考虑Pareto最优的列车运行图与维修天窗协调优化

列车运行图与维修天窗之间的冲突始终无法避免,且维修天窗开设时间的长短显著影响列车总运行时间。针对此问题,综合考虑维修天窗对列车运行造成的限速约束、车站到发线数量约束等,建立列车总运行时间最小,以及维修天窗实际开设时长与理想时长总偏差最小的双目标混合整数规划模型;对困难约束设置中间辅助变量将模型线性化以提高求解效率,并设计约束转换算法求解双目标模型的Pareto最优;微观化处理铁路线,将站内资源和站间资源细化为一系列行车资源单元,得到更加符合实际旅客运输需求的运行图。以某地区铁路线夜间开行列车及维修天窗开设计划为研究背景,调用商业软件求解双目标函数模型的Pareto最优,并对双目标模型的最小支配解和最优支配解进行对比分析;针对最优支配解下的列车进入、离开行车资源单元的时间、停站作业时间及维修天窗的开始时间及开设时长,绘制列车运行图。求解结果表明:模型在满足维修天窗最小开设时长的同时,能够兼顾列车运行总时间最小和维修天窗开设时长更充裕。基于最优支配解绘制的列车运行图表明:微观路网下的列车运行时刻表优化结果更符合实际旅客运输生产作业需要。研究结果可为铁路运营管理部门进一步优化列车运行图编制与维修天窗开设提供参考。

面向供应链分销的多维空间Pareto边界自动谈判模型研究

随着电子商务的快速发展,自动谈判逐渐成为提升供应链系统效率的一种手段。为了优化多方参与的供应链分销谈判应用,本文将多边多属性谈判问题转化为多目标优化模型,采用改进的非支配遗传算法NSGA-Ⅲ计算多维空间的Pareto边界;然后,设计多线程谈判模型,将参与多方谈判的买卖各方拆解为多个双边谈判线程,分别在多维Pareto边界上进行谈判;进而,采用动态时间依赖策略(DTD),使Agent根据对方报价在Pareto边界上动态调整让步策略,快速达成协议。为验证模型的有效性,本文进行了大量模拟自动谈判实验。实验结果表明,所提出的改进算法和谈判流程优于领域最新研究成果,能有效提升多边多属性谈判效率,有助于多方达成共赢局面。

基于Pareto蚁群算法的双目标路径规划研究

针对复杂建筑环境人员应急疏散单一路径不能满足火灾环境变化需求的问题,基于改进蚁群算法,结合Pareto双目标解集思想,提出一种组合优化解集的双目标蚁群算法,通过排序优化的思想,实现人员多路径动态疏散规划。在构造Pareto解集的阶段协同考虑疏散路径长度以及火灾风险程度2个优化目标,计算各个解之间的支配关系。利用排序优化蚁群算法的正反馈机制将各组解的信息素按一定比例作为最优路径信息素的积累,加快解集的寻找。最后将其与传统双目标蚁群算法相比较,结果表明:优化后的双目标算法更加适合复杂建筑人员疏散路径规划问题,在寻找多组满足要求解的同时展示目标之间的利弊关系,供决策者选择合适的路径,提高疏散效率。

Pareto解集旋转的分类多策略预测动态多目标优化

为更有效地解决Pareto解集(Pareto set,PS)旋转的动态多目标优化问题,提出PS旋转的分类多策略预测方法(rotation-based forecasting method,RFM)。将PS的旋转类型分为PS中心点旋转、PS原点旋转和非标准旋转;针对以上不同的PS旋转类型,自适应地选择合适的预测模型,建立不同点集的时间序列,为后续进化提供初始种群。引入拉丁超立方策略(Latin hypercube strategy,LHS)生成的随机种群与上述预测种群共同构建新种群,保证种群的多样性。为验证算法的有效性,将RFM算法与DNSGA-II、PPS、SPPS和MMP算法在8个标准的动态测试函数上进行实验对比。实验结果表明,RFM算法取得了6个最优IGD值、7个最优SP值、3个最优MS值,证明了RFM算法可以更有效地解决基于PS旋转的动态多目标优化问题。同时验证了RFM算法的普适性,在FDA系列函数上进行实验对比,实验结果表明,该算法在处理非旋转的动态多目标优化问题中仍具有较优性能。

