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    发表于 2012-1-7 21:23 |只看该作者 |倒序浏览
    |招呼Ta 关注Ta
    本帖最后由 wuyuwenxmyz 于 2012-1-8 00:12 编辑

    参赛题目:
    A题   交巡警服务平台设置与调度模型
    摘 要
    本文针对城市中的交巡警服务平台设置与调度问题,根据不同的假设分别建立了五个模型.解决了关于交巡警平台布局以及管理范围分配等问题,为交巡警服务平台的设置与调度提供了有力的理论参考.
            模型一首先运用Floyd算法求出了A区各个路口与各个交巡警服务平台间的最短路径,得到一个的距离矩阵.通过定义最短距离优先原则,我们为各交巡警服务平台分配了管辖范围,并且“实际管辖分配率”达到了最大,基于这个模型,我们运用Voronoi对A区域进行了区域划分.之后我们对该模型中部分路段无法确定归属的情形进一步分析,设计了一个基于分配路段的分配方案,较好地弥补了模型一的不足.
    模型二将交通要道的快速全封锁问题简化为一个非标准指派问题,并得到了一个目标函数.我们通过增加虚拟路口使该非标准指派问题转化为一个标准指派问题,并运用改进匈牙利算法进行求解,得到一个全局最优解,即“行动时间”为8.0155,继而得到最优的快速全封锁策略.
    模型三中我们对出警时间与工作量分配定义了优先级.基于该优先级,我们优先考虑“3分钟到达”的情形并进行优化,新增了29、39、61、92这四个交巡警服务平台,使A区所有路口均能满足3分钟内可以到达.之后我们通过局部求最均衡工作量,运用贪心算法重新划分24个交巡警服务平台管辖区域,使各服务平台工作量均衡度得到提高.
    模型四中我们对区域面积、人口、发案率、巡警服务站点个数四个指标进行了数据分析,发现区域面积、人口与巡警服务站台个数不相关,从而排除了这两个指标量的干扰.在模型三所定义的优先级下,首先对全市现有交巡警服务平台设置的合理性进行评价.这里我们基于实际情况,定义了一个“6分钟到达原则”,发现D,E两区设置不合理.为解决这一不合理问题,我们考虑重置交巡警服务平台位置,运用模拟退火算法进行了100000次迭代,得到最优解.对于偏差较大的数据,根据实际情况,增设了一至二个服务平台.最后运用模型三对工作量分配的优化方法,对全市交巡警服务平台重新划分了管辖区域.
    模型五中我们假定犯罪嫌疑人速度为60km/h.在设定围堵方案时,考虑了犯罪嫌疑人的所有逃逸路线,将其简化为一棵n叉树,将封堵路口及已经到达过的路口视为一个叶子结点.从而该问题转化为一个求解最小树的问题,我们通过MATLAB编程求解,给出了具体围堵方案.

    关键词:设置与调度问题 优先级 指派问题 贪心算法 模拟退火算法 




    B题   风电功率预测问题
    摘 要
    本文分别运用数据迭代、GM(1,1)灰色理论、ARMA和BP神经网络模型对该风电场2006年5月31日至6月6日各个时点的风电功率PA,PB,PC,PD,P4,P58进行预测,通过对预测误差的综合分析发现BP神经网络的精确度最高;研究第一问所得误差数据发现:机组数的增加会影响模型预测的精度,且众多风电机的汇聚会使得总体的预测误差减小.将ARMA模型与BP神经网络相结合可以有效高精度,但由于ARMA模型自身所存在的误差以及外界条件的影响,故风电功率预测精度不可能无限提高.
    对问题一,分别建立数据迭代模型、BP神经网络模型、GM(1,1)模型和ARMA模型,对5月31日至6月6日各个时点进行风电功率预测.迭代模型的误差范围是14.5%—22.7%,GM(1,1)的预测误差集中在45%左右,ARMA模型的预测误差范围约为16.3%—25%,BP神经网络的预测误差范围约为5.7%—20.4%,故BP神经网络模型预测效果最好.
    对问题二,通过计算问题一中四个模型的相对误差,并比较各组风电功率,四组总的风电功率值和58台机组的风电功率值得出随着机组数的增加会影响模型的预测精度这一结论.并通过相应的电工方面的知识对这一结论就行合理性解释.
    对问题三,我们对问题中的BP神经网络模型进行优化处理得到基于ARMA的神经网络模型,并且重新对问题一的要求进行求解,得到了更加精确的预测结果.通过MATLAB进行仿真画出相应的实际曲线和预测曲线的对比图,直观的反映了模型的正确性.并通过分析得出由于ARMA自身存在的误差以及机组发电功率受外部条件的风速,异常性气候等因素的影响造成不能无限提高风电功率的预测精度这一结论.

