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升级   38.4% TA的每日心情 | 慵懒 2013-5-29 19:03 |
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签到天数: 185 天 [LV.7]常住居民III
群组: 2012第三期美赛培训 群组: 数学建摸协会 群组: 科技写作基础培训 群组: 中国矿业大学数模培训 群组: 数学建模培训课堂2 |
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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