuration via using the problem-specific information.