An affine scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming

This paper proposes an arlene scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming. This method is designed to get a stationary point for such a problem with polynomial interpolation models instead of the objective function in trust region subproblem. Combined with both trust region strategy and line search technique, at each iteration, the affine scaling derivative-free trust region subproblem generates a backtracking direction in order to obtain a new accepted interior feasible step. Global convergence and fast local convergence properties are established under some reasonable conditions. Some numerical results are also given to show the effectiveness of the proposed algorithm.     

GLOBAL CONVERGENCE OF THE DAI-YUAN CONJUGATE GRADIENT METHOD WITH PERTURBATIONS

In this paper, the authors propose a class of Dai-Yuan （abbr. DY） conjugate gradient methods with linesearch in the presence of perturbations on general function and uniformly convex function respectively. Their iterate formula is xk＋1 = xk ＋ αk（sk ＋ ωk）, where the main direction sk is obtained by DY conjugate gradient method, ωk is perturbation term, and stepsize αk is determined by linesearch which does not tend to zero in the limit necessarily. The authors prove the global convergence of these methods under mild conditions. Preliminary computational experience is also reported.     

Truck and Trailer Routing Problem Solving by a Backtracking Search Algorithm

Truck and trailer routing problem(TTRP) is one of the most frequently encountered problem in city distribution, particularly in populated and intensive downtown. This paper addresses this problem and designs a novel backtracking search algorithm(BSA) based meta-heuristics to solve it.The initial population is created by T-sweep heuristic and then based on the framework of backtracking search algorithm, four types of route improvement strategies are used as building blocks to improve the solutions of BSA in the process of mutation and crossover. The computational experiments and results indicate that the proposed BSA algorithm can provide an effective approach to generate high-quality solutions within the satisfactory computational time.     

带部分回溯的过滤束搜索算法及其在Job Shop 问题中的应用

束搜索(Beam search)方法是在分枝定界方法基础上发展起来的一种启发式优化方法,由于这类方法在确定分枝搜索方向时仅考虑了当前的局部信息,因此易陷入局部极值.在过滤束搜索(filteredbeam search)方法的基础上提出了一种改进思路,即在局部评价和全局评价的基础上增加部分回溯.通过引入有效的部分回溯策略,部分被舍弃的结点被重新评估并最终找到更好的解,从而可避免过早陷入局部极值.通过对48个标准问题的计算和比较,结果显示改进后的方法能有效提高解的质量.     

用于非直接对抗性体育比赛的编排算法

本文以非直接对抗性体育比赛的“最佳编排法”为基础,针对“最佳编排法”中没有考虑到的缺项现象设计了一种编排算法。该算法以偶图匹配、回溯技术为数学工具。     

利用深度优先搜索方法求解作业排序

作业排序通常是在一定的限制条件和优化目标的约束下，对有限的资源进行分配。采用搜索方法求解这类问题常会遇到冲突的状态结点，引起多次回溯。同时，由于问题状态空间庞大，搜索过程相当费时。本文通过研究作业排序问题状态空间的特点，引入冲突指派集的概念，提出了基于冲突指派集的深度优先搜索方法，缩小了搜索范围，提高了搜索效率。     

Nonmonotonic Reduced Projected Hessian Method Via an Affine Scaling Interior Modified Gradient Path for Bounded-Constrained Optimization

The authors propose an affine scaling modified gradient path method in association with reduced projective Hessian and nonmonotonic interior backtracking line search techniques for solving the linear equality constrained optimization subject to bounds on variables. By employing the QR decomposition of the constraint matrix and the eigensystem decomposition of reduced projective Hes- sian matrix in the subproblem, the authors form affine scaling modified gradient curvilinear path very easily. By using interior backtracking line search technique, each iterate switches to trial step of strict interior feasibility. The global convergence and fast local superlinear/quadratical convergence rates of the proposed algorithm are established under some reasonable conditions. A nonmonotonic criterion should bring about speeding up the convergence progress in some ill-conditioned cases. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.     

