最小封堵圈的扩张算法设计

在发生突发事件之后,及时制定有效的封堵方案才能掌握抓捕嫌疑犯的主动权.提出了对逃跑罪犯实施完全封堵的最小包围圈的计算机算法,通过规则图形的仿真演示,验证了该算法的正确性.最后以某市案发时候的警力分布和交通图作为实例,模拟了对嫌疑犯实施封堵时计算最小包围圈的最优方案.结果证明该算法具有简洁、可靠的优点.     

校园最佳游览路线问题的数学模型分析

将某高校的校园示意图转化为赋权连通图，求得该连通图的邻接矩阵，利用Floyd算法及图论软件包构造一个最短路径矩阵，得到一个赋权完全图，将求校园最佳游览路线问题归结为图论中的最佳推销员回路问题，建立混合整数线性规划模型，并利用优化软件求得最优解．从而解决了校园开放日游览计划中提出的关于校园最佳游览路线和校园游览车最优配置问题．     

乘用车物流运输装载模型研究

对乘用车物流运输计划问题进行了研究,首先,建立了以单辆轿运车实载率最大为目标的单车最佳装载方案模型,以该方案配送乘用车辆直到运输任务完成以获得初始轿运车数,其次以空载率最小为目标设计了数量调整模型对初始轿运车数进行优化,得到最优装载方案模型.基于上述优化模型计算最小的轿运车数,建立在轿运车数量限制下的最短行驶里程模型,选择总行驶里程最小的装载方案作为最优的配送方案.最后建立基于路径的物流运输装载模型,运用Floyd算法计算任意起讫点间的最短路径,设计了一种全局搜索算法得到一种合理的配送方案,并以空载率最小为目标对方案进行优化.     

多无人机协同任务规划问题

研究无人机任务规划问题,从无人机侦查和轰炸两方面入手.首先,运用迭代算法求解出从基地到雷达区域边际上任一目标出入口的最短路径.在此基础上,以无人机在雷达范围内滞留时间最短,以及被探测次数最少为目标,建立多目标最优化模型.通过改进交叉算子的遗传算法找出最优侦查路径.对于轰炸任务,以无人机在雷达范围内滞留时间最短,以及轰炸总时间最短为目标,建立多目标最优化模型.采用改变惯性权重的自适应粒子群算法找出最佳轰炸路线.由于计算时间较长,本文对68个目标进行聚类分析,提出针对轰炸任务的快速算法,相较原轰炸方案,其计算效率提高80%以上.     

机器人避障问题

研究机器人在平面区域中绕过静态障碍物到达指定目的地的问题, 分别考虑了路程最短和时间最短两种目标下的最优路径, 给出了计算机自动搜索最优路径的模型和算法。     

弹性光网络一类调度问题的一个新模型和算法

采用网络功能虚拟化技术的弹性光网络是一种新型的网络,其数据中心的合理部署,路由的科学规划及频谱的最优分配是一个关键而具有挑战的问题.为了解决这个问题,建立了弹性光网络资源分配和任务调度问题一个新的优化模型,新模型以虚拟网络功能在数据中心部署的负载最均衡,经过数据中心节点的路径最短以及频谱占用最少为目标,可同时使虚拟网络功能在数据中心部署,路径规划和频谱分配方案最优.为有效求解该模型,分别设计了一个经过所选数据中心的最短路径策略,虚拟网络功能在数据中心的部署策略以及频谱分配策略,构造了初始种群的产生方法,设计了新的变异算子,在此基础上,提出了求解模型的一个新的进化算法.最后进行了仿真实验,结果表明,最大频隙号和数据中心VNF部署数目的标准差相比对比算法有明显降低,验证了所建模型和算法的有效性.     

圆弧-线段型加工路径的最优速度规划

在数控加工中,速度规划是优化加工时间的核心问题.文章针对圆弧一线段型路径,提出最优速度规划算法.文章通过建立加工时间最短的速度规划模型,基于"Bang-Bang"控制,对圆弧进行最优速度规划.通过圆弧相邻线段的速度可达性检验修调速度,提出圆弧样条的最优速度规划算法.与高速小线段拐角过渡插补算法相比,实验结果表明文章的算法更加高效.     

