2012數(shù)學(xué)建模美賽論文1

1、for office use onlyt1 _t2 _t3 _t4 _team control number14820 problem chosenbfor office use onlyf1 _f2 _f3 _f4 _a computational-intelligence system for the river trip the big long river is well known as one of the natural wonders worldwide. besides viewing the spectacular landscape, an extremely attra

2、ctive recreational activity is river rafting on the big long river. given the rise in popularity of river rafting, the park managers have been asked to allow more trips to travel down the river. the paper develops a method to provide a management strategy by using statistical data and computational-

3、intelligence-system (cis). cis is a computer program that models complicated, dynamic camp sites number y interactions in the river corridor of the big long river. the system employs a data acquisition and simulator system. the database is a 1813 matrix which gives every trips travel arrangement. th

4、e computer simulation contains data analysis and artificial intelligence in creating an individual-based modeling system. the paper mainly use the model of the computational-intelligence-system(cis) to search for how to make the optimal management strategies which mainly contain two parts: the first

5、 part: the optimal schedule cis obey the principles of no two sets of campers can occupy the same site at the same time. cis can put out the specific distribute of the camping sites, and the optimal schedules according to the value of the variables.the second part: transfer problem according to the

6、results of the first part, the table about changing boats can be obtained through calculation. finally, using program, assume y=25, we gain a optimal schedule, named table 4. the table shows that the park entertains 318 travel trips in a tourist season, and the choice of ship types also is showed in

7、 the table 5.contentsanalysis of the sweet spot.11 introduction.1 1.1 background 1 1.2 problem 12 assumptions.23 symbols and definitions .24 model.24.1 analysis of the issue 1.24.1.1 what is the “carrying capacity” of the river.24.1.2 the situations that adapt the “carrying capacity”.34.1.3 result o

8、f the issue 1 .34.2 analysis of the issue 2.34.2 .1 what is the meaning of fully used camping sites?.34.2.2 how to make the best arrangement?.34.2.3 result of the issue 2 .74.3 analysis of the issue 3.114.3.1 why should passengers need to change boats?.114.3.2 how to decide which boat should use?.11

9、4.3.3 result of the issue 3 .125 strengths and weakness of the model.136 references.137 appendix 148 memo 17 team # 14820 page 1 of 171 introductionthe big long river is well known as one of the natural wonders worldwide. besides viewing the spectacular landscape, an extremely attractive recreationa

10、l activity is river rafting on the big long river. river trips are directed by schedules, which show the day trips start, the nature of any passenger exchanges that occur, and the day and location where the trips over .the model in this study will help the park managers make a determine to allow mor

11、e trips to travel down the river. 1.1 backgroundthe big long river(225 miles) is inaccessible to hikers, if you want to experience a wilderness life, you have to take a river trip that requires a few days camping. all trips must be start from first launch to final exit end. the trips have different

12、types, you can select 6 to 18 nights either way. besides, you can also choose two different travel ways, one is oar- powered rubber raft, which travels on average 4 mph, the other is motorized boat, which travels on average 8 mph.1.2 problemthe growing number of tourists in recent years, scenic area

13、s need a program so that more visitors can enjoy themselves. the question asks us to schedule an optimal mix of trips and make sure the campsites could be utilized in the best way possible, no matter which kind of boats.currently there are y camp sites on the big long river, which distributed fairly

14、 uniformly throughout the river corridor. and the big long river accepted x trips each year, but it opened only six months each year because of the cold for river trips in the rest month of the year. in addition to the above conditions, we should remember that no two sets of the campers can occupy t

15、he same site at the same time and with minimal contact with other groups of boats on the river.ultimately, taking into account the above conditions, we should give a reasonable time schedule so that the more trips can travel down the big long river. in fact, the questions include 3 parts as follows:

16、 how to balance the carrying capacity of the big long river? how best to make full use of the camping sites? when should people change boats?team # 14820 page 2 of 172 assumptionssuppose that the camping sites only fairly distribute along one side of the river.suppose that all the trips obey the arr

17、angements of the scenic when travelling.suppose that the weather of the scenic is good in 6 months.suppose that drifting only during the daytime, people must stay at the camping sites during the nights.boat speed is defined here as the average of the speed of the big long river. 3 symbols and defini

18、tions x represents the total trips in 6 months. y represents the total numbers of the camping sites. n is the total times that camping sites to be used in 29 days. m is the number of camping sites which could be used in 29 days. w is the camping point of utilization. is the numbers of the ith teams

19、ik k is the number of all the teams in 29 days travel. 4 model4.1 analysis of the issue 14.1.1 what is the “carrying capacity” of the river?what is the scientific definition for carrying capacity? carrying capacity refers to the maximum population that a given environment and resource base can susta