    关键词:风电功率预测 ARMA GM(1,1) BP神经网络 ARMA神经网络 




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    1号选手答卷
    A题翻译
    The setting and scheduling model for traffic patrol police service platform
    Abstract:This article aims at the problem of the traffic patrol police service platform setting and scheduling.Five models are built according to different hypothesis.It solves the problem of  traffic patrol police platform layout and the distribution of  management region.And it also provides a strong theoretical reference for the setting and scheduling of traffic patrol police service platform.
            In model one , the Floyd algorithm is primarily applied to seek the shortest path between each intersection in A area and each traffic patrol police service platform.Thus we get a 2092 distance matrix. By defining the shortest path first principle,we distribute the jurisdiction scope for every traffic patrol police service platform and make the actual jurisdiction distribution rate reach the maximum. Voronoi chart algorithm is used to regionalize the A area based on the model.Then  we do a further analysis about the situation that some section can not determine the ownership and design a distribution plan which based on distributing section to make up for the defect of model one.
            In model two, the problem of fast blockading all the major traffic artery is simplified into the non-standard assignment problem and a target function is found.We turn the non-standard assignment problem into a standard one by adding some virtual crossroads.The improved Hungary algorithm is applied to get a global optimal solution ,namely "action time" is 8.0155 . Finally we get the best strategy of fast blockading.
            In model three , the priority of responding time and workload distribution are defined.Based on this ,we give priority to the “three minutes arrive “ case and optimize it.Four traffic patrol police service platform called 29,39,61,92 are added to make sure that all the crossroads can be reached in three minutes .Then we explore the most balanced workload inlocal region and apply the greedy algorithm to redistrict  the jurisdictional areaof the 24 traffic patrol police service platform .Thus the  workload balanced degree of each service platform is improved.
            In model four , data analysis about the four indexes which include the regional area,the population, the incidence and the number of police service site is conducted.Area and population are found out not related to the number of police service platform.So the interference of the two indexes are ruled out .Based on the  definition of priority in model three ,the setting rationality of the existing service platform in the city is initally evaluated .Here a “six minutes arrive”principle is  defined based on the actual situation. Thus the setting of D and E district are thought  to be unreasonable.To solve this problem ,we consider resetting the traffic patrol police service platform position and use the simulated annealing algorithm to do  1000000 iteration to get the optimal solution. For the data with large deviations, one to two service platforms are added according to the actual condition.Finally, the optimization method of the workload distribution in model three is used to redistrict  the jurisdictional area of every traffic patrol police service platform in the city .
            In model five, the speed of the criminal suspect is assumed to be 6 km/h.While  setting the containment scheme,we think about all the escape routes of the suspect.The routes are simplified to a tree with n forks.And the sealing crossroads and  the crossing which have been reached are seen as leaf nodes. Thus the problem is transformed into solving a minimum spanning tree.It has been solved through  MATLAB programming and the specific containment scheme has been found.
    Keywords: setting and scheduling problem
            the priority   
            assignment problem  
             greedy algorithm  
             simulated annealing algorithm       