多波次导弹发射任务策略优化

针对第十四届中国研究生数学建模竞赛E题的多波次导弹发射中的规划问题展开研究.首先,简化各道路节点路径信息后通过Dijkstra算法和模拟退火算法,制定了整体最短暴露时间对应的具体发射点位及机动路线方案,得到最短暴露时间127.7h;再采用穷举法及模拟退火制定合理布设两个转载地域以及确定最优隐蔽节点的策略;最后,在考虑规避敌方打击以及单个发射装置最大暴露时间最短等其他因素下,将多目标优化问题转化为单目标优化问题.     

一种求解二次函数模型信赖域子问题的分段切线算法

在Hessian矩阵正定的前提下,建立一种最优曲线的微分方程模型.针对此微分方程模型,提出一种求解二次函数模型信赖域子问题的分段切线算法,并分析和证明分段切线路径的合理性.数值结果表明新算法是有效且可行的.     

一种基于Dijkstra算法的机器人避障问题路径规划

移动机器人的避障问题是移动机器人控制领域的研究热点.针对给定的移动机器人避障问题,探讨了最短路径及最短时间路径的路径规划问题.对于最短路径问题,建立了简化的路径网格模型,将其抽象为由节点及边构成的两维图,再使用经典的Dijkstra算法获得可行的最短路径.对于最短时间路径问题,通过分析移动机器人弯道运行的速度曲线,基于几何方法得出了移动时间与过渡圆弧圆心之间严格的数学关系,此后借助MATLAB优化函数获得最佳的移动路径.算法可为类似机器人避障问题的解决提供借鉴.     

A column generation approach for location-routing problems with pickup and delivery

In this paper we formulate an integer programming model for the Location and Routing Problem with Pickup and Delivery. We propose a column generation scheme and implement, for the subproblem, a label-setting algorithm for the shortest path with pickup and delivery and time windows problem. We also propose a set of heuristics to speed up this process. To validate the model, we implement the column generation scheme and test it on different instances developed in this paper. We also provide an analysis of how the costs of opening depots and the fixed cost of routes affect the optimal solution.     

A column generation method for inverse shortest path problems

In this paper we formulate an inverse shortest path problem as a special linear programming problem. A column generation scheme is developed that is able to keep most columns of the LP model implicit and to generate necessary columns by shortest path algorithms. This method can get an optimal solution in finitely many steps. Some numerical results are reported to show that the algorithm has a good performance.The authors gratefully acknowledge the partial support of Croucher Foundation.     

Hybrid co-evolutionary particle swarm optimization and noising metaheuristics for the delay constrained least cost path problem

This paper presents a co-evolutionary particle swarm optimization (PSO) algorithm, hybridized with noising metaheuristics, for solving the delay constrained least cost (DCLC) path problem, i.e., shortest-path problem with a delay constraint on the total “cost” of the optimal path. The proposed algorithm uses the principle of Lagrange relaxation based aggregated cost. It essentially consists of two concurrent PSOs for solving the resulting minimization-maximization problem. The main PSO is designed as a hybrid PSO-noising metaheuristics algorithm for efficient global search to solve the minimization part of the DCLC-Lagrangian relaxation by finding multiple shortest paths between a source-destination pair. The auxiliary/second PSO is a co-evolutionary PSO to obtain the optimal Lagrangian multiplier for solving the maximization part of the Lagrangian relaxation problem. For the main PSO, a novel heuristics-based path encoding/decoding scheme has been devised for representation of network paths as particles. The simulation results on several networks with random topologies illustrate the efficiency of the proposed hybrid algorithm for the constrained shortest path computation problems.     

A heuristic approach to hard constrained shortest path problems

Constrained shortest path problems have many applications in areas like network routing, investments planning and project evaluation as well as in some classical combinatorial problems with high duality gaps where even obtaining feasible solutions is a difficult task in general.We present in this paper a systematic method for obtaining good feasible solutions to hard (doubly constrained) shortest path problems. The algorithm is based essentially on the concept of efficient solutions which can be obtained via parametric shortest path calculations. The computational results obtained show that the approach proposed here leads to optimal or very good near optimal solutions for all the problems studied.From a theoretical point of view, the most important contribution of the paper is the statement of a pseudopolynomial algorithm for generating the efficient solutions and, more generally, for solving the parametric shortest path problem.     