20、in. understanding the impacts of human recreation on natural resources is of critical importance in constructing effective management strategies. according to this problem ,it means that the maximum number of trip boats can be accepted by the big long river ever half of a year. the experience tells

21、us that if the machine works all day without rest, it will soon get some trouble. so all machines have regular working time. it is similar to the big long river.team # 14820 page 3 of 174.1.2 the situations that adapt the “carrying capacity”.clearly, less trip boats make better carrying capacity. bu

22、t it will get less income for the scenic. so we use the machine working model to describe the rivers carrying capacity . each month the park has one day closed. thus, the big long river can both accept more people and its carrying capacity is still maintain a balance. 4.1.3 the result of issue 1cons

23、idering the open days of the big long river,we assume that drifting in the same way in each month. that is to say the trips are in cycle for every month.thats more easier for manager to arrange the drifting plan. also we assume the open days of each month is 29 days.so the open days of the scenic ar

24、e 174 days(296=174) each year in total. in this way the river could get the opportunity to relieve stress,and the scenic could earn as much as possible.after all,the environmental factors are very important. 4.2 analysis of the issue 24.2.1 what is the meaning of fully used camping sites?according t

25、o the first problem,the trips are in cycle for every month.all trips need to travel in the day time,so the camping sites should be used as many as possible at night.and then the scenic would have much chance to offer traveler better service.4.2.2 the application of the cis(computational-intelligence

26、-system)obeying the principles of no two sets of campers can occupy the same site at the same time, a computational-intelligence-system (cis) is a computer program that models complicated, dynamic camp sites number y interactions in the river corridor of the big long river. the system employs a data

27、 acquisitionand simulator system. the data acquisition is a 18*13 matrix which give every trips travel arrangement at night within the extent of the big long river service. the computer simulation contains data analysis and artificial intelligence in creating an individual-based modeling system.the

28、paper mainly use the model of the computational-intelligence-system(cis) to search for how to make the best management strategieswe know there are 18 camping sites along the river at least .in order to simplify the problem, assuming that a total of 25 spacing uniform distribution of camping sites. a

29、ccording to the principles of drifting the same distance everyday.we team # 14820 page 4 of 17can also find out 13 different types of trips,which have different travel days,from 6 to 18 nights.now we can list 13 different drift mode of camping locations. shown in table 1.table 1the camping locations

30、 of 13 different drift modethen we need to calculate the schedule of optimal mix of trips, of varying duration on the basis of no two sets of campers can occupy the same site at the same time .for this purpose we establish the model of computational-intelligence-system (cis ).the value of simulation

31、 methods as a tool for understanding and managing natural resources is evident. we set cycle of the schedule 29 days in order to facilitate management to manage and make the river set aside a certain purification time. there are y camp sites on the big long river, distributed fairly uniformly throug

32、hout the river corridor. we arrange camp sites in turn :1, 2, 3,4.y.stept1: according to the basic principle of the same daily driving distance for each trip in the course of travel we arrange camping trips per night to stay at the nearest site,we build 1813 matrix, the rows represent the number of

33、travel nights ,and the columns represent the order of nights.the number in the matrix is the number of camping sites.(shown in table 2) we define this 1813 matrix g.stept2: traverse the first row of the g matrix,if (ijk),retain only kjiaaa111ia1column and deletecolumns ,if is diffident from all the

34、other elements kjaa1,1ia1in the first row retaincolumn. after the program we get a new matrix,we define this ia1matrix g(1).stept3:travel typescamping sites6 nights4,8,13,17,21,257 nights4,7,11,1418,21,258 nights3,6,9,13,16,19,22,259 nights3,6,8,11,14,17,19,22,2510 nights3,5,8,10,13,15,18,20,23,2511

35、 nights2,5,7,9,11,14,16,18,20,23,2512 nights2,4,6,8,10,13,15,17,19,21,23,2513 nights2,4,6,8,10,12,13,15,17,19,21,23,2514 nights2,4,5,7,9,11,13,14,16,18,20,21,23,2515 nights2,3,5,7,8,10,12,13,15,17,18,20,22,23,2516 nights2,3,5,6,8,9,11,13,14,16,17,19,20,22,23,2517 nights1,3,4,6,7,9,10,12,13,15,16,18,

36、19,21,22,24,2518 nights1,3,4,6,7,8,10,11,13,14,15,17,18,19,21,22,24,25team # 14820 page 5 of 17 deform the g(1) matrix we will get a matrix,(0 means a one )3(00) 1 (mggdimensional matrix) .traverse the second row of the m(3) matrix,if (ijk),retain only column and delete, columns ,if kjiaaa222ia2ja2k

37、a2 is diffident from all the other elements in the second row retaincolumn. after ia2ia2the program we get a new matrix,we define this matrix g(2).stept4: deform the g (2) matrix we will get a matrix ,(0 means a )4() 1 (00)2(mggonedimensional matrix) .traverse the third row of the m(3) matrix,if(ijk

