最佳灾情巡视路线的数学模型

本文将求最佳巡视路线问题转化为图论中求最佳推销员回路的问题,并用近似算法去寻求近似最优解。对分组问题定义了均衡度用以衡量分组的均衡性。对问题1和问题2先定出几个分组的准则进行初步分组,并用近似算法求每一组的近似最佳推销员回路,再根据均衡度进行微调,得到较优的均衡分组和每组的近似最佳推销员回路,对问题1得出总路程较短且各组尽可能均衡的路线,各组的巡视路程分别为 216.4公里,191.1 公里,192.3公里,总路程为599.8公里。对问题2,证明了应至少分为4组,并求出了分为4组时各组的较优巡视路线,各组的巡视时间分别为22.74小时,22.59小时,21.69小时,22.54小时,对问题3,求出完成巡视的最短时间为6.43 小时,并用较为合理的分组的准则,分成 22个组。对问题 4,研究了在不影响分组的均衡条件下,T,t,V的允许变化范围,并得出了这三个变量的关系式,并由此对分三个组的情况进行了具体讨论。     

最优搜索理论的进展

自1975年 L.D.Stone 的《Theory of Optimal Search》一书问世以来,最优搜索理论的研究重点已从静止目标的搜索问题转向随机运动目标的搜索问题,在优化的数学理论和算法上取得许多重要进展,最优搜索理论的应用也日趋广泛.本文对最优搜索理论在近十多年来的进展做一归纳性描述,并对今后的发展方向提出看法.文[1]已系统论述了静止目标的最优搜索问题,本文进一步考虑随机运动目标的搜索问题.     

在线时间序列搜索的风险补偿模型

对于在线时间序列搜索问题,在假设对未来信息有一定的预期下,提出了在线时间序列搜索的风险补偿模型,进一步研究了模型的求解,给出了模型的一个最优策略,并通过数值计算讨论了最优策略的补偿函数随参数变化规律.数值实验结果表明,随着风险容忍度的增大与预期区间下限的增大,补偿函数均增大且趋于收敛;随着预期概率的增大与预期区间上限的减少,补偿函数分别增大.研究结果丰富了在线时间序列搜索的理论且具有实际应用价值.     

基于混沌优化和自适应反向学习的秃鹰搜索算法

针对秃鹰搜索算法求解精度低、收敛速度较慢、容易陷入局部最优的问题,提出一种基于混沌优化和自适应反向学习的秃鹰搜索算法.首先,在选择搜索空间阶段引入正弦混沌映射更新秃鹰群位置,增加随机性,优化全局搜索能力;其次,在俯冲捕获猎物阶段加入指数自适应,平衡了全局搜索和局部搜索,同时加快收敛速度;最后,对更新后的最优秃鹰位置使用反向学习策略,提高跳出局部最优的可能性.选取12个测试函数对算法的性能进行了测试,结果表明本文改进的秃鹰搜索算法具有更优的求解精度和收敛速度.     

基于量子粒子群算法的电力系统负荷多目标优化分配

针对电力系统经济负荷优化分配问题,提出了一种基于量子粒子群的多目标优化算法.该算法通过将改进后的量子进化算法融合到粒子群中,采用量子位对粒子的当前位置进行编码,用量子旋转门实现对粒子最优位置的搜索,用量子非门实现粒子位置的变异以避免早熟收敛.这种搜索机制能够遍历解空间,增强种群的多样性,并能用量子位的概率幅将最优解表述为解空间中的多种表述形式,从而增强全局最优的可能性.最后,通过算例进行仿真分析,结果表明算法的搜索能力和优化效率均优于普通粒子群算法.     

秘书问题研究综述：何时停止搜索信息?

秘书问题是一类序贯观察与选择问题,描述了一种动态的信息搜索与决策过程,其问题实质是决定何时停止观察选项、而不是哪一个选项被选择.已有研究成果从解决该问题的策略方法角度,可以分为最优解策略与启发式策略,二者的差异主要体现在理论依据与研究方法上.最优解策略基于决策者完全理性假设,运用数学模型论证了解决该问题的最优决策行为。但许多实证研究发现,人们往往并没有遵循最优决策行为。相比较最优解策略而言,人们通常停止搜索信息太早或者说搜索量太少。这种基于决策者有限理性假设的描述性研究,在解释人们最优选择行为偏离的基础上,提出了解决秘书问题的一些启发式策略.最后,本文通过对已有研究成果的梳理与分析,提出了进一步研究的问题与方向。     