双边定时截尾下Pareto分布的参数的极大似然估计的EM算法

给出了当寿命分布为Pareto分布时,双边定时截尾寿命试验下形状参数的极大似然估计。由于似然方程形式较复杂,无法得到参数的显式表达式。但可证明此极大似然估计是唯一存在的,并利用EM算法求出了此参数的一种估计。

Pareto法分析66例急性中毒住院儿童病例特点及药学建议

目的通过分析急性中毒住院儿童病例,总结病例特点及规律,为预防和减少儿童急性中毒提供科学依据。方法采用帕累托图(Pareto)法回顾性统计分析医院因急性中毒而收治住院的66例儿童病例资料,对患儿年龄分布、中毒季节、引起患儿中毒的品种分布、药品种类分布、剂型分布特点进行统计分析。结果儿童急性中毒年龄、季节、中毒品种、中毒药物剂型的主要因素有:1~3岁,第二、三季度,药品,片剂。中毒药品的主要因素为中枢神经系统用药、心血管系统用药、呼吸系统用药、影响变态反应药物。中毒药物例次最多的为氯硝西泮片。结论急性中毒以1~3岁儿童为主;主要发生在第二、三季度;以药品为主,剂型以片剂为主;国家有关部门应进一步完善相关立法、推广儿童药品安全包装、控制处方限量等源头控制;通过增强科普教育及监护人安全意识,进而有效降低儿童急性中毒的发生率。

基于Pareto-GA多目标的企业管理系统优化研究——以某造纸厂为例

传统造纸厂管理优化通常只针对单一目标,忽略了质量和安全等重要方面。因此,提出了一种面向造纸厂的多个目标优化方法,并结合Pareto排序以及遗传算法搜索机制改进的Pareto-遗传算法作为求解方法,以实现对造纸厂监管系统的优化设计。研究结果显示,使用Schaffer's F6 Function进行测试时,改进的Pareto-遗传算法在72次迭代后达到最大适应度值0.93,优于其他两种算法。进一步将工期、成本、质量和安全多目标问题分解为两个子问题,成功获得3组Pareto最优解,为管理者提供不同需求下的优化方案。同时,提出的造纸厂管理系统优化设计方案能够提升造纸厂管理的效率和安全性,具有重要的理论价值和实际应用前景。

Improved non-dominated sorting genetic algorithm (NSGA)-II in multi-objective optimization studies of wind turbine blades

The non-dominated sorting genetic algorithm （NSGA） is improved with the controlled elitism and dynamic crowding distance. A novel multi-objective optimization algorithm is obtained for wind turbine blades. As an example, a 5 MW wind turbine blade design is presented by taking the maximum power coefficient and the minimum blade mass as the optimization objectives. The optimal results show that this algorithm has good performance in handling the multi-objective optimization of wind turbines, and it gives a Pareto-optimal solution set rather than the optimum solutions to the conventional multi objective optimization problems. The wind turbine blade optimization method presented in this paper provides a new and general algorithm for the multi-objective optimization of wind turbines.

Non-dominated sorting quantum particle swarm optimization and its application in cognitive radio spectrum allocation

In order to solve discrete multi-objective optimization problems, a non-dominated sorting quantum particle swarm optimization (NSQPSO) based on non-dominated sorting and quantum particle swarm optimization is proposed, and the performance of the NSQPSO is evaluated through five classical benchmark functions. The quantum particle swarm optimization (QPSO) applies the quantum computing theory to particle swarm optimization, and thus has the advantages of both quantum computing theory and particle swarm optimization, so it has a faster convergence rate and a more accurate convergence value. Therefore, QPSO is used as the evolutionary method of the proposed NSQPSO. Also NSQPSO is used to solve cognitive radio spectrum allocation problem. The methods to complete spectrum allocation in previous literature only consider one objective, i.e. network utilization or fairness, but the proposed NSQPSO method, can consider both network utilization and fairness simultaneously through obtaining Pareto front solutions. Cognitive radio systems can select one solution from the Pareto front solutions according to the weight of network reward and fairness. If one weight is unit and the other is zero, then it becomes single objective optimization, so the proposed NSQPSO method has a much wider application range. The experimental research results show that the NSQPS can obtain the same non-dominated solutions as exhaustive search but takes much less time in small dimensions; while in large dimensions, where the problem cannot be solved by exhaustive search, the NSQPSO can still solve the problem, which proves the effectiveness of NSQPSO.

