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2019美赛O奖论文-MCM2019B-1924588.pdf
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美国大学生数学竞赛获奖论文,历届,单项文件,内容丰富,大学生数学,数学竞赛,参考资料,极具参考价值
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Team # 1924588
Team Control Number
For office use only
1924588
For office use only
T1
F1
T2
F2
T3
Problem Chosen
F3
T4
B
F4
2019
MCM/ICM Summary Sheet
Multi-Directional Comprehensive Disaster Response
System Based on Optimization
Summary
According to the actual situation of Puerto Rico, we designed a disaster response system
from the perspective of disaster area demand, company cost, realizability and security.
First, we identified the number and type of UAVs(unmanned aerial vehicle) in the UAV
fleet based on the geographical location and needs of Puerto Rican hospitals. Minimum UAVs
are used to save costs. Solving this optimization problem, we get two schemes: scheme one
needs four UAVs (B, C, D and H), the number of which is 1B, 1C, 1D and 3H; scheme two
needs four UAVs (B, C, G and H), the number of which is 2B, 1C, 1G and 3H. Each scheme
needs three containers.
Second, we designed the packaging configuration for containers. The number of medical
packages is large, so the heuristic algorithm is not effective. We propose a one-dimensional
maximum utilization packing scheme of “medical package first, UAV later”. It can not only
realize the greater use of container space, but also be easy to achieve when loading containers.
The maximum space utilization rate is 93.22% and the minimum utilization rate is 68.14%.
Third, we gridded the main roads in Puerto Rico's main disaster areas and transformed
the continuous problems into discrete ones. We identified the optimal location of the disaster
response system by using grid search method. The three containers’ locations are as follows:
18.47 , 66.()55NW
,
18.34 , 66.()03NW
,
18.34 , 65.()69NW
.
Fourth, the payload packaging configuration of UAV is designed by using optimization
methods. Drone B load 2MED1,drone C load 1MED1+1MED3, drone D load 4MED1+2MED3
or 3MED1+3MED2 or 2 MED1+1MED2+2MED3. UAV flight delivery routes need to avoid
mountain and high buildings, so we use Voronio Diagram and Dijkstra algorithm to get
delivery route. The flight schedule of UAV is obtained according to the delivery route.
Fifth, in order to make the UAV reconnaissance the road as wide as possible, flight
schedule of the UAV are obtained by using ant colony optimization (ACO). It can use the
limited flight time to reconnoitre the road as much as possible.
To sum up, we considered many factors to design DroneGo system.
Keywords: Optimization; ACO; Gridding; Voronio; Dijkstra
Team # 1924588
Contents
1 Introduction ..................................................................................................................................................... 1
1.1 Problem Background........................................................................................................................... 1
1.2 Restatement of the Problem .............................................................................................................. 1
1.3 Literature Review ................................................................................................................................. 2
2 Assumptions and Justifications ................................................................................................................ 2
3 Notations .......................................................................................................................................................... 3
4 Model Establishment .................................................................................................................................... 3
4.1 Identify Drones and Medical Packages ........................................................................................ 4
4.1.1 Determining the Number of Unmanned Aerial Vehicles.......................................... 4
4.1.2 Selection of Unmanned Aerial Vehicle Types ............................................................... 5
4.1.3 Selection of Container Number and Cargo Loading Scheme.................................. 5
4.2 ISO Cargo Containers Packing Configuration ........................................................................... 6
4.3 Optimization model of the best container location ............................................................... 11
4.3.1 Road Grid Model.................................................................................................................... 11
4.3.2 Mapping Hospital Location to Grid Model ................................................................. 12
4.3.3. Establishment of Optimization Model .......................................................................... 12
4.3.4 Result .......................................................................................................................................... 13
4.4 Drone Payload Packaging Configuration .................................................................................. 14
4.5 UAV Delivery Route and Timetable ............................................................................................ 14
4.5.1 Delivery Route Division ...................................................................................................... 15
4.5.2 Delivery Route Planning Model ....................................................................................... 15
4.5.3 Delivery Route Solution ...................................................................................................... 16
4.5.4 Delivery schedule................................................................................................................... 17
4.6 Drone Flight Plan ................................................................................................................................ 17
4.6.1 Model establishment ............................................................................................................. 17
4.6.2 Using Ant Colony Optimization (ACO) to Solve the Problem ............................. 18
4.6.3 Result .......................................................................................................................................... 19
5 Testing Our Model ...................................................................................................................................... 20
6 Evaluation of Our Model .......................................................................................................................... 20
References.............................................................................................................................................................. 22
Team # 1924588
MEMO
From: Team 1924588, MCM 2019
To: The Chief Operating Officer (CEO) of HELP, Inc.
