2012數(shù)學建模美賽論文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 TripThe BigLongRiver is well known as one of the natural wonders worldwide. Besides viewing the spectacular landscape, an extremely attractive

2、recreational activity is river rafting on the BigLongRiver. 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 methodto provide a management strategy byusing statistical dataand Computational-Intelligence

3、-System (CIS).CIS is a computer program that models complicated, dynamic camp sites number Y interactions in the river corridor of the BigLongRiver. The system employs a data acquisitionand simulator system. The database is a 18×13 matrix which gives every trips travel arrangement. The computer

4、 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 part: the

5、 optimal scheduleCIS 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 ProblemAccording to the results of th

6、e first part,the table about changing boats can be obtained through calculation. Finally, using program,assume Y=25, we gain a optimalschedule, named table 4.The table shows that the park entertains 318travel trips in a tourist season, and the choice of ship types also is showed in the Table 5.Conte

7、ntsANALYSIS OF THE SWEET SPOT11 INTRODUCTION11.1 Background 1 1.2 problem 12 ASSUMPTIONS23 SYMBOLS AND DEFINITIONS24 MODEL24.1 Analysis of the issue 124.1.1 What is the “carrying capacity” of the river24.1.2 The situations that adapt the “Carrying Capacity”34.1.3 Result of the issue 134.2 Analysis o

8、f the issue 234.2 .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 274.3 Analysis of the issue 3114.3.1 Why should passengers need to change boats?114.3.2 How to decide which boat should use?114.3.3 Result of the issue 3125 STRENGT

9、HS AND WEAKNESS OF THE MODEL136 REFERENCES137 APPENDIX 148 Memo 17 1 IntroductionThe BigLongRiver is well known as one of the natural wonders worldwide. Besides viewing the spectacular landscape, an extremely attractive recreational activity is river rafting on the Big Long River.River trips are dir

10、ected 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 more trips to travel down the river.1.1 BackgroundThe Big Long River(225 m

11、iles) 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 types, you can select 6 to 18 nights either way. Besides, you can als

12、o 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 areas need a program so that more visitors can enjoy themselves. The questio

13、n 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 uniformly throughout the river corridor. And the Big Long River accepte

14、d 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 occupythe same site at the same time and with minimal contact with other groups of

15、 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:u How to balance the carrying capacity of the BigLongRiver?u How best to make f

16、ull use of the camping sites?u When should people change boats?2Assumptionsl Suppose that the camping sites only fairly distribute along one side of the river.l Suppose that all the trips obey the arrangements of the scenic when travelling.l Suppose that the weather of the scenic is good in 6 months

17、.l Suppose that drifting only during the daytime,people must stay at the camping sites during the nights.l Boat speed is defined here as the average of thespeed of the BigLongRiver.3 Symbols and Definitionsu X represents the total trips in 6 months.u Y represents the total numbers of the camping sit

18、es. u N is the total times that camping sites to be used in 29 days. u M is the number of camping sites which could be used in 29 days.u W is the Camping point of utilization.u is the numbers of the Ith teams u K is the number of all the teams in 29 days travel.4 Model4.1 Analysis of the issue 1 Wha

19、t 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 sustain.Understanding the impacts of human recreation on natural resources is of critical importance in

20、 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 us that if the machine works all day without rest,it will soon get some trouble.So all machines have

21、regular working time.It is similar to the BigLongRiver. The situations that adapt the “Carrying Capacity”.Clearly,less trip boats make better carrying capacity.But it will get less income for the scenic. So we use the "machine working" model to describe the river's"Carrying Capaci

22、ty" . 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. 4.1.3The result of issue 1Considering the open days of the BigLongRiver,we assume that drifting in the same way in each month. That

23、is to say the trips are in cycle for every month.That's 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 are 174 days(29×6=174) each year in total. In this way the River could get the opportunity to re

24、lieve 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 to the first problem,the trips are in cycle for every month.All trips need to travel in the da

25、y 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.4.2.2The application of the CIS(Computational-Intelligence-System)Obeying the principles of no two sets of campers can occupy the same site at the same

26、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 acquisitionand simulator system. The data acquisition is a 18*13 matrix which give every trips

27、 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 paper mainly use the model of the Computational-Intelligence-System(CIS) to search for how to m

28、ake 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.According to the principles of drifting the same distance everyday.We can also find out 13 differen

29、t 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 1TheCamping Locations of 13 Different Drift ModeTravel typesCamping sites6 nights4,8,13,17,21,257 nights4,7,11,1418,21,258 nights3,6,9,13,16,19,2

30、2,259 nights3,6,8,11,14,17,19,22,2510 nights3,5,8,10,13,15,18,20,23,2511 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,

31、8,9,11,13,14,16,17,19,20,22,23,2517 nights1,3,4,6,7,9,10,12,13,15,16,18,19,21,22,24,2518 nights1,3,4,6,7,8,10,11,13,14,15,17,18,19,21,22,24,25Then 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 sam

32、e time .For this purpose we establish the model of Computational-Intelligence-System (CIS ).The value of simulation 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 a

