With the expression theorem of convex polyhedron, this paper gives the general expression for the solutions in standard linear programming problems. And the calculation procedures in determining the optimal solutions ...With the expression theorem of convex polyhedron, this paper gives the general expression for the solutions in standard linear programming problems. And the calculation procedures in determining the optimal solutions are also given.展开更多
Co-ordination of directional over current relays(DOCR) requires the selection and setting of relays so as to sequentially isolate only that portion of the power system where an abnormality has occurred.The problem of ...Co-ordination of directional over current relays(DOCR) requires the selection and setting of relays so as to sequentially isolate only that portion of the power system where an abnormality has occurred.The problem of coordinating protective relays in electrical power systems consists of selecting suitable settings such that their fundamental protective function is met,given operational requirements of sensitivity,selectivity,reliability and speed.Directional over current relays are best suited for protection of an interconnected sub-station transmission system.One of the major problems associated with this type of protection is the difficulty in coordinating relays.To insure proper coordination,all the main/back up relay pairs must be determined.This paper presents an effective algorithm to determine the minimum number of break points and main/back up relay pairs using relative sequence matrix(RSM).A novel optimization technique based on evolutionary programming was developed using these main/back up relay pairs for directional over current relay coordination in multi-loop networks.Since the problem has multi-optimum points,conventional mathematics based optimization techniques may sometimes fail.Hence evolutionary programming(EP) was used,as it is a stochastic multi-point search optimization algorithm capable of escaping from the local optimum problem,giving a better chance of reaching a global optimum.The method developed was tested on an existing 6 bus,7 line system and better results were obtained than with conventional methods.展开更多
A novel chaotic search method is proposed,and a hybrid algorithm combining particle swarm optimization(PSO) with this new method,called CLSPSO,is put forward to solve 14 integer and mixed integer programming problems....A novel chaotic search method is proposed,and a hybrid algorithm combining particle swarm optimization(PSO) with this new method,called CLSPSO,is put forward to solve 14 integer and mixed integer programming problems.The performances of CLSPSO are compared with those of other five hybrid algorithms combining PSO with chaotic search methods.Experimental results indicate that in terms of robustness and final convergence speed,CLSPSO is better than other five algorithms in solving many of these problems.Furthermore,CLSPSO exhibits good performance in solving two high-dimensional problems,and it finds better solutions than the known ones.A performance index(PI) is introduced to fairly compare the above six algorithms,and the obtained values of(PI) in three cases demonstrate that CLSPSO is superior to all the other five algorithms under the same conditions.展开更多
Considering the decision-making variables of the capacities of branch roads and the optimization targets of lowering the saturation of arterial roads and the reconstruction expense of branch roads, the bi-level progra...Considering the decision-making variables of the capacities of branch roads and the optimization targets of lowering the saturation of arterial roads and the reconstruction expense of branch roads, the bi-level programming model for reconstructing the branch roads was set up. The upper level model was for determining the enlarged capacities of the branch roads, and the lower level model was for calculating the flows of road sections via the user equilibrium traffic assignment method. The genetic algorithm for solving the bi-level model was designed to obtain the reconstruction capacities of the branch roads. The results show that by the bi-level model and its algorithm, the optimum scheme of urban branch roads reconstruction can be gained, which reduces the saturation of arterial roads apparently, and alleviates traffic congestion. In the data analysis the arterial saturation decreases from 1.100 to 0.996, which verifies the micro-circulation transportation's function of urban branch road network.展开更多
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
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
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
The problem of stochastically allocating redundant com- ponents to increase the system lifetime is an important topic of reliability. An optimal redundancy allocation is proposed, which maximizes the expected lifetime...The problem of stochastically allocating redundant com- ponents to increase the system lifetime is an important topic of reliability. An optimal redundancy allocation is proposed, which maximizes the expected lifetime of a reliability system with sub- systems consisting of components in parallel. The constraints are minimizing the total resources and the sizes of subsystems. In this system, each switching is independent with each other and works with probability p. Two optimization problems are studied by an incremental algorithm and dynamic programming technique respectively. The incremental algorithm proposed could obtain an approximate optimal solution, and the dynamic programming method could generate the optimal solution,展开更多
