A target is assumed to move according to a Brownian motion on the real line. The searcher starts from the origin and moves in the two directions from the starting point. The object is to detect the target. The purpose...A target is assumed to move according to a Brownian motion on the real line. The searcher starts from the origin and moves in the two directions from the starting point. The object is to detect the target. The purpose of this paper is to find the conditions under which the expected value of the first meeting time of the searcher and the target is finite, and to show the existence of a search plan which made this expected value minimum.展开更多
The essence of the linear search is one-dimension nonlinear minimization problem, which is an important part of the multi-nonlinear optimization, it will be spend the most of operation count for solving optimization p...The essence of the linear search is one-dimension nonlinear minimization problem, which is an important part of the multi-nonlinear optimization, it will be spend the most of operation count for solving optimization problem. To improve the efficiency, we set about from quadratic interpolation, combine the advantage of the quadratic convergence rate of Newton's method and adopt the idea of Anderson-Bjorck extrapolation, then we present a rapidly convergence algorithm and give its corresponding convergence conclusions. Finally we did the numerical experiments with the some well-known test functions for optimization and the application test of the ANN learning examples. The experiment results showed the validity of the algorithm.展开更多
Selecting the optimal parameters for support vector machine (SVM) has long been a hot research topic. Aiming for support vector classification/regression (SVC/SVR) with the radial basis function (RBF) kernel, we summa...Selecting the optimal parameters for support vector machine (SVM) has long been a hot research topic. Aiming for support vector classification/regression (SVC/SVR) with the radial basis function (RBF) kernel, we summarize the rough line rule of the penalty parameter and kernel width, and propose a novel linear search method to obtain these two optimal parameters. We use a direct-setting method with thresholds to set the epsilon parameter of SVR. The proposed method directly locates the right search field, which greatly saves computing time and achieves a stable, high accuracy. The method is more competitive for both SVC and SVR. It is easy to use and feasible for a new data set without any adjustments, since it requires no parameters to set.展开更多
A target is assumed to move randomly on one of two disjoint lines L1 and L2 according to a stochastic process . We have two searchers start looking for the lost target from some points on the two lines separately. Eac...A target is assumed to move randomly on one of two disjoint lines L1 and L2 according to a stochastic process . We have two searchers start looking for the lost target from some points on the two lines separately. Each of the searchers moves continuously along his line in both directions of his starting point. When the target is valuable as a person lost on one of disjoint roads, or is serious as a car filled with explosives which moves randomly in one of disjoint roads, in these cases the search effort must be unrestricted and then we can use more than one searcher. In this paper we show the existence of a search plan such that the expected value of the first meeting time between the target and one of the two searchers is minimum.展开更多
In this paper, we study the quasi-coordinated search technique for a lost target assumed to move randomly on one of two disjoint lines according to a random walk motion, where there are two searchers beginning their s...In this paper, we study the quasi-coordinated search technique for a lost target assumed to move randomly on one of two disjoint lines according to a random walk motion, where there are two searchers beginning their search from the origin on the first line and other two searchers begin their search from the origin on the second line. But the motion of the two searchers on the first line is independent from the motion of the other two searchers on the second line. Here we introduce a model of search plan and investigate the expected value of the first meeting time between one of the searchers and the lost target. Also, we prove the existence of a search plan which minimizes the expected value of the first meeting time between one of the searchers and the target.展开更多
It is well known that the line search methods play a very important role for optimization problems. In this paper a new line search method is proposed for solving unconstrained optimization. Under weak conditions, thi...It is well known that the line search methods play a very important role for optimization problems. In this paper a new line search method is proposed for solving unconstrained optimization. Under weak conditions, this method possesses global convergence and R-linear convergence for nonconvex function and convex function, respectively. Moreover, the given search direction has sufficiently descent property and belongs to a trust region without carrying out any line search rule. Numerical results show that the new method is effective.展开更多
In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Comb...In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.展开更多
Many difficult engineering problems cannot be solved by the conventional optimization techniques in practice. Direct searches that need no recourse to explicit derivatives are revived and become popular since the new ...Many difficult engineering problems cannot be solved by the conventional optimization techniques in practice. Direct searches that need no recourse to explicit derivatives are revived and become popular since the new century. In order to get a deep insight into this field, some notes on the direct searches for non-smooth optimization problems are made. The global convergence vs. local convergence and their influences on expected solutions for simulation-based stochastic optimization are pointed out. The sufficient and simple decrease criteria for step acceptance are analyzed, and why simple decrease is enough for globalization in direct searches is identified. The reason to introduce the positive spanning set and its usage in direct searches is explained. Other topics such as the generalization of direct searches to bound, linear and non-linear constraints are also briefly discussed.展开更多