数字孪生体可信度评估过程及指标研究

随着数字孪生技术应用领域的扩展,为满足数字孪生体可信度要求和推动数字孪生体可信度评估工作,对数字孪生体可信度评估过程和指标进行了研究。分析了数字孪生体的开发过程,给出了基于IDEF0(integrated computer aided manufacturing-definition method)的柔性多层级数字孪生体可信度评估过程模型构建方法。提出了过程—阶段—活动层(P-S-A)和活动—元素—特性层(A-E-F)两类指标体系,分别辅助解决缺陷回溯问题和复杂对象评估问题,并给出了指标体系范例。     

雷达海杂波反演大气波导的改进回溯搜索算法

了克服基本回溯搜索算法在大气波导反演问题中出现的收敛速度慢、容易陷入局部最优的缺点,提出一种基于反向学习机制和正交交叉机制的改进回溯搜索优化算法。该算法利用反向学习机制来选择较好的初始化种群,而正交交叉机制用来帮助算法加强全局搜索能力,避免算法陷入局部最优,从而提高算法的精度。通过常见测试函数的优化问题以及大气波导的反演问题来检验算法的性能。结果表明,所提算法具有较高的精度和较快收敛速度。     

严格逆向过程的罗经回溯对准方法

针对逆向导航技术在实际导航中的应用,通过对逆向导航的迭代过程研究,提出了一种基于罗经法对准的严格正逆向迭代对准。所提方法在收敛速度和对准精度上具有一定优势,并从计算量的角度讨论了算法的实用性和可行性,在一定程度上兼顾了对准精度和快速性,对惯导设备的快速反应能力具有重要的现实意义。通过实测数据对所提算法的有效性进行了验证,同时使用不同数据段对准和不同初始姿态下的对准进一步展示了算法的一般性。     

基于活动-出行超网络的交通流分配模型研究综述

传统基于出行的交通流分配模型未考虑个体的出行需求源于参与活动的需要这一内在驱动力,忽视了出行与出行之间的连贯性。基于活动的交通流分配模型能够弥补传统交通流分配模型的缺点,综合考虑活动时间窗、活动地点、活动性质等活动属性对道路交通流时空分布的影响,从而更准确地为城市道路规划、城市规划提供理论指导。围绕现有文献,首先介绍描述出行者活动-出行行为过程的超网络结构模型;然后,评述基于活动-出行超网络的交通流分配模型研究;最后,分别从决策主体、决策内容与决策情境视角探讨未来的研究内容。     

多功能相控阵雷达实时驻留的自适应调度算法

灵活有效的调度算法是实现多功能相控阵雷达工作性能优化和资源合理利用的基础。从调度代价的角度建立了实时驻留调度的数学模型,提出一种求解次优调度序列的自适应算法。该算法利用任务自身工作方式属性及任务中所含目标的先验信息分配任务的综合优先级,采用一步回溯的策略来确定每个驻留任务的调度属性,利用二次规划获取其最佳执行时间,并与传统的基于优先级调度算法进行了比较。仿真结果表明,提出的自适应调度算法提高了任务调度成功率,降低了截止期错失率。     

基于标签随机有限集滤波器的多扩展目标跟踪算法

针对现有随机有限集(random finite set, RFS)扩展目标滤波器不能输出航迹的问题,提出了基于标签RFS滤波器的多扩展目标跟踪算法。该算法首先采用随机超曲面模型将目标建模为星-凸扩展形态,然后利用标签策略表征集合中的离散元素,结合基于延迟逻辑的多假设跟踪理论,采用N 次回扫策略对多帧量测进行平滑处理。仿真实验结果表明,该算法可以在目标跟踪过程中形成完整航迹并对目标扩展形态进行有效估计,特别是在低信噪比探测场景中,所提算法跟踪精度明显优于传统RFS滤波算法,进一步提高了滤波器的稳定性和有效性。     