38、),retain only column and delete, kjiaaa333ia3ja3columns ,if is diffident from all the other elements in the second row ka3ia3retaincolumn. after the program we get a new matrix,we define this matrix g(3).ia3.stept n: deform the g (n-2) matrix we will get a matrix ,(0 means )() 3(00) 2(nmngnga one di

39、mensional matrix) .traverse the (n-1)th row of the m(n-1) matrix,if (ijk),retain onlycolumn and delete ,knjninaaa)1()1()1(ina)1(jna)1(, columns ,if is diffident from all the other elements in the second kna)1(ina)1(row retaincolumn. after the program we get a new matrix,we define this matrix ina)1(g

40、(n-1).table 2 the matrix gteam # 14820 page 6 of 17if the number of rows of the g(n-1) matrix is beyond 29, stop running the program the result is the schedule for the trips to travel.the specific program is shown as figure 1.analyze data build 1813 matrix gtraverse the first row of the g matrix, re

41、move columns so that elements in the first row of g are diffident from each other ,get g(1) matrixput out the specific distribute of the camping sitesdeform the g(1) matrix, get a matrix =m(3) traverse the second row of the m(3) matrix, remove columns so that elements in the second row of m(3) are d

42、iffident from each other ,get g(2) matrixdeform the g(n-2) matrix, get a matrix =m(n) (2)00(3)g ng nno yes stop n+1729figure 1 .the flow chart of the programteam # 14820 page 7 of 174.2.3 the result of issue 2 the managers of the big long river can modify launch schedules to influence the patterns o

43、f rafting traffic on the river, and thus to optimize the flow patterns on the river. application of cis model:when y = 25，we can get higher utilizations of the camping sites.the specific results are shown in table 3.and the table 6 and table 7 in the appendix are the results of y=18 and y=32.table 3

44、the specific distribute of the camping sitesfrom table 3 we can get some informations,they are as follows:the number of 6,10,11,18 nights travel are more than 7,8,9,12,13,14 nights travel,besides,there are no travel trips of 15,16,17 nights.there are 318 trips go to enjoy the drifting every year,its

45、 6 months in fact.this is broadly in line with the actual situation.team # 14820 page 8 of 17the optimal schedule is shown as table 4.-1 and 4-2. the table 4-1 is a schedule from april to june.table 4-1the optimal schedule triptrip lengthlengthaprilmayjune6 nights4.1-4.6 4.2-4.7 4.3-4.8 4.4-4.94.5-4

46、.10 4.9-4.144.14-4.15 4.24-4.295.1-5.6 5.2-5.75.3-5.8 5.4-5.95.5-5.10 5.9-5.145.14-5.15 5.24-5.296.1-6.6 6.2-6.76.3-6.8 6.4-6.96.5-6.10 6.9-6.146.14-6.15 6.24-6.297 nights4.1-4.7 4.23-4.294.10-4.16 4.11-4.175.1-5.7 5.23-5.295.10-5.16 5.11-5.176.1-6.7 6.23-6.296.10-6.16 6.11-6.178 nights4.1-4.8 4.10-

47、4.174.12-4.19 4.22-4.295.1-5.8 5.10-5.175.12-5.19 5.22-5.296.1-6.8 6.10-6.176.12-6.19 6.22-6.299 nights4.13-4.21 4.16-4.244.19-4.27 4.21-4.295.13-5.21 5.16-5.245.19-5.27 5.21-5.296.13-6.21 6.16-6.246.19-6.27 6.21-6.2910 nights4.1-4.10 4.2-4.114.3-4.12 4.4-4.134.20-4.29 4.14-4.234.11-4.20 4.15-4.245.

48、1-5.10 5.2-5.115.3-5.12 5.4-5.135.20-5.29 5.14-5.235.11-5.20 5.15-5.246.1-6.10 6.2-6.116.3-6.12 6.4-6.136.20-6.29 6.14-6.236.11-6.20 6.15-6.2411 nights4.19-4.29 4.17-4.274.1-4.11 4.2-4.124.3-4.13 4.4-4.144.5-4.15 4.6-4.164.7-4.17 4.17-4.274.19-4.295.19-5.29 5.17-5.275.1-5.11 5.2-5.125.3-5.13 5.4-4.1

49、45.5-5.15 5.6-5.165.7-5.17 5.17-5.275.19-5.296.19-6.29 6.17-6.276.1-6.11 6.2-6.126.3-6.13 6.4-6.146.5-6.15 6.6-6.166.7-6.17 6.17-6.276.19-6.2912 nights4.15-4.265.15-5.266.15-6.2613 nights4.16-4.28 4.14-4.265.16-5.28 5.14-5.266.16-6.28 6.14-6.2614 nights4.12-4.25 4.13-4.265.12-5.25 5.13-5.266.12-6.25