为提高配送运输的效率,降低综合成本,针对卡车-无人机灵活协同路径问题设计优化方法。首先,综合多卡车-多无人机灵活协同和无人机连续运输的特点,以最小化运营成本与客户等待成本为目标,构建混合整数线性规划(mixed integer linear prog...为提高配送运输的效率,降低综合成本,针对卡车-无人机灵活协同路径问题设计优化方法。首先,综合多卡车-多无人机灵活协同和无人机连续运输的特点,以最小化运营成本与客户等待成本为目标,构建混合整数线性规划(mixed integer linear programming,MILP)模型。其次,设计两阶段启发式求解框架,在两个阶段分别优化无人机和卡车路径。最后,结合破坏算子、修复算子和k-opt算子构造混合邻域,提出自适应混合邻域搜索(adaptative hybrid neighborhood search,AHNS)算法进行每个阶段的优化。在Solomon数据集上进行数值实验,结果表明:相较于CPLEX求解器,所提方法可以在短时间内获取质量较高的满意解;相较于迭代局部搜索算法、变邻域搜索算法和蚁群算法,所提方法的求解质量在小、中和大规模算例中分别平均提高了5.49%、6.88%和27.82%;与纯卡车运输模式相比,卡车-无人机协同运输模式更适合小、中规模场景的作业,可以降低4.70%~8.56%的综合成本。研究结果可为卡车-无人机联合运输实践提供理论基础。展开更多
文摘A target is assumed to move according to a Brownian motion on the real line. The searcher starts from the origin and moves in the two directions from the starting point. The object is to detect the target. The purpose of this paper is to find the conditions under which the expected value of the first meeting time of the searcher and the target is finite, and to show the existence of a search plan which made this expected value minimum.
文摘The essence of the linear search is one-dimension nonlinear minimization problem, which is an important part of the multi-nonlinear optimization, it will be spend the most of operation count for solving optimization problem. To improve the efficiency, we set about from quadratic interpolation, combine the advantage of the quadratic convergence rate of Newton's method and adopt the idea of Anderson-Bjorck extrapolation, then we present a rapidly convergence algorithm and give its corresponding convergence conclusions. Finally we did the numerical experiments with the some well-known test functions for optimization and the application test of the ANN learning examples. The experiment results showed the validity of the algorithm.
基金supported by the National Basic Research Program (973) of China (No. 2009CB724006)the National Natural Science Foun-dation of China (No. 60977010)
文摘Selecting the optimal parameters for support vector machine (SVM) has long been a hot research topic. Aiming for support vector classification/regression (SVC/SVR) with the radial basis function (RBF) kernel, we summarize the rough line rule of the penalty parameter and kernel width, and propose a novel linear search method to obtain these two optimal parameters. We use a direct-setting method with thresholds to set the epsilon parameter of SVR. The proposed method directly locates the right search field, which greatly saves computing time and achieves a stable, high accuracy. The method is more competitive for both SVC and SVR. It is easy to use and feasible for a new data set without any adjustments, since it requires no parameters to set.
文摘A target is assumed to move randomly on one of two disjoint lines L1 and L2 according to a stochastic process . We have two searchers start looking for the lost target from some points on the two lines separately. Each of the searchers moves continuously along his line in both directions of his starting point. When the target is valuable as a person lost on one of disjoint roads, or is serious as a car filled with explosives which moves randomly in one of disjoint roads, in these cases the search effort must be unrestricted and then we can use more than one searcher. In this paper we show the existence of a search plan such that the expected value of the first meeting time between the target and one of the two searchers is minimum.
文摘In this paper, we study the quasi-coordinated search technique for a lost target assumed to move randomly on one of two disjoint lines according to a random walk motion, where there are two searchers beginning their search from the origin on the first line and other two searchers begin their search from the origin on the second line. But the motion of the two searchers on the first line is independent from the motion of the other two searchers on the second line. Here we introduce a model of search plan and investigate the expected value of the first meeting time between one of the searchers and the lost target. Also, we prove the existence of a search plan which minimizes the expected value of the first meeting time between one of the searchers and the target.
文摘It is well known that the line search methods play a very important role for optimization problems. In this paper a new line search method is proposed for solving unconstrained optimization. Under weak conditions, this method possesses global convergence and R-linear convergence for nonconvex function and convex function, respectively. Moreover, the given search direction has sufficiently descent property and belongs to a trust region without carrying out any line search rule. Numerical results show that the new method is effective.
文摘In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.
基金supported by the Key Foundation of Southwest University for Nationalities(09NZD001).
文摘Many difficult engineering problems cannot be solved by the conventional optimization techniques in practice. Direct searches that need no recourse to explicit derivatives are revived and become popular since the new century. In order to get a deep insight into this field, some notes on the direct searches for non-smooth optimization problems are made. The global convergence vs. local convergence and their influences on expected solutions for simulation-based stochastic optimization are pointed out. The sufficient and simple decrease criteria for step acceptance are analyzed, and why simple decrease is enough for globalization in direct searches is identified. The reason to introduce the positive spanning set and its usage in direct searches is explained. Other topics such as the generalization of direct searches to bound, linear and non-linear constraints are also briefly discussed.