33、side a certain purification time. There are Y camp sites on the BigLongRiver, distributed fairly uniformly throughout 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 ar

34、range camping trips per night to stay at the nearest site,we build 18×13 matrix, the rows represent the number of 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 18×13 matrix G.Stept2: Tr

35、averse the first row of the G matrix,If (i<j<k),retain only column and deletecolumns ,If is diffident from all the other elements in the first row retaincolumn. After the program we get a new matrix,we define this matrix G(1).Stept3: Deform the G(1) matrix we will get a matrix,(0 means a one d

36、imensional matrix) .Traverse the second row of the M(3) matrix,If (i<j<k),retain only column and delete, columns ,If is diffident from all the other elements in the second row retaincolumn. After the program we get a new matrix,we define this matrix G(2).Stept4: Deform the G (2) matrix we will

37、 get a matrix ,(0 means a onedimensionalmatrix) .Traverse the third row of the M(3) matrix,If(i<j<k),retain only column and delete, columns ,If is diffident from all the other elements in the second row retaincolumn. After the program we get a new matrix,we define this matrix G(3).Stept n: Def

38、orm the G (n-2) matrix we will get a matrix ,(0 means a one dimensional matrix) .Traverse the (n-1)th row of the M(n-1) matrix,If (i<j<k),retain onlycolumn and delete, columns ,If is diffident from all the other elements in the second row retaincolumn. After the program we get a new matrix,we

39、define this matrix G(n-1).Table 2 The matrix GIfthe 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 18×13 matrix GTraverse the first row of the G matrix, Re

40、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

41、iffident from each other ,get G(2) matrixDeform the G(n-2) matrix, get a matrix =M(n) No Yes Stop n+1729Figure 1 .The flow chart of the program4.2.3The result of issue 2The managers of the BigLongRiver can modify launch schedules to influence the patterns of rafting trafficonthe River, and thus to o

42、ptimize the flowpatterns 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 3The Specific Distribute of the Camping sitesFr

43、om Table3 we can get some informations,they are as follows:l 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.l There are 318 trips go to enjoy the drifting every year,it's 6 months in fact.This is broadly in l

44、ine with the actual situation.l The 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 Trip LengthAPRILMAYJUNE6nights4.1-4.6 7 nights8 nights9 nights10 nights11 nights5.19-5.29 5.17-5.275.1-5.11 5.2-5.125.3-5.13 5.45.5-5.15 5.

45、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 nights13 nights5.16-5.28 5.14-5.266.16-6.28 6.14-6.2614 nights18 nightsTable 4-2 is a schedule from July to September,Table 4-1:The Optimal Schedule Trip LengthJULYAUG

46、SEPT6 nights7.1-7.6 7 nights8 nights9 nights7.10 nights11 nights12 nights13 nights14 nights18 nightsl The 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

47、 rate was 78.1% in 29 days. According to the formula: (1)W e get the camping utilization rate W=N/M=566/(25×29)×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=18×

48、;29=522，W=N/M×100%=62.4%Situation 2:Y=32,N=579,M=32×29=928,W=N/M×100%=62.4% Therefore with the 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 le

49、ngth of the BigLongRiver is 225 miles long,and the trips range from 6 to 18 nights of camping on the river, 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 u

50、se motorized boats,the shorter may use oar- powered rubber rafts .4.3.2How to decide which boat should use? 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 dis

51、tance is divided into three types :×2 miles ;×××5 miles ;×××× 9 miles. Which boat to choose depends on the drifting distance of the next day.For Class A, because of its shorter distance , arrangements for visitors are oar-powered rubber raft to play. For Class

52、 B, moderate due to its distance , visitors could use any oar-powered rubber raft or motorized boat according to personal preference. For Class C, because of it's longer distance , arrangements for the tourists are motorized boat.From table 3,the detail ways of choosing boats can be made as Tabl

53、e 5Table 5 The specific ways to choose boats4.3.3The results of issue 3 Table 5 shows detail information. For example ,18 nights trips that starts traveling from April 1, oar-powered rubber raft could be used every day. 10 nights trips that starts traveling from April 20,its first , fifth, eighth da

54、ys could either use oar-powered rubber rafts or motorized boats according to their personal preferences ,the remaining days could use oar-powered rubber rafts. 8 nights trips that starts traveling from April 10 ,the motorized boats should be used in the eighth day ,and according to personal preferen

55、ces,either could be used in the second,sixth day , the remaining days should use oar-powered rubber rafts.5. Strengths and Weakness of the ModelStrengths1.In this paper, the best schedule get from the CIS model is easy of the actual operation and the results are more accurate.2.The methods used in t

56、his article can be extended to all aspects of daily life : the bus how to achieve optimal scheduling problem , how to solve the medical examination as queuing problem and make full use of the parking lot and parking spaces.3.This paper uses a simplified model with a cycle of 29 days to simplify the calculation process , but it also makes a smaller number of the date of utilization rate of less than the best arrangement .4.The utilization W changes accor