50、 6.13-6.2618 nights4.1-4.18 4.2-4.194.3-4.20 4.4-4.214.5-4.22 4.6-4.234.7-4.245.1-5.18 5.2-5.195.3-5.20 5.4-5.215.5-5.22 5.6-5.235.7-5.246.1-6.18 6.2-6.196.3-6.20 6.4-6.216.5-6.22 6.6-6.236.7-6.24team # 14820 page 9 of 17table 4-2 is a schedule from july to september,table 4-1:the optimal schedule t

51、riptrip lengthlengthjulyaugsept6 nights7.1-7.6 7.2-7.77.3-7.8 7.4-7.97.5-7.10 7.9-7.147.14-7.15 7.24-7.298.1-8.6 8.2-8.78.3-8.8 8.4-8.98.5-8.10 8.9-8.148.14-8.15 8.24-8.299.1-9.6 9.2-9.79.3-9.8 9.4-9.99.5-9.10 9.9-9.149.14-9.15 9.24-9.297 nights7.1-7.7 7.23-7.297.10-7.16 7.11-7.178.1-8.7 8.23-8.298.

52、10-8.16 8.11-8.179.1-9.7 9.23-9.299.10-9.16 9.11-9.178 nights7.1-7.8 7.10-7.177.12-7.19 7.22-7.298.1-8.8 8.10-8.178.12-8.19 8.22-8.299.1-9.8 9.10-9.179.12-9.19 9.22-9.299 nights7.13-7.21 7.16-7.247.19-7.27 7.21-7.298.13-8.21 8.16-8.248.19-8.27 8.21-8.299.13-9.21 9.16-9.249.19-9.27 9.21-9.2910 nights

53、7.1-7.10 7.2-7.117.3-7.12 7.4-7.137.20-7.29 7.14-7.237.11-7.20 7.15-7.248.1-8.10 8.2-8.118.3-8.12 8.4-8.138.20-8.29 8.14-8.238.11-8.20 8.15-8.249.1-9.10 9.2-9.119.3-9.12 9.4-9.139.20-9.29 9.14-9.239.11-9.20 9.15-9.2411 nights7.19-7.29 7.17-7.277.1 -7.11 7.2-7.127.3-7.13 7.4-7.147.5-7.15 7.6-7.167.7-

54、7.17 7.17-7.277.19-7.298.19-8.29 8.17-8.278.1-8.11 8.2-8.128.3-8.13 8.4-8.148.5-8.15 8.6-8.168.7-8.17 8.17-8.27 8.19-8.299.19-9.29 9.17-9.279.1-9.11 9.2-9.129.3-9.13 9.4-9.149.5-9.15 9.6-9.169.7-9.17 9.17-9.279.19-9.2912 nights7.15-7.268.15-8.269.15-9.2613 nights7.16-7.28 7.14-7.268.16-8.28 8.14-8.2

55、69.16-9.28 9.14-9.2614 nights7.12-7.25 7.13-7.268.12-8.25 8.13-8.269.12-9.25 9.13-9.2618 nights7.1-7.18 7.2-7.197.3-7.20 7.4-7.217.5-7.22 7.6-7.237.7-7.248.1-8.18 8.2-8.198.3-8.20 8.4-8.218.5-8.22 8.6-8.238.7-8.249.1-9.18 9.2-9.199.3-9.20 9.4-9.219.5-9.22 9.6-9.239.7-9.24team # 14820 page 10 of 17th

56、e camping point of utilization is clearly shown as figure 1.figure 1 - camping point of utilization after some fun-tuning we get the best travel schedule.the statistics get all camping utilization rate was 78.1% in 29 days. according to the formula: (1) n/mw w e get the camping utilization rate w=n/

57、m=566/(2529)100%=78.1% in order to test the scope of application of the conclusion,article also give two more results about the camping point of utilization.situation 1:y=18, n=326,m=1829=522，w=n/m100%=62.4%situation 2:team # 14820 page 11 of 17y=32,n=579,m=3229=928,w=n/m100%=62.4% therefore with th

58、e change of y, the utilization of the camp is also changing. then the total numbers of the trips are varying.4.3 analysis of the issue 34.3.1 why should passengers need to change boats? the length of the big long river is 225 miles long,and the trips range from 6 to 18 nights of camping on the river

59、, start to finish. different types of travel may drift different distance each day.so in order to make a suitable drifting time,the best way is to choose the suitable boats.the longer distance use motorized boats,the shorter may use oar- powered rubber rafts .4.3.2 how to decide which boat should us

60、e? according to the table 3,the daily drifting distance of each trip can be found out.in this case , the distance between two adjacent camping sites is 225/ 26 = 8.7 miles,so the daily travel distance is divided into three types :a : daily drifting distance are 8.7 and 8.72 miles ;b : daily drifting