    1号选手答卷
    B题翻译
    The problem of wind power forecasting
    Abstract:This article applies data iteration, the GM (1, 1) grey theory, the ARMA model and the BP neural network model to forecast the wind power Pa, Pb, Pc, Pd, P4, P58 of the wind farm at all time points from May 31, 2006 to June 6.The accuracy of the BP neural network is thought to be the highest through the comprehensive analysis of prediction error.By studying the error data of question one,we can find out that the increase of wind turbines will affect the accuracy of model prediction and the wind motor converge will decrease general prediction error.The combination of the ARMA model and the BP neural network can improve accuracy effectively.But the prediction accuracy of wind power can not be increased infinitely due to the error of  the ARMA model and the influence of external fators.
            For question one , the data iterative model, the BP nerval network model,the GM (1, 1) model and the ARMA model are built to forecast the wind power at all time points  from May 31 to June 6. The results shows that the error range of the data iterative model is about 14.5% to 22.7%. The prediction error of the GM (1, 1) model is around 45%.The error range of the ARMA model is about 16.3%-25%.And the error  range of the BP neural network model is about 5.7% to 20.4%.So the BP neural network model is considered to have the best predictive result.
            For question two ,by calculating the relative error of the four models in question one ,and comparing the respective wind power ,the total wind power value of the four groups and the wind power value of the 58 units ,we can conclude that the   prediction accuracy of the model will be affected by the increase of the unit number . The corresponding electrical knowledge is used to explain the conclusion  reasonably .
            For question three , the BP nerval network model is optimized to build a new neural network model which is based on the ARMA.We solve the question one again and get a more accurate result.The comparsion chart about the prediction curves and the corresponding practical curves is drawn through the MATLAB simulation.The chart reflects the validity of the model intuitively.We analyse the chart and conclude that the prediction accuracy of wind power can not be increased infinitely due to the error of the ARMA model and the influence of external fators such as the wind speed and Abnormal climate.
    Keywords: wind power   
             ARMA   
             GM (1, 1)  
             the BP neural network
              the ARMA neural network       
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    2号选手答卷
    A题翻译
            In this **, we set up five models aimed at the installation and dispatch for platform of traffic police service based on different assumptions,which solved issues about the layout of traffic police platform and distribution of management scope and provides a strong theoretical reference for the installation and dispatch for platform of traffic police service.
            Model 1 get the shortest path between every intersection and every traffic patrol service platform in section A using Floyd algorithm,and get a distance matrix of 20*92. We make a distribution of management scope for platform of traffic police service by defining the priority principle of short distance,and the ratio of the actual distribution of Jurisdiction reaches the highest,we use Voronoi figure algorithm to make a regional division of region A,and later we make a further analysis of the situation where we can not determine the ownership of some sections in this model.We raised a distribution solution based on distribution section which has made up for the disadvantage of model1.
            Model 2 transfer the problem of block of all traffic arteries quickly to a non-standard assignment problem as simplization, and solve it through improved Hungary algorithm,gaining a global optimal solution,that is the action time is 8.0155,and then get optimal strategy for fast full blockade.
            In model 3,We define the priority of the police time and workload distribution,we give the situation of “reach in 3 minutes”priority and optimize it based on this priority,and add 29,39,61,92 these 4 platforms of traffic patrol service to guarantee all intersections can be reached in 3 minutes,and then we get the most balanced workload in the local and redivide the jurisdiction of 24 platforms of traffic patrol service using greedy algorithm,to improve the equilibrium degrees of workload of service platforms.
            In model 4 we make data analysis of four indicators ,which are regional area, population, crime rate and the number of patrol service site,and find that regional area, population and the number of patrol service site are irrelevant, thus exclude the interference of these two indicators.In the priority defined in model 3, first, evaluate the reasonableness of the city's existing platforms of traffic police service.Accoring to the actual situation,we define a “reach in 6 minutes principle”here,finding that the setting of region D and E is unreasonable.To solve this problem,we consider to reset the location of the platform,and we carry out iterations for 100000 times using simulated annealing algorithm and get the optimal solution.As to the data with large deviation, we
            add 1 or 2service paltform according to the fact.Finally, redivide the jurisdiction of the city’s platforms of traffic patrol service using the approach to optimize the workload in model3.
              In model 5,we assume that the speed of the suspect is 60km/h. Take all the escape routes the suspect might choose into account when setting containment programs, Simplify it to an n-ary tree, and treat the block intersections and junctions have been reached as a leaf node.Thus we transfer it into a question aimed to seek a minimum spanning tree.We have solved it through MATLAB,and provided detailed containment program.


