CD音轨智能编辑转录的数学模型及递归算法

本文应用整数背包问题有关理论，对CD音轨智能编辑转录剖进行了讨论，提出了一个数学模型及相应的递归算法，该数学模型及算法可以推广，用于解决其他一些优化组合问题。     

拟阵贪婪算法在景区装饰灯中的应用

该文立足于实际，就如何在景区设置装饰灯问题给出了数学模型及求解步骤。在解决过程中采用了拟阵的贪婪算法，此算法简洁、易行。     

基于MATLAB求解任意城市间的最短路问题

本文首先介绍最短路问题的数学模型及Dijkstra算法，紧接着采用Dijkstra算法的改进算法——Floyd算法，然后将求城市道路网两点间最短路径目标约束转化为求最短路问题．随之建立最短路模型，并描述了用MATLAB程序进行求解的过程。最后用实例验证了模型和算法的可用性。     

用0-1背包解法优化研究生学习的开销

将求解研究生费用开销问题转变为0-1背包问题，给出了数学模型和算法设计，并分析算法实现的复杂度问题。     

基于最大最小公平算法的应急医疗人力资源分配优化模型

针对突发事件背景下医疗人力资源供需不平衡的问题，展开了对应急分配模型的研究。在岗位安排及员工职业技能评估的基础上，考虑了不同工作对职业技能的需求问题，进而建立了人员分配的数学模型。同时通过引入最大最小公平算法，提出了人力资源分配算法，并结合算例进行了仿真。所提方法为应急环境中医院多重维度下人力与工作任务的双向匹配建立了数学模型，提出了求解方案，为指导实际应急场景下的资源分配问题提供了理论支撑。     

模拟退火算法在装箱问题中的应用

装箱问题是个NPC问题^[1]，该文采用了模拟退火算法解决这一问题。文中给出了数学模型，模拟退火算法的步骤并结合实例进行了收敛性分析．算法理想能迅速得出配装方案。     

整数背包问题的应用及其算法研究

本文应用整数背包问题有关理论,对CD曲目智能编辑转录和条型钢材优化切割等应用问题进行了讨论,提出了一个解决此类问题的数学模型,之后,分别给出了求其最优解和近似解的算法,并提供了该数学模型及算法的应用建议。     

玻璃板材下料优选算法设计及实现

玻璃板材按等级优选技术在全自动玻璃产线的下料工艺中起重要作用，优选的结果优劣直接影响玻璃板材出材率及综合利用率，而优选的结果优劣取决于玻璃板材考虑等级的下料优选算法。针对全自动玻璃板材下料设备优选算法实现的问题，提出适用于自动扫描的玻璃板材及矩形件规范化量化方法，并结合量化方法给出规范化矩形件订单定义，作为任务输入给优选算法；提出适用于下料设备自动下料的矩形件优选下料的三种矩形件优选方式，即加权优选方式、数量优选方式及价值优选方式，并结合等级优选以适应自动化生产线的要求，解决如何优选的问题。然后，建立数量优选系数及矩形件优选的数学模型；设计下料优选算法软件实现的智能化架构及编制相应优选实现软件。选取实例对所建立的数学模型进行综合评价，评价结果表明，运用所提优选算法的出材率提高约10%,能明显提高生产效率，能实现矩形件产品的精确统计。所建立的三种矩形件优选方式的数学模型能有效地提高玻璃板材出材率和综合利用率。     

基于可视化计算建筑工程量的非正交轴线跟踪法

论述了建筑预算工程量计算的可视化计算模型，给出了非正交网格图的轴线跟踪算法，采取的数学模型及处理模式是独特的，解决了工程量计算的主要问题，具有准确，可靠、速度快等特点。     

Prim算法在架设通信网络系统中的应用

通信网络系统架设属于典型的图论优化问题,针对通信网络系统的特点,抽象问题,简化模型,以通信网络系统架设费用最小为优化目标,应用Prim算法进行通信网络系统架设模型研究.首先简述了七城市之间架设通信网络系统问题,然后应用数学建模知识对隐含在该问题中的图论模型进行抽象研究,进而构造问题的数学模型,最后应用Prim算法设计了该通信网络系统架设的实现流程及相应代码的编写.程序执行结果表明:准确构建了问题的数学模型及应用Prim算法正确求解了该数学模型;并且权值因子的可变性使得该程序具有较强的通用性,易于在实际中使用.     

The Definition and Numerical Method of Final Value Problem and Arbitrary Value Problem

Many Engineering Problems could be mathematically described by FinalValue Problem, which is the inverse problem of InitialValue Problem. Accordingly, the paper studies the final value problem in the field of ODE problems and analyses the differences and relations between initial and final value problems. The more general new concept of the endpoints-value problem which could describe both initial and final problems is proposed. Further, we extend the concept into inner-interval value problem and arbitrary value problem and point out that both endpoints-value problem and inner-interval value problem are special forms of arbitrary value problem. Particularly, the existence and uniqueness of the solutions of final value problem and inner-interval value problem of first order ordinary differential equation are proved for discrete problems. The numerical calculation formulas of the problems are derived, and for each algorithm, we propose the convergence and stability conditions of them. Furthermore, multivariate and high-order final value problems are further studied, and the condition of fixed delay is also discussed in this paper. At last, the effectiveness of the considered methods is validated by numerical experiment.     