Multi-objective optimization of water supply network rehabilitation with non-dominated sorting Genetic Algorithm-II

Through the transformation of hydraulic constraints into the objective functions associated with a water supply network rehabilitation problem, a non-dominated sorting Genetic Algorithm-II (NSGA-II) can be used to solve the altered multi-objective optimization model. The introduction of NSGA-II into water supply network optimal rehabilitation problem solves the conflict between one fitness value of standard genetic algorithm (SGA) and multi-objectives of rehabilitation problem. And the uncertainties brought by using weight coefficients or punish functions in conventional methods are controlled. And also by in-troduction of artificial inducement mutation (AIM) operation, the convergence speed of population is accelerated;this operation not only improves the convergence speed, but also improves the rationality and feasibility of solutions.

由Chvátal定理引出的关于Weibull分布和Pareto分布的研究

受Chvátal定理的启发,本文研究了随机变量不超过其期望的概率的下确界问题.利用分析的方法,我们得到了当随机变量的分布为Weibull分布或Pareto分布时该随机变量不超过其期望的概率的下确界.

GREEDY NON-DOMINATED SORTING IN GENETIC ALGORITHM-ⅡFOR VEHICLE ROUTING PROBLEM IN DISTRIBUTION

Vehicle routing problem in distribution （VRPD） is a widely used type of vehicle routing problem （VRP）, which has been proved as NP-Hard, and it is usually modeled as single objective optimization problem when modeling. For multi-objective optimization model, most researches consider two objectives. A multi-objective mathematical model for VRP is proposed, which considers the number of vehicles used, the length of route and the time arrived at each client. Genetic algorithm is one of the most widely used algorithms to solve VRP. As a type of genetic algorithm （GA）, non-dominated sorting in genetic algorithm-Ⅱ （NSGA-Ⅱ） also suffers from premature convergence and enclosure competition. In order to avoid these kinds of shortage, a greedy NSGA-Ⅱ （GNSGA-Ⅱ） is proposed for VRP problem. Greedy algorithm is implemented in generating the initial population, cross-over and mutation. All these procedures ensure that NSGA-Ⅱ is prevented from premature convergence and refine the performance of NSGA-Ⅱ at each step. In the distribution problem of a distribution center in Michigan, US, the GNSGA-Ⅱ is compared with NSGA-Ⅱ. As a result, the GNSGA-Ⅱ is the most efficient one and can get the most optimized solution to VRP problem. Also, in GNSGA-Ⅱ, premature convergence is better avoided and search efficiency has been improved sharply.

基于Pareto控制的多目标PSO算法在铣削参数优化中的应用

工艺参数是影响零件加工质量和效率的关键因素,工艺参数的优化和调节是改善加工工艺的最有效方法。针对铣削加工参数优化问题,提出了一种基于应用实例的多目标切削参数优化方法。首先,以材料去除率、切削力和刀具寿命为目标函数,建立了统一的切削工艺参数多目标优化数学模型。随后,使用切削数据对目标函数进行组合,建立了该问题的数学模型,研究了适用的求解方法以获得最优解,并通过实验验证了参数优化的有效性。该方法可为加工参数的选择提供指导和依据。

极值服从广义Pareto分布的扭转载荷外推方法研究

提出了一种极值样本服从广义Pareto分布(generalized pareto distribution,GPD)函数的扭转载荷时域外推方法,基于极值样本的均值超出函数,首先确定一个区间范围,并以形状参数最小的均方误差为目标,通过自抽样法确定最佳阈值,再采用极大似然估计法对GPD函数的形状参数和尺度参数进行估计,获取扭转随机载荷谱的极值样本,服从GPD分布规律。以商用车驾驶室的稳定杆为研究对象,介绍了扭转载荷采集的方法,基于所提出的扭转载荷时域外推方法进行外推研究,并分别从穿级计数、功率谱密度、雨流图和潜在伪损伤量等方面对外推前后的载荷谱进行了对比分析。结果表明:所构建的载荷外推算法对商用车驾驶室稳定杆扭转载荷外推有较好适应性。

给定边数的超仙人掌图的第二大Pareto H-特征值

设λ_(2)(H)是超图H的第二大Pareto H-特征值,探讨了超仙人掌图的Pareto H-特征值,特别地,通过刻画超仙人掌的极值图,给出了超仙人掌图的第二大Pareto H-特征值的上界并刻画出了该上界所对应的极值超图.