“应召”搜索问题的最优搜索路线

解决了确定性二次搜索（即“应召”搜索）问题的最优搜索路线。在搜索时间期望值最小、最远可能航程最短、最长可能时间最短三个准则下分别找出了相应的最优搜索路线,并从理论上严格证明了三者的统一性。这个结论在军事领域具有很重要的应用价值     

区间自适应遗传算法优化无约束非线性规划问题

针对无约束非线性规划传统优化方法存在的问题,将区间自适应遗传算法引入无约束非线性规划优化中,算法可以利用当前进化信息,自适应移动搜索区间,找到全局最优解,故可缩短搜索区间长度,提高编码精度,降低算法计算量,解决了传统遗传算法处理优化问题时,给定区间必须包含最优解这一问题,这也是本算法有别于其他优化算法的独特优势,为某些最优解所在区间难以估计的无约束非线性规划问题的优化提供了一条有效可行的途径.系统阐述了区间自适应遗传算法的原理,给出了算法优化无约束非线性规划问题的步骤,以MatlabR2016b仿真方式对算法进行了实例测试,结果表明,方法是一种计算稳定、正确、有效、可靠实用的无约束非线性规划优化方法.     

一种改进的蚁群算法及其在TSP中的应用

蚁群算法是一种求解复杂组合优化问题的新的拟生态算法,也是一种基于种群的启发式仿生进化算法,属于随机搜索算法的一种,并用于较好地解决TSP问题.然而此算法也有它自己的缺陷,如易于陷入局部优化、搜索时间长等.通过对基本蚁群算法的介绍及相关因素的分析,提出了一种改进的蚁群算法,用于解决TSPLAB问题的10个问题,并与参考文献中的F-W、NCSOM、ASOM算法进行比较,计算机仿真结果表明了改进算法的有效性.如利用改进的蚁群算法解决lin105问题,其最优解为14382.995933(已知最优解为14379),相对误差是0.0209%,计算出的最小值几乎接近于已知最优解.     

基于混合单亲遗传算法的车辆运输问题求解

本文运用混合单亲遗传算法(Hybrid Partheno Genetic Algorithm,)求解车辆运输问题.我们用罚函数法将约束优化问题转化为无约束优化问题,HPGA采用序号编码的方式进行运算.生成初始种群时,在拟染色体中插入车辆序号,尽可能生成符合约束的子路径,由子路径拼接成完整的运输路径,降低罚函数的计算量;选择操作中内嵌最优保存策略,保证算法全局收敛;取消双亲交叉操作,每条染色体上独立改变基因产生新的个体,避免发生早熟早收敛现象;提出邻域搜索,使得GA能对某些指定区域进行重点搜索,加快算法在最优解附近的寻优速度;以CVRP作为HPGA的测试模型,采用Christofides和Eilon提出的标准VRP测试算例进行数值实验,和其他算法进行对比分析,验证了HPGA计算量少、收敛速度快和不会产生早熟早收敛现象.     

A commuter departure-time model based on cumulative prospect theory

With a focus on planning of departure times during peak hours for commuters, an optimal arrival-time choice is derived using cumulative prospect theory. The model is able to explain the influence of behavioral characteristics on the choice of departure time. First, optimal solutions are derived explicitly for both early and late-arrival prospects. It is shown that the optimal solution is a function of a subjective measure, namely, the gain–loss ratio (GLR), indicating that the actual arrival time of a commuter depends on his or her attitude to the deviation between gains and losses. Some properties of the optimal solution and the GLR are discussed. These properties suggest that the more that the pleasure of gain exceeds the pain of loss, the greater the correlation between actual and preferred arrival times. Finally, a sensitivity analysis of the results is performed, and the use of the model is illustrated with a numerical example based on a skew-normal distribution.     

基于近邻传播聚类的地铁运营时段划分

地铁在每天不同时段客流量差异较大,运营时段的科学划分,是低峰与高峰列车运行计划合理交替的前提。目前地铁运营时段划分主要依据人工经验,主观性强且难以保证精度。以10min为时间间隔,把全天运营时间6∶00～23∶00分为102个时间点样本,将地铁沿线各车站每个时间点的进站客流量作为样本描述变量。采用近邻传播聚类算法将各时间点归并为不同类别,并引入CH、Hart以及IGP等聚类有效性评估指标对聚类结果加以检验以确定最优类别数,从而得到运营时段的最优划分方案和最佳时段分割点。天津地铁二号线实例研究表明,基于近邻传播聚类算法得到的运营时段划分结果更能体现实际客流需求波动特性,在此基础上优化行车计划后,旅客等待时间明显下降。     

网格环境下制造资源优化配置的区间规划模型

针对网格环境下影响制造资源优化配置的关键参数具有区间性的特点,基于区间数建立了资源优化配置模型,以任务完工的总成本最低为目标,将资源的价格及任务的成本限制转换为区间数,并充分考虑了资源工作时间限制以及任务时间要求,给出线性区间规划模型及其解法,并通过算例分析表明该方法的可行性与有效性.该模型在反映市场需求以及应对市场变化基础上,可得出合理的优化配置方案.     