邮路规划与邮车调度最优化理论研究

对小规模MTSP问题,建立了可精确求解方案的0-1规划模型,并在满足邮政运输需求的前提下给出了最佳方案.问题一首先以县支局、县局为顶点构建无向赋权图,通过Floyd算法求解各局间的最短距离;然后以Fijk为决策变量,以邮车工作时间、车辆运载能力为主要约束,建立以总空载损失费用最小为目标的0-1非线性规划模型,运用规划软件Lingo求解.问题二考虑到市邮路成本,我们采用分层规划策略,首先以市支局、县局为顶点构建无向赋权图,求解出最短路矩阵,建立以邮路运行成本最小为目标的0-1非线性规划模型IIA求解;然后,建立各县区的最短路矩阵,同样建立规划模型IIB求解各县运输方案.问题三由于县局地理位置不变,对区邮路无影响,故以全市各县支局为中心采用逐步最优方法对所有县区支局重新划分;然后采用模型IIB求解.第四问中考虑县局迁移,我们建立近似的启发式算法完成县局选址,并运用规划模型II求解的到新方案.最后,我们对两种区域划分调整方法还进行了定量的分析.     

铁路应急设施非概率可靠性选址优化研究

为解决小样本、贫信息下铁路应急资源储备点的可靠性选址问题,创新性地将选址-路径问题与区间非概率可靠性方法结合起来,考虑灾情发生后应急设施点在可接受的时间范围内响应受灾点的需求能力及其稳定程度,采用区间值度量路段阻抗,基于区间非概率可靠性理论及区间运算规则,提出路径的非概率可靠性度量及可靠最短路径选择方法;建立基于区间时间阻抗下可靠最短路径的无容量设施选址模型,提出约束条件限制的Monte Carlo改进算法,确定了铁路资源储备点选址的最优方案。实例表明,本文的优化方案能更好地保证救援的时间可靠性,改进的求解算法具有更小的时间复杂度,有效地缩短了运算时间,改善了解的质量。本文的方法与模型体系对于实现铁路应急设施可靠性选址,为决策者提供决策支持,提高铁路应急响应能力具有重要的指导意义。     

An Algorithm for Solving the Shortest Path Improvement Problem on Rooted Trees Under Unit Hamming Distance

Shortest path problems play important roles in computer science, communication networks, and transportation networks. In a shortest path improvement problem under unit Hamming distance, an edge-weighted graph with a set of source–terminal pairs is given. The objective is to modify the weights of the edges at a minimum cost under unit Hamming distance such that the modified distances of the shortest paths between some given sources and terminals are upper bounded by the given values. As the shortest path improvement problem is NP-hard, it is meaningful to analyze the complexity of the shortest path improvement problem defined on rooted trees with one common source. We first present a preprocessing algorithm to normalize the problem. We then present the proofs of some properties of the optimal solutions to the problem. A dynamic programming algorithm is proposed for the problem, and its time complexity is analyzed. A comparison of the computational experiments of the dynamic programming algorithm and MATLAB functions shows that the algorithm is efficient although its worst-case complexity is exponential time.     

A fuzzy shortest path with the highest reliability

This paper concentrates on a shortest path problem on a network where arc lengths (costs) are not deterministic numbers, but imprecise ones. Here, costs of the shortest path problem are fuzzy intervals with increasing membership functions, whereas the membership function of the total cost of the shortest path is a fuzzy interval with a decreasing linear membership function. By the max–min criterion suggested in [R.E. Bellman, L.A. Zade, Decision-making in a fuzzy environment, Management Science 17B (1970) 141–164], the fuzzy shortest path problem can be treated as a mixed integer nonlinear programming problem. We show that this problem can be simplified into a bi-level programming problem that is very solvable. Here, we propose an efficient algorithm, based on the parametric shortest path problem for solving the bi-level programming problem. An illustrative example is given to demonstrate our proposed algorithm.     

考虑绕行特征的电动汽车快速充电站选址问题及自适应遗传算法

快速充电站选址是电动汽车运营的重要内容之一。本文考虑电动汽车用户会通过绕行一定距离对车辆进行充电这一特征,建立了一个以电动汽车快速充电站建站成本和旅客整体绕行成本之和最小的双层整数规划模型。本文首先给出了用于生成绕行路径集合的A^*算法,然后设计了一种包含局部迭代搜索的自适应遗传算法对该模型进行求解。为了测试算法性能,通过两个不同规模的算例图与已有求解FPLM问题的遗传算法进行了比较,数值试验部分证明了算法的正确性和有效性。最后引入浙江省的高速路网图,从建站成本和截流量两方面对电池续航里程带来的影响进行了相关的灵敏度分析。     

解一般TSP问题的并行算法

任何连通的带权图均有ＴＳＰ的解．本文用图的最短路径矩阵代替加权邻接矩阵，使所有带权图，ＨＰ模型都能够接受．由于采用并行算法，可以较快获得问题的最优解．