SOLVING RESOURCE—CONSTRAINED PROJECT SCHEDULING PROBLEMS WITH BI—CRITERIA HEURISTIC SEARCH TECHNIQUES

In this paper we formulate a bi-criteria search strategy of a heuristic learning algorithm forsolving multiple resource-constrained project scheduling problems. The heuristic solves problems intwo phases. In the pre-processing phase, the algorithm estimates distance between a state and the goalstate and measures complexity of problem instances. In the search phase, the algorithm uses estimatesof the pre-processing phase to further estimate distances to the goal state. The search continues in astepwise generation of a series of intermediate states through search path evaluation process withbacktracking. Developments of intermediate states are exclusively based on a bi-criteria new stateselection technique where we consider resource utilization and duration estimate to the goal state. Wealso propose a variable weighting technique based on initial problem complexity measures.Introducing this technique allows the algorithm to efficiently solve complex project schedulingproblems. A numerical example illustra     

A line search filter secant method for nonlinear equality constrained optimization

<正> This paper formulates and analyzes a line search method for general nonlinear equalityconstrained optimization based on filter methods for step acceptance and secant methods for searchdirection.The feature of the new algorithm is that the secant algorithm is used to produce a searchdirection,a backtracking line search procedure is used to generate step size,some filtered rules areused to determine step acceptance,second order correction technique is used to reduce infeasibility andovercome the Maratos effect.Global convergence properties of this method are analyzed:under mildassumptions it is showed that every limit point of the sequence of iterates generated by the algorithmis feasible,and that there exists at least one limit point that is a stationary point for the problem.Moreover,it is also established that the Maratos effect can be overcome in our new approach by addingsecond order correction steps so that fast local superlinear convergence to a second order sufficient localsolution is achieved.Finally,the results of numerical experiments are reported to show the effectivenessof the line search filter secant method.     

广义计算理论研究

概要讨论广义计算的一般化理论 ,包括广义计算模型、广义计算系统、广义学习模型等 ,同时介绍广义计算系统实例 .     

具有广泛学习策略的回溯搜索优化算法

回溯搜索优化算法(backtracking search optimization algorithm, BSA)是一种新型的进化算法。同其他进化算法类似,该算法仍存在收敛速度较慢的缺点。针对这一问题,在详细分析该算法原理的基础上,提出了具有广泛学习策略的改进算法。为了充分利用种群搜索到的较优位置,该策略首先利用提出的最优学习进化方程,通过与引入的随机进化方程之间随机选择来提高算法的收敛速度和搜索精度;另一方面,该策略利用提出的最优学习搜索方程,通过控制种群的搜索方向,促使种群尽快收敛至全局最优解。最后对20个复杂测试函数进行了仿真实验,并与其他3种目前流行的算法进行了比较,统计结果和Wilcoxon符号秩检验结果均表明,所提出的改进算法在收敛速度以及搜索精度方面具有明显优势。     

广义判断下AHP(GJAHP)的一致性检验与可接受性的进一步探讨

广义判断下的AHP(GJAHP)是在单准则下通过构造广义判断矩阵的数学模型而建立的一种广义AHP.本文提出了广义判断矩阵一致性的一种非参数统计检验方法--spearman秩相关系数法, 给出了广义辅助矩阵的构造性定义, 并进一步探讨了广义判断矩阵的可接受性。最后本文给出了GJAHP的应用实例。     

The well-posedness for generalized fuzzy games

This paper establishes the stable results for generalized fuzzy games by using a nonlinear scalarization technique. The authors introduce some concepts of well-posedness for generalized fuzzy games. Moreover, the authors identify a class of generalized fuzzy games such that every element of the collection is generalized well-posed, and there exists a dense residual subset of the collection, where every generalized fuzzy game is robust well-posed.     

综合网络DEA模型有效性理论分析

针对综合DEA模型无法反映系统内部子过程的相互作用对绩效的影响,提出一种综合网络DEA模型,并给出该混合模型的相关定义及定理,得到综合网络DEA模型由参数取值不同,各(弱)网络DEA有效性间的关系;指出了综合网络DEA有效的决策单元,也为评价决策单元总体有效性的综合DEA有效,同时该单元内部子过程也均为综合DEA有效;证明决策单元为(弱)综合网络DEA有效时,评价决策单元总体有效性的综合DEA最优解与相应综合多目标规划的(弱)Pareto解之间的对应关系。这些结果进一步丰富了DEA有效性理论。