Optimal and robust controllers for periodic and multirate systems

The problem of optimal rejection of bounded persistent disturbances is solved in the case of linear discrete-time periodic systems. The solution consists of solving an equivalent time-invariant standard l¹ optimization problem subject to an additional constraint. This constraint assures the causality of the resulting periodic controller. By the duality theory, the problem is shown to be equivalent to a linear programming problem, which is no harder than the standard l¹ problem. Also, it is shown that the method of solution presented applies exactly to the problem of disturbance rejection in the case of multirate sampled data systems. Finally, the results are applied to the problem of robust stabilization of periodic and multirate systems     

多一次Paillier求逆问题与并发安全的鉴别方案

从计算难解性的角度重新考察Paillier的陷门单向函数,并提出多一次Paillier求逆问题这一关于Paillier求逆问题的推广问题.从计算难解性的角度考察了多一次Paillier求逆问题与Bellare等人提出的多一次RSA求逆问题之间的关系,并证明了在计算难解性的意义上。多一次Paillier求逆问题等价于多一次RSA求逆问题.以此为基础,进而提出一种新的鉴别方案,并证明在多一次Paillier求逆问题的难解性假设下这一鉴别方案具备并发安全性.     

有软时窗约束带取送作业的车辆路径问题及其禁忌搜索算法研究

有软时窗约束带取送作业的车辆路径问题是在基本的车辆路径问题上增加了取送作业和时间窗约束的一种变化形式,是一个典型的NP-难问题.本文建立了问题模型,运用改进的禁忌搜索算法测试了根据实际状况构造的一个大规模算例.快速获得的高质量解验证了模型的正确性和算法性能的优良性.     

成像卫星星地联合成像调度

成像卫星星地联合调度问题,涉及调度对象众多,约束条件复杂,需要考虑任务的观测、回传2个过程,是一个具有两层时间窗口约束的双层优化问题,统一建模困难。根据问题的特点,采用基于阶段优化的方式,降低了问题的复杂性。把问题分为观测调度阶段和数据回传调度阶段,分别给出了优化目标和约束条件,建立了基于阶段优化的成像卫星星地联合调度模型,实现了从任务观测到数据回传的全过程调度。仿真实例表明,该方法能够有效解决多星多站的协同任务调度问题。     

Specification and analysis of real-time problem solvers

The authors provide a method for the specification of real-time artificial intelligence (AI) problem solvers. Using this method, a formal specification of a real-time problem is presented. In addition, a method for analyzing real-time AI problem solvers is examined using a case study of two real-time problem solvers, namely DYNORAII and RTA* for the real-time path planning problem. New results on worst-case and average-case complexity of the problem, and of the algorithms that solve it, and an experimental evaluation of DYNORAII and RTA* for deadline compliance and response-time minimization are provided     

隐蔽集的研究及发展

SAT问题的隐藏结构与问题难度有很大的关系,近年来成为人工智能的一个研究热点。隐蔽集(Backdoor)作为典型的隐藏结构之一,能使剩下的问题在多项式时间内求解。在深入研究隐蔽集的基础上,首先对隐蔽集的发展、相关概念、参数复杂性及隐蔽集与骨架(Backbone)之间的关系作了全面的论述;接着分别从CSP问题、SAT问题和QBF问题3个方面具体介绍了目前比较流行的隐蔽集求解方法;最后给出了3个未解决的问题,并对隐蔽集的发展趋势进行了展望。     

A new formulation and approach for the black and white traveling salesman problem

This paper proposes a new formulation and a column generation approach for the black and white traveling salesman problem. This problem is an extension of the traveling salesman problem in which the vertex set is divided into black vertices and white vertices. The number of white vertices visited and the length of the path between two consecutive black vertices are constrained. The objective of this problem is to find the shortest Hamiltonian cycle that covers all vertices satisfying the cardinality and the length constraints. We present a new formulation for the undirected version of this problem, which is amenable to the Dantzig–Wolfe decomposition. The decomposed problem which is defined on a multigraph becomes the traveling salesman problem with an extra constraint set in which the variable set is the feasible paths between pairs of black vertices. In this paper, a column generation algorithm is designed to solve the linear programming relaxation of this problem. The resulting pricing subproblem is an elementary shortest path problem with resource constraints, and we employ acceleration strategies to solve this subproblem effectively. The linear programming relaxation bound is strengthened by a cutting plane procedure, and then column generation is embedded within a branch-and-bound algorithm to compute optimal integer solutions. The proposed algorithm is used to solve randomly generated instances with up to 80 vertices.     

Guided Local Search for Solving SAT and Weighted MAX-SAT Problems

In this paper, we show how Guided Local Search (GLS) can be applied to the SAT problem and show how the resulting algorithm can be naturally extended to solve the weighted MAX-SAT problem. GLS is a general, penalty-based meta-heuristic, which sits on top of local search algorithms to help guide them out of local minima. GLS has been shown to be successful in solving a number of practical real-life problems, such as the traveling salesman problem, BT"s workforce scheduling problem, the radio link frequency assignment problem, and the vehicle routing problem. We present empirical results of applying GLS to instances of the SAT problem from the DIMACS archive and also a small set of weighted MAX-SAT problem instances and compare them with the results of other local search algorithms for the SAT problem.