求解多目标流水车间调度Pareto最优解的遗传强化算法

针对多目标流水车间调度Pareto最优问题,本文建立了以最大完工时间和最大拖延时间为优化目标的多目标流水车间调度问题模型,并设计了一种基于Q-learning的遗传强化学习算法求解该问题的Pareto最优解.该算法引入状态变量和动作变量,通过Q-learning算法获得初始种群,以提高初始解质量.在算法进化过程中,利用Q表指导变异操作,扩大局部搜索范围.采用Pareto快速非支配排序以及拥挤度计算提高解的质量以及多样性,逐步获得Pareto最优解.通过与遗传算法、NSGA-II算法和Q-learning算法进行对比实验,验证了改进后的遗传强化算法在求解多目标流水车间调度问题Pareto最优解的有效性.

An Optimization Approach for Convolutional Neural Network Using Non-Dominated Sorted Genetic Algorithm-Ⅱ

In computer vision,convolutional neural networks have a wide range of uses.Images representmost of today’s data,so it’s important to know how to handle these large amounts of data efficiently.Convolutional neural networks have been shown to solve image processing problems effectively.However,when designing the network structure for a particular problem,you need to adjust the hyperparameters for higher accuracy.This technique is time consuming and requires a lot of work and domain knowledge.Designing a convolutional neural network architecture is a classic NP-hard optimization challenge.On the other hand,different datasets require different combinations of models or hyperparameters,which can be time consuming and inconvenient.Various approaches have been proposed to overcome this problem,such as grid search limited to low-dimensional space and queuing by random selection.To address this issue,we propose an evolutionary algorithm-based approach that dynamically enhances the structure of Convolution Neural Networks(CNNs)using optimized hyperparameters.This study proposes a method using Non-dominated sorted genetic algorithms(NSGA)to improve the hyperparameters of the CNN model.In addition,different types and parameter ranges of existing genetic algorithms are used.Acomparative study was conducted with various state-of-the-art methodologies and algorithms.Experiments have shown that our proposed approach is superior to previous methods in terms of classification accuracy,and the results are published in modern computing literature.

A FLEXIBLE OBJECTIVE-CONSTRAINT APPROACH AND A NEW ALGORITHM FOR CONSTRUCTING THE PARETO FRONT OF MULTIOBJECTIVE OPTIMIZATION PROBLEMS

In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a given multiobjective programming problem. The presented scalarized problem extends the objective-constraint problem. It is demonstrated that how adding variables to the scalarized problem, can lead to find conditions for (weakly, properly) Pareto optimal solutions. Applying the obtained necessary and sufficient conditions, two algorithms for generating the Pareto front approximation of bi-objective and three-objective programming problems are designed. These algorithms are easy to implement and can achieve an even approximation of (weakly, properly) Pareto optimal solutions. These algorithms can be generalized for optimization problems with more than three criterion functions, too. The effectiveness and capability of the algorithms are demonstrated in test problems.

逐步增加Ⅱ型截尾下Pareto分布形状参数的Bayes估计

基于逐步增加Ⅱ型截尾样本,首先得出Pareto分布形状参数的极大似然估计,考虑两个损失函数和形状参数的两个先验分布,得出该分布形状参数的4个Bayes估计。由数值模拟结果发现,上述四个Bayes估计值的均方误差均小于极大似然估计值,其中,当损失函数为二次损失函数,形状参数的先验分布为共轭先验分布时的Bayes估计的均方误差较小,估计效果更理想,且实例分析与数值模拟结果相符。其次在二次损失函数下,针对形状参数先验分布选取共轭先验分布,给出Pareto分布形状参数的多层Bayes估计和E-Bayes估计。

基于Pareto解集的工业园区微网优化配置研究

工业园区各类能源耦合性较差,不同能源系统独立运行,能源利用率较低,需从多类能源互联集成和互补融合入手,提高能源的综合利用效率和可再生能源的利用率。提出了一种工业园区综合能源微网方案,以总成本、污染治理费、电网可靠性、风光互补性为目标函数和约束条件,建立了多能微电网优化模型。设计了一种基于Pareto最优解集的多目标差分算法并采用熵权法确定每个评价指标的权重,将多目标运算转化为单目标运算。仿真结果表明,该算法在微电网端可有效降低传统能源的消耗,加强清洁能源的有效利用,减少碳排放量并降低系统运行成本。