Software testing is a very important phase of the software development process. It is a very difficult job for a software manager to allocate optimally the financial budget to a software project during testing. In thi...Software testing is a very important phase of the software development process. It is a very difficult job for a software manager to allocate optimally the financial budget to a software project during testing. In this paper the problem of optimal allocation of the software testing cost is studied. There exist several models focused on the development of software costs measuring the number of software errors remaining in the software during testing. The purpose of this paper is to use these models to formulate the optimization problems of resource allocation: Minimization of the total number of software errors remaining in the system. On the assumption that a software project consists of some independent modules, the presented approach extends previous work by defining new goal functions and extending the primary assumption and precondition.展开更多
In order to slove the large-scale nonlinear programming （NLP） problems efficiently, an efficient optimization algorithm based on reduced sequential quadratic programming （rSQP） and automatic differentiation （AD）...In order to slove the large-scale nonlinear programming （NLP） problems efficiently, an efficient optimization algorithm based on reduced sequential quadratic programming （rSQP） and automatic differentiation （AD） is presented in this paper. With the characteristics of sparseness, relatively low degrees of freedom and equality constraints utilized, the nonlinear programming problem is solved by improved rSQP solver. In the solving process, AD technology is used to obtain accurate gradient information. The numerical results show that the combined algorithm, which is suitable for large-scale process optimization problems, can calculate more efficiently than rSQP itself.展开更多
This paper studies the optimal policy for joint control of admission, routing, service, and jockeying in a queueing system consisting of two exponential servers in parallel.Jobs arrive according to a Poisson process.U...This paper studies the optimal policy for joint control of admission, routing, service, and jockeying in a queueing system consisting of two exponential servers in parallel.Jobs arrive according to a Poisson process.Upon each arrival, an admission/routing decision is made, and the accepted job is routed to one of the two servers with each being associated with a queue.After each service completion, the servers have an option of serving a job from its own queue, serving a jockeying job from another queue, or staying idle.The system performance is inclusive of the revenues from accepted jobs, the costs of holding jobs in queues, the service costs and the job jockeying costs.To maximize the total expected discounted return, we formulate a Markov decision process(MDP) model for this system.The value iteration method is employed to characterize the optimal policy as a hedging point policy.Numerical studies verify the structure of the hedging point policy which is convenient for implementing control actions in practice.展开更多
基金Supported by National High Technology Research and Development Program of China （863 Program） （2006AA04Z183）, National Nat- ural Science Foundation of China （60621001, 60534010, 60572070, 60774048, 60728307）, and the Program for Changjiang Scholars and Innovative Research Groups of China （60728307, 4031002）
文摘With the expression theorem of convex polyhedron, this paper gives the general expression for the solutions in standard linear programming problems. And the calculation procedures in determining the optimal solutions are also given.
文摘Co-ordination of directional over current relays(DOCR) requires the selection and setting of relays so as to sequentially isolate only that portion of the power system where an abnormality has occurred.The problem of coordinating protective relays in electrical power systems consists of selecting suitable settings such that their fundamental protective function is met,given operational requirements of sensitivity,selectivity,reliability and speed.Directional over current relays are best suited for protection of an interconnected sub-station transmission system.One of the major problems associated with this type of protection is the difficulty in coordinating relays.To insure proper coordination,all the main/back up relay pairs must be determined.This paper presents an effective algorithm to determine the minimum number of break points and main/back up relay pairs using relative sequence matrix(RSM).A novel optimization technique based on evolutionary programming was developed using these main/back up relay pairs for directional over current relay coordination in multi-loop networks.Since the problem has multi-optimum points,conventional mathematics based optimization techniques may sometimes fail.Hence evolutionary programming(EP) was used,as it is a stochastic multi-point search optimization algorithm capable of escaping from the local optimum problem,giving a better chance of reaching a global optimum.The method developed was tested on an existing 6 bus,7 line system and better results were obtained than with conventional methods.
基金Projects(50275150,61173052) supported by the National Natural Science Foundation of ChinaProject(14FJ3112) supported by the Planned Science and Technology of Hunan Province,ChinaProject(14B033) supported by Scientific Research Fund Education Department of Hunan Province,China
文摘A novel chaotic search method is proposed,and a hybrid algorithm combining particle swarm optimization(PSO) with this new method,called CLSPSO,is put forward to solve 14 integer and mixed integer programming problems.The performances of CLSPSO are compared with those of other five hybrid algorithms combining PSO with chaotic search methods.Experimental results indicate that in terms of robustness and final convergence speed,CLSPSO is better than other five algorithms in solving many of these problems.Furthermore,CLSPSO exhibits good performance in solving two high-dimensional problems,and it finds better solutions than the known ones.A performance index(PI) is introduced to fairly compare the above six algorithms,and the obtained values of(PI) in three cases demonstrate that CLSPSO is superior to all the other five algorithms under the same conditions.