    2号选手答卷
    B题翻译
            This ** makes predictions about the wind power PA PB PC PD P4 P58 of every time during May 31th,2006 to June 6th in the wind power station, respectively use date iteration Model,GM(1,1)grey theory Model,ARMA Model and BP Neural Network Model.Through the comprehensive analysis of the prediction error,we find that BP Neural Network has the highest accuracy;the discussion about  error information of question1 shows that increase in the number of units can affect the accuracy of model prediction,and the convergence of a number of wind turbine will decrease the integral prediction error.The combination of ARMA Model and BP Neural Network Model will increase the accuracy effectively, but it can not increase infinitely as ARMA Model has error itself and the influence of external conditions.
      For question 1, create date iteration Model,GM(1,1)grey theory Model,ARMA Model and BP Neural Network Model to make predictions about wind power of every time during May 31th,2006 to June 6th.The iteration Model is within an error range between 14.5 percent to 22.7 percent, GM(1,1)grey theory Model is concentrated about 45 percent, ARMA Model is between 16.3 percent to 25 percent, and BP Neural Network Model is between 5.7 percent to 20.4 percent,so BP Neural Network Model has the best prediction.
      For question 2, by calculating the relative error of the four models in question 1,and compare the wind power in every unit,the total wind power,and the power of 58 units,we can conclude that increase in the number of units can affect the accuracy of model prediction,and make rational explantion about it by corresponding knowledge of electrician.
       For question 3,we can get Neural Network Model based on ARMA by the optimization of BP Neural Network Model in the question,and re-solve question 1,and get more accurate prediction result. Draw the comparison chart of actual curve and the corresponding prediction curve through MATLAB, which reflects the validity of the model intuitively,and conclude that the wind power can not increase infinitely as ARMA Model has error itself and the influence of external conditions ,such as Wind speed and abnormal climate.
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    3号选手答卷
    A题翻译
    The novel model suited for setting and scheduling platforms of police and patrol service
    Abstract :In order to tackle the problem of setting and scheduling platforms of police and patrol service,this ** constructs five models on the basis of different assumptions,and it solves the difficulties in platform layout of police and patrol service,along with the distribution of management scopes,and so on,which provides a strong theoretical reference to the solution of setting and scheduling platforms of police and patrol service.
      In the first model,we use the Floyd Algorithm to get a 20*92 distance matrix of the shortest path between crossroads and platforms of police and patrol service in region A.By defining the priority principle of shortest distance,different management scopes are distributed for every platform ,** the rate of actual presidial distribution largest.On the basis of this model,we divide region A with the use of Voronoi Diagram Algorithm,and then a further analysis about the situation where part of the roads cannot determine their affiliation is made to design an allocation scheme based on distribution sections,which perfectly make up for the deficiency of the first model.
      In the second model,the entire fast blockade problem of traffic main artery is simplified as a nonstandard assignment problem with an objective function.We convert this nonstandard assignment problem into a standard assignment problem through the increase of virtual intersections,and then the improved Hungary Algorithm is used to solve this problem.Consequently,we get a global optimal solution whose action time is 8.0155,with the optimal entire fast blockade strategy.
      In the third model,priorities in the patrol schedule and workload distribution are defined.Considering this case,we prefer to firstly take "Arrive within 3 minutes" situation into account,and optimize it by adding four platforms,namely 29,39,61,92 to satisfy the condition of arriving within 3 minutes for all the crossroads in region A.Subsequently,for the purpose of working out the most balanced partial workload,Greedy Algorithm is used to redistrict the management scopes of 24 service platforms,which improves the balanced degree of workload in every service platform.
      In the fourth model,according to the analysis of the data of four indexes,namely region area,population,incidence rate,the number of police service sites,we find that the region area and population are irrelevant with the number of service sites.As a result,we rule out the interference of these two indexes.Next,based on the priorities defined in the third model,evaluations are made to assess the rationality of the current setup of police and patrol service platforms.Considering the actual situation,we define the "Arriving within 6 minutes principle",discovering the inconsequences in region D and region E.To settle this matter,we consider to reset the positions of service platforms.With the simulated annealing algorithm,we make 100000 iterations and get the optimal solution.For some data with great deflection,one or two platforms are added according to the actual situation.Finally,by the optimal strategy on workload distribution given in the third model,we redistrict the management scopes of police and patrol service platforms in the whole city.
      In the fifth model,suppose the velocity of a suspect is 60km/h,and considering all the potential escape routes,we simplify this problem as a N binary tree,with sealing crossroads and intersections having been passed by regarded as leaf nodes in the process of designing ring-fence scheme.Thus,this problem can be transformed into a minimum spanning tree solution.Consequently,we work out a specific ring-fence scheme by using MATLAB software.
    Key Words: setting and scheduling problem, priority, assignment problem, Greedy Algorithm, simulated annealing algorithm


    3号选手答卷
    B题翻译
    The prediction problem of wind electric power
    Abstract:With data iteration model,Grey system theory GM(1,1) model,ARMA model and BP neural network model,this ** predicts six wind electric powers PA,PB,PC,PD,P4,P58 at several time points in the wind farm from 31st May in 2006 to 6th June.According to the comprehensive analysis of prediction errors,we find that BP neural network model has the most accurate results.In the error data of the first question,we have the increase in the number of motor groups will influence the accuracy of model prediction,and the convergence of numerous wind electric motors can reduce the overall forecasting errors.In addiction,the precision can be effectively improved by combining ARMA model with BP neural network model.However,due to the intrinsic error of ARMA model and the influence of the external conditions,the prediction accuracy of wind electric powers cannot be improved infinitely.
      For the first question,we construct data iteration model,Grey system theory GM(1,1) model,ARMA model and BP neural network model to predict wind electric powers at several time points from 31st May in 2006 to 6th June.The error range of data iteration model varies from 14.5% to 22.7%,while that of Grey system theory GM(1,1) model mainly concentrate on 45%,and that of ARMA model and BP neural network model are from 16.3% to 25% and from 5.7% to 20.4% respectively.Thus,BP neural network model is the best one.
      For the second question,on the basis of results in the first question,comparing the wind electric powers of each motor group,the total wind electric powers of four motor groups,and the wind electric powers of 58 motor groups,we conclude that the increase in the number of motors groups will influence the accuracy of model prediction.At the same time,we give reasonable explanations about this conclusion combining with corresponding knowledge in electrician aspects.
      For the third question,we optimize the BP neural network model and then get the neural network model based on ARMA.Further more,we recompute the first question and get more accurate prediction conclusions.By drawing out the comparison chart of the corresponding actual curve and predicted curve with MATLAB simulation,the accuracy of this model is directly reflected.In addition,through the analysis of this experiment,we have the prediction accuracy of wind electric powers cannot be improved infinitely due to various factors like the intrinsic error of ARMA model,wind speed,abnormal climate,and so on.
    Key Words:wind electric power, ARMA, GM(1,1), BP neural network, ARMA neural network
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    4号选手答卷
    A题翻译
            The set and dispatch models for the police patrol service spots
    Abstract