Date: January 28, 2019
Subject: Findings and recommendations for DroneGo disaster response system
Dear CEO, we are honored to inform you our achievements and recommendations for you.
After a careful study of DroneGo system and the devastation in Puerto Rico, we get the following
results. First of all, from the perspective of cost saving for HELP, Inc., we believe that drones used for
disaster relief should not be disposable, but should be equipped with replaceable batteries during
transportation or realize the reuse of drones by means of designing solar energy charging on the drone
or something. On this premise, we figured out that the DroneGo system only needs six drones to
achieve the disaster relief mission. Three drones are used for medical supply delivery and video
reconnaissance, the other drones,which are named tethered drone, are uesd to provide wireless
networks and transmit the data. As for the cargo containers' quantity, we think that three cargo
containers can transport more medical packages so that the hospitals in Puerto Rico can last a longer
time. And then, we designed a packaging scheme for cargo containers to keep as many medical
packages as possible. Please refer to the text for the specific package plan. We have found the three
best locations for cargo containers, respectively at
18.47 , 66.()55NW
,
18.34 , 66.()03NW
and
18.34 , 65.()69NW
. Next, we took the obstacles such as mountains and buildings into consideration,
and designed a bunch of safe and efficient delivery routes for drones. At the same time, the delivery
schedule are formulated for each of the drone. Finally, in order to enable the drone to reconnoitre the
main roads as much as possible, we used ant colony optimization(ACO) algorithm to get the best
reconnaissance routes of each drone, and work out the time plan of drone based on the combination of
medical supply delivery and video reconnaissance.
Through our model analysis, we can draw the conclusion that a small number of drones can
complete the medical supply delivery mission. However, if we want to achieve a wider range of road
reconnaissance in disaster areas, we need to increase the number of drones invested.
Based on the results and conclusions above, we put forward the following suggestions for you:
⚫ Replaceable batteries or solar recharging devices should be designed to reuse the drones.
⚫ Select the three best locations of
18.47 , 66.()55NW
,
18.34 , 66.()03NW
,
18.34 , 65.()69NW
,which can not only reduce the number of drones used, but also make the
reconnaissance range as large as possible.
⚫ When planning the route of drones, then influence of obstacles should be considered carefully to
complete the missions of medical supply delivery and video reconnaissance safely and
successfully.
⚫ If you think that all the main roads must be reconnoitred, you can achieve this goal by using more
drones.
We sincerely hope that DroneGo disaster response system will be carried out perfectly.
Please contact us if you have any problems.
Team # 1924588 Page 1 of 29
1 Introduction
1.1 Problem Background
The U.S. territory of Puerto Rico was hit by a severe hurricane in 2017 that caused
significant damage. The combined destructive power of the hurricane's storm surge and
wave action caused extensive damage to buildings and roads, particularly along the east and
southeast coast of Puerto Rico. The storm left 3.4 million people on the island without power.
The storm destroyed the majority of the island's cellular communication networks. The
electrical power and the cell service outages lasted for up across indicates much of the island.
Widespread flooding blocked and damaged many highways and roads across the island,
making it nearly impossible for emergency services ground vehicles to plan and navigate
their routes. Demand for medical services has continued to surge for some time as people
with chronic diseases have turned to hospitals and temporary shelters for treatment.
1.2 Restatement of the Problem
Non-governmental organizations (NGOs) usually provide adequate and timely response
to natural disasters. We need to design a transportable disaster response system called
"DroneGo." for HELP, Inc. to improve its response capabilities. We also need to select some
of the candidate drones to make up DroneGo fleet for medical supply and video
reconnaissance. In addition, we also need to put drones and medical packages into ISO
containers with reasonable design and deploy them to the affected areas. The simple
structure of the DroneGo disaster response system is shown in figure 1:
Figure 1 DroneGo disaster response system
In order to solve those problems, we will proceed as follows:
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