基金Project(2006CB705507) supported by the National Basic Research and Development Program of ChinaProject(20060533036) supported by the Specialized Research Foundation for the Doctoral Program of Higher Education of China
文摘Considering the decision-making variables of the capacities of branch roads and the optimization targets of lowering the saturation of arterial roads and the reconstruction expense of branch roads, the bi-level programming model for reconstructing the branch roads was set up. The upper level model was for determining the enlarged capacities of the branch roads, and the lower level model was for calculating the flows of road sections via the user equilibrium traffic assignment method. The genetic algorithm for solving the bi-level model was designed to obtain the reconstruction capacities of the branch roads. The results show that by the bi-level model and its algorithm, the optimum scheme of urban branch roads reconstruction can be gained, which reduces the saturation of arterial roads apparently, and alleviates traffic congestion. In the data analysis the arterial saturation decreases from 1.100 to 0.996, which verifies the micro-circulation transportation's function of urban branch road network.
基金supported by the Fundamental Research Funds for the Central Universities(K50511700004)the Natural Science Basic Research Plan in Shaanxi Province of China(2013JM1022)
文摘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 (60632050)National Basic Research Program of Jiangsu Province University (08KJB520003)
文摘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 National Natural Science Foundation of China (60873099)
文摘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Supported by National Natural Science Foundation of China （61304079, 61125306, 61034002）, the Open Research Project from SKLMCCS （20120106）, the Fundamental Research Funds for the Central Universities （FRF-TP-13-018A）, and the China Postdoctoral Science. Foundation （201_3M_ 5305_27）_ _ _
文摘为有致动器浸透和未知动力学的分离时间的系统的一个班的一个新奇最佳的追踪控制方法在这份报纸被建议。计划基于反复的适应动态编程(自动数据处理) 算法。以便实现控制计划，一个 data-based 标识符首先为未知系统动力学被构造。由介绍 M 网络，稳定的控制的明确的公式被完成。以便消除致动器浸透的效果， nonquadratic 表演功能被介绍，然后一个反复的自动数据处理算法被建立与集中分析完成最佳的追踪控制解决方案。为实现最佳的控制方法，神经网络被用来建立 data-based 标识符，计算性能索引功能，近似最佳的控制政策并且分别地解决稳定的控制。模拟例子被提供验证介绍最佳的追踪的控制计划的有效性。
基金supported by the National Natural Science Foundation of China(7117217271101158+3 种基金71272058)the Program for New Century Excellent Talents in University(NCET-10-0043)the Key Project Cultivation Fund of the Scientific and Technical Innovation Program of Beijing Institute of Technology(2011CX01001)the Special Fund of International Science and Technology Cooperation Program of Beijing Institute of Technology(GZ2014215101)
文摘The problem of stochastically allocating redundant com- ponents to increase the system lifetime is an important topic of reliability. An optimal redundancy allocation is proposed, which maximizes the expected lifetime of a reliability system with sub- systems consisting of components in parallel. The constraints are minimizing the total resources and the sizes of subsystems. In this system, each switching is independent with each other and works with probability p. Two optimization problems are studied by an incremental algorithm and dynamic programming technique respectively. The incremental algorithm proposed could obtain an approximate optimal solution, and the dynamic programming method could generate the optimal solution,
文摘Software testing is a very important phase of the software development process. It is a very difficult job for a software manager to allocate optimally the financial budget to a software project during testing. In this paper the problem of optimal allocation of the software testing cost is studied. There exist several models focused on the development of software costs measuring the number of software errors remaining in the software during testing. The purpose of this paper is to use these models to formulate the optimization problems of resource allocation: Minimization of the total number of software errors remaining in the system. On the assumption that a software project consists of some independent modules, the presented approach extends previous work by defining new goal functions and extending the primary assumption and precondition.
文摘In order to slove the large-scale nonlinear programming （NLP） problems efficiently, an efficient optimization algorithm based on reduced sequential quadratic programming （rSQP） and automatic differentiation （AD） is presented in this paper. With the characteristics of sparseness, relatively low degrees of freedom and equality constraints utilized, the nonlinear programming problem is solved by improved rSQP solver. In the solving process, AD technology is used to obtain accurate gradient information. The numerical results show that the combined algorithm, which is suitable for large-scale process optimization problems, can calculate more efficiently than rSQP itself.
基金supported by the National Social Science Fund of China (19BGL100)。
文摘This paper studies the optimal policy for joint control of admission, routing, service, and jockeying in a queueing system consisting of two exponential servers in parallel.Jobs arrive according to a Poisson process.Upon each arrival, an admission/routing decision is made, and the accepted job is routed to one of the two servers with each being associated with a queue.After each service completion, the servers have an option of serving a job from its own queue, serving a jockeying job from another queue, or staying idle.The system performance is inclusive of the revenues from accepted jobs, the costs of holding jobs in queues, the service costs and the job jockeying costs.To maximize the total expected discounted return, we formulate a Markov decision process(MDP) model for this system.The value iteration method is employed to characterize the optimal policy as a hedging point policy.Numerical studies verify the structure of the hedging point policy which is convenient for implementing control actions in practice.