    In this work, the set and dispatch of the police patrol services are discussed. Specifically, five models are constructed and solved based on five different assumptions. These models address the problems such as the distribution of the traffic police patrol service spots (TPPSS) as well as the range of their area-of-charge and provide theoretical support for the setting-up and the management of the traffic police patrol system.

    Model one uses the Floyd algorithm to compute the shortest distances from each intersection to the TPPSS’ in certain region A. This gives a 20 by 29 distance matrix. Furthermore, based on the principle that the shortest distance takes the highest priority, an area-of-charge is assigned to each of every TPPSS’. By doing so, the “practical area-of-charge” is maximized. Based on such model, the Voronoi algorithm further partitions the region A. In addition, the areas with coverage ambiguity are further analyzed. Such analysis provides a new dispatching strategy which nicely complements certain draw-backs of the original model.

    The second model converts the rapid arterial highway blockage situation to a non-standard assignment problem and obtains an objective function. Furthermore, virtual intersections are added which transfer the non-standard model to a standard one, which is further solved, in a global optimal sense, by the Hungarian algorithm. 8.0155 second is computed as the “action time” which further gives the optimal rapid blockage strategy.

    In the third model, different priorities are assigned to police dispatching times and their work-loads. Based on such priority list, we optimize the situation according to the “three-minute arrival” promise by adding the 29th, 29th, 61st, and 92nd TPPSS’. As a result, all the intersections can be approached within three minutes. In addition to that, we compute the local equilibrium work-load and re-arrange the area-of-charge for the 24 TPPSS’ with greedy algorithm. Finally, the variation among the work-load for each TPPSS is reduced.

    In the forth model, we analyze the correlations among the four factors: area, population, crime rate, and number of TPPSS. The analysis indicates that the area and the population is not correlated with the number of TPPSS. Therefore, with those two factors removed, the necessity of each TPPSS in the entire city is evaluated. Here, based on the practical situation, the arrival promise is relaxed to six minutes and we found that the TPPSS D and E are not necessary. To that end, we re-allocate all the TPPSS’ with simulated annealing algorithm (100,000 iterations). For data with relative large variations, for practical reason, one or two TPPSS’ are added. Finally, based on the work-load dispatching strategy in model three, the area-of-charge for the TPPSS’ are re-arranged.

    In model five, assuming the suspect has a fleeing speed of 60km/h, we aim to design an optimal besiege strategy. To that end, we consider all the possible paths as a tree structure in which the blocked and arrived intersections as leaves. By doing this, the original problem can be solved by minimal spanning tree algorithm. With Matlab programming, detailed blockage strategy is provided.

            Key words: set and dispatch, priority assignment, greedy algorithm, simulated annealing.
           
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            Abstract
            In this **, we focus on the prediction of wind power. Our main goal is to reach an accurate prediction result as much as possible. To achieve this, firstly, we compare prediction results of four varied models. Next, we discuss the factors that influence the predictive accuracy based on the previous discussion. Finally, we present a novel model to solve the problem.
            First, we present four models:data iteration model, GM (1, 1) gray model, Auto-Regressive and Moving Average Model (ARMA) and BP neural network model, predicting the wind power of various points from May 31 to June 6, 2006. And we found that BP neural network works best.
            Secondly, we calculate the relative errors of the four models, and conduct a comprehensive comparison. Then we reach a conclusion: With the increasing of the number of units, the accuracy of predictions had been affected.
            Finally, we develop a novel neural network model based on ARMA, in order to reach a more accurate result. Moreover, the correctness of the model has been proved. Even so, the accuracy of predictions can’t go higher due to inevitable factors like abnormal climate.
           
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