Three is easy, two is hard: open shop sum-batch scheduling problem refined

For the two-machine open shop sum-batch problem to minimize the makespan an optimal schedule is known to contain one, two or three batches on each machine, and finding a two-batch optimal schedule is NP-hard. We adapt the open shop algorithm by de Werra for finding a three-batch optimal schedule in linear time.     

Optimal investment, consumption and retirement choice problem with disutility and subsistence consumption constraints

In this paper we consider a general optimal consumption-portfolio selection problem of an infinitely-lived agent whose consumption rate process is subject to subsistence constraints before retirement. That is, her consumption rate should be greater than or equal to some positive constant before retirement. We integrate three optimal decisions which are the optimal consumption, the optimal investment choice and the optimal stopping problem in which the agent chooses her retirement time in one model. We obtain the explicit forms of optimal policies using a martingale method and a variational inequality arising from the dual function of the optimal stopping problem. We treat the optimal retirement time as the first hitting time when her wealth exceeds a certain wealth level which will be determined by a free boundary value problem and duality approaches. We also derive closed forms of the optimal wealth processes before and after retirement. Some numerical examples are presented for the case of constant relative risk aversion (CRRA) utility class.     

Nonlinear optimal feedback control for lunar module soft landing

In this paper, the task of achieving the soft landing of a lunar module such that the fuel consumption and the flight time are minimized is formulated as an optimal control problem. The motion of the lunar module is described in a three dimensional coordinate system. We obtain the form of the optimal closed loop control law, where a feedback gain matrix is involved. It is then shown that this feedback gain matrix satisfies a Riccati-like matrix differential equation. The optimal control problem is first solved as an open loop optimal control problem by using a time scaling transform and the control parameterization method. Then, by virtue of the relationship between the optimal open loop control and the optimal closed loop control along the optimal trajectory, we present a practical method to calculate an approximate optimal feedback gain matrix, without having to solve an optimal control problem involving the complex Riccati-like matrix differential equation coupled with the original system dynamics. Simulation results show that the proposed approach is highly effective.     

EQUIVALENCE OF THREE DIFFERENT KINDS OF OPTIMAL CONTROL PROBLEMS FOR STOKES EQUATIONS

This article presents an equivalence theorem for three different kinds of optimal control problems,which are optimal target control problems,optimal norm control problems,and optimal time control problems.Controlled systems in this study are internally controlled Stokes equations.     

Optimal Harvesting for a Logistic Population Dynamics Driven by a Lévy Process

The optimal harvesting problem for a stochastic logistic jump-diffusion process is studied in this paper. Two kinds of environmental noises are considered in the model. One is called white noise which is described by a standard Brownian motion, and the other is called jumping noise which is described by a Lévy process. For three types of yield functions (time averaging yield, expected yield and sustainable yield), the optimal harvesting efforts, the corresponding maximum yields and the steady states of population mean under optimal harvesting strategy are respectively given. A new equivalent relationship among these three different objective functions is showed by the ergodic method. This method provides a new approach to the optimal harvesting problem. Results in this paper show that environmental noises have important effect on the optimal harvesting problem.     

On optimal operating conditions for a data processing system: A stochastic approach

In this paper, we consider the problem of determining optimal operating conditions for a data processing system. The system is burned‐in for a fixed burn‐in time before it is put into field operation and, in field operation, it has a work size and follows an age‐replacement policy. Assuming that the underlying lifetime distribution of the system has a bathtub‐shaped failure rate function, the properties of optimal burn‐in time, optimal work size and optimal age‐replacement policy will be derived. It can be seen that this model is a generalization of those considered in the previous works, and it yields a better optimal operating conditions. This paper presents an analytical method for three‐dimensional optimization problem. An algorithm for determining optimal operating conditions is also given. Copyright © 2007 John Wiley & Sons, Ltd.