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首页2020数维杯优秀论文:城市雪后交通优化算法与道路清扫策略
2020数维杯优秀论文:城市雪后交通优化算法与道路清扫策略
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更新于2024-06-15
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"2020年数维杯国际赛的优秀论文C20201009824详细探讨了城市道路冰雪清除问题的优化解决方案。该团队针对冬季雪后交通受阻,提出了一个高效的市区冰雪清理计划。他们利用Floyd算法求解区域内任意两点之间的最短路径,确保交通畅通。 首先,通过聚类分析将城市划分为N个子区域,使得每个子区域内的雪清除工作量大致均衡。然后,将根据路口之间的连接关系将地图转换为无向图。为了考虑清扫作业的效率,论文引入了一个新的概念,即根据扫雪车一次清扫的路宽与道路总宽度的比例,调整相邻点间的边数。这种处理方法有助于优化路线设计,使每条道路都能得到清理,并最大限度地减少行驶总距离。 论文进一步采用匈牙利算法(一种经典的匹配算法)来确定每个子区域内的最优驾驶方案,确保在有限的工作量下,道路覆盖全面且整体行驶距离最小化。这个方法不仅关注效率,还兼顾了资源的合理分配,是解决城市道路冰雪清除问题的一种创新策略。这份优秀论文展示了如何结合数据结构、算法和实际需求,有效应对冬季道路管理挑战,为智慧城市基础设施管理提供了有价值的研究成果。"
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Team # 20201009824
10
( )
1
1 1, 2, ,141
n
ij
i
Xj
=
==
(1-8)
The 141 intersections are divided into n areas, i.e
141
11
=n
n
ij
ji
X
(1-9)
The basic constraints are as follows,
( )
1
141
11
1 1, 2, ,141
. =n
01
n
ij
i
n
ij
ji
ij
Xj
S T X
X or
=
==
==
=
(1-10)
4.1.2 Model Solution Method
In real life, in order to achieve the goal of smooth roads after the snow stopped as
soon as possible, the whole urban area should be divided into several small areas, and
several small areas should be cleaned up at the same time. N intersections were rando
mly selected as the initial center points in the large area, and Floyd algorithm was use
d to calculate the shortest path length between each intersection and different center p
oints. Then, cluster analysis method was used to determine the center point and the co
rresponding area scope to make the objective function fully reach, so as to realize the
reasonable division of the area. The algorithm idea is as follows:
Floyd algorithm:
Step 1: Given that each intersection point are
1, 2, , N
, determine the matrix
0
D
,
where element
( , )ij
is equal to the length of the shortest arc (if any) from vertex
i
to vertex
j
. If th
ere is no such arc, then
0
ij
d =
. For
i
, let
0
0
ii
d =
.
Step 2: apply the following recursive formula to the
m
D
element whose
1, 2, ,mN=
is determined by the elements of
1m
D
−
in turn
1 1 1
min ,
m m m m
ij im mj ij
d d d d
− − −
=+
(1-11)
Whenever an element is identified, write down the path it represents.
At the end of the algorithm, the elements
( , )ij
of the matrix
n
D
represent the
shortest length from the intersection
i
to the intersection
j
.
Region division algorithm based on K-means clustering algorithm:
Step 1: in order to facilitate snow removal, the urban area should be divided into
n small areas and cleaned up at the same time. and randomly initializes n central point,
Team # 20201009824
11
which is denoted as
( )
12
, , , 0
t t t
n
u u u t =
(1-12)
Among them: t is the number of iterative steps
Step 2: By calculating the distance between each point and the center point, each
point is allocated to the nearest center point, forming N regions.
Step 3: Based on these classification points, consider the balance of snow removal
task volume in each region at the same time, and change the area where the points that
can greatly affect the balance of snow removal task volume in each region are located.
The center point is recalculated by changing the mean of all points in the region.
Step 4: Set
1, 2,3,t =
and repeat the above steps until no points are reallocated
to different regions, and output the classification points contained in each region.
According to the model established above and the solution method, the region
division diagram is drawn when n=10。
Figure1-1 Road and intersection images
From the figure above, it can be clearly seen that the approximate distribution of
each region and most regions are regular graphs.
4.1.3 Route planning model for clean vehicles
According to the regional division model of clean vehicles established before, the
regional division is realized reasonably. To minimize snow removal time, determine the
best route plan for cleaning vehicles in any small area. The core of this problem is to
consider the minimum working time of cleaning vehicles to complete snow removal
tasks in this area and find an optimal path for snow removal.
According to the above analysis, as driving over the cleared road will reduce the
efficiency of snow clearing, it is hoped that the cleaning car will spend as much time as
possible in cleaning the road, and as little time as possible in the empty road.
Establishment of objective function:
Team # 20201009824
12
The total working time of snow removal completed by the cleaning vehicle is the
sum of snow removal time and empty travel time of the cleaning vehicle, i.e
w c d
T T T=+
(1-13)
c
T
is the snow clearing time and
d
T
is the empty travel time.
The snow clearing time of the cleaning vehicle is:
141
1
,
ij ij
j
c
cw
XC
T i = n
VL
=
=
( 1,2, )
(1-14)
c
V
is the snow clearing speed within unit time, and
w
L
is the one-time snow
clearing width of snowmobile.
The empty travel time of the cleaning vehicle is:
f
d
d
d
T
V
=
(1-15)
d
V
is the driving speed of empty distance in unit time, and
f
d
is the driving distance
of each empty distance.
The total working time of the cleaning vehicle to complete snow removal is as
small as possible, and since the total amount of snow removal by the cleaning vehicle
is determined, that is, the time of snow removal by the cleaning vehicle is determined,
the empty travel time of the cleaning vehicle is as small as possible, i.e
f
d
d
MIN
V
(1-16)
The basic constraints are as follows,
( )
1
141
11
1 1, 2, ,141
. =n
01
n
ij
i
n
ij
ji
ij
Xj
S T X
X or
=
==
==
=
(1-17)
4.1.4 Model Solution Method
In the actual process, in order to minimize the working time of snow removal, the
optimal route planning of cleaning vehicles in any small area should be determined to
minimize the empty driving time of cleaning vehicles, that is, the sum of each empty
driving distance should be minimized. To solve this model, the idea of oil route problem
is used. The algorithm idea is as follows:
If the road runs in both directions, we simplify it to an undirected graph
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