两种改进的最优路径规划算法

27 3 Vol.27 No.3
2005 6 Journal of University of Science and Technology Beijing Jun. 2005
1) 2) 1) 3) 4) 1)
1)100083 2),063009
3)063000 4)100102
Dijkstra A*Dijkstra
A*
A*
A*
Dijkstra
A*
; ; Dijkstra ; A*
TP 18; TP 273 + .23
[1]
Dijkstra
[2] [3]
Dijkstra [4] A*
[5] A* [6] A*
[7]
[8]
[9] Dijkstra
A*
1 Dijkstra
1.1 Dijkstra
u0 v
Dijkstra
u 0, v
u0 [10,11]
(1) d u 0 = 0 w u 0
2004–08–10 2004–11–20
(No.2001BA 605A-02)
(1971 ) , ,
d w = u00 t u0 du0w
()
(2)wd w d w =
d w , d t +l t,w
l t, w t w
() d w
u0 w t w tw
d w d s d s =
d w w s d s /t w
u0sd s
tw s
(3) v u0
v t s (2)
1.2 Dijkstra
Dijkstra
1
Dijkstra 1 A
y
20
G
3.2
18
2. 9
4.4 D
K
16 B
3.5
4.5
3.2
4.1 2
14 4.2 E H
A
2.9
3.4 N 2.8
12
5.6
I
2.2
3.4
3
C
L
4.2 P
4.2
10
5
3.5
M
3 2. 2
F 4
J
O
2. 2
8
0 2 4 6 8 10 12 14
x
1
Fig.1 Map for simulation of optimum path planning

•368 • 2005 3
Dijkstra
1
1 A P
A— C— F— J— M— O— P A P d A, P =
18.3 A P A
d w =
min d w , d t +l t, w Dijkstra
A P
T P = 15+14+13+ +2 = 119
1 Dijkstra A
Table 1 Calculation process for an optimum path by use of Dijkstra's algorithm
A B C D E F G H I J K L M N O P
1 — 4.2 3.4
2 — 4.2 3.4/A 9.0 6.9
3 — 4.2/A — 8.6 8.3 6.9
4 — — — 8.6 8.3 6.9/C 11.9 10.9
5 — — — 8.5 8.3/8 — 10.3 11.2 10.9
6 — — — 8.6/B — — 11.5 10.3 11.2 10.9
7 — — — — — — 11.5 10.3/D 11.2 10.9 13.5 13.7
8 — — — — — — 11.5 — 11.2 10.9/F 13.5 13.7 13.1
9 — — — — — — 11.5 — 11.2/E — 13.5 13.7 13.1
10 — — — — — — 11.5/D — — — 13.5 13.7 13.1
11 — — — — — — — — — — 13.5 13.7 13.1/J 16.1
12 — — — — — — — — — — 13.5/H 13.7 — 18.0 16.1
13 — — — — — — — — — — — 13.7/H — 15.9 16.1
14 — — — — — — — — — — — — — 15.9/L 16.1 18.7
15 — — — — — — — — — — — — — — 16.1/M 18.3
1.3 Dijkstra
Dijkstra
1.4 Dijkstra
1
d w = d w , d t +l t, w w
w
t l t, w d t
d w
d w l t, w
d w Dijkstra
(2) d w ,
l t, w
d w = d w , d t +l t, w
d w
Dijkstra
2 Dijkstra 1
A
Dijkstra 1
Dijkstra
Dijkstra A P
T * P = 47Dijkstra
(
)
1.5
Dijkstra
C
5
16 24 32
55 43 75
62 111 78
139 2
2
Dijkstra Dijkstra
()

Vol.27 No.3 •369 •
Dijkstra
2 Dijkstra Dijkstra
Table 2 Computing overhead of the improved Dijkstra's and traditional
Djkstra's algorithm
Dijkstra Dijkstra
16 119 47 (39.5%)
32 465 134 (28.8%)
43 861 234 (27.2%)
62 1 830 441 (24.1%)
78 2 926 540 (18.5%)
2 A*
2.1 A*
A*
[12] A*
f n =g n +h n
g n u0n
h n nv
h n h * n (h * n
)
2.2 A*
A*
(1)
(2)
(3) (2)
2.3 A*
A*
Dijkstra
A*
[13]
3 A*1 A N
f n =g n +h n
g n A
h n N
A*Dijkstra
Node(x y) A(0 13) B(3 16) C(3
11)
A*A
N A— C— E— H— L— N
A, N = 16.6
1 Dijkstra
A— B— E— H— L— N 15.9 A*
A*
2.4 A*
A*
A*
A*
4 A*1 A
N
(1) A*A— C— E— H— L
— N 16.6
(2) C
A— B— E— H— L— N 15.9
(3) E
A— C— F— I— L— N 17.1
(4) H
A— C— E— I— L— N 17.2
(5) L
A— C— E— H— K— N 18.7

•370 • 2005 3
5
A— B— E— H— L— N 15.9
A*
1 Dijkstra
2.5
A*
C
78 (1 77
)
A*77
45 A*
77 68
8
A*1
A*A*
A*
3
Dijkstra A*
(1)Dijkstra
(2)A*
(Dijkstra )
[1]
2000, 18(4) 327
[2]
1998, 15(2) 23
[3]
2002, 24(2) 35
[4] Dijkstra
2001, 38(3) 307
[5] A*
1998, 31(6) 24
[6] A*
2004, 24 (5): 19
[7] A*
2000, 16(3) 21
[8] Frank Blischke and Bernd Hessing Dynamic Route Guidence
Different Approaches to the System Concepts Soc Automatic
Eng Inc, 1998
[9] ,,,.
. , 2003(1): 12
[10] ..2000
(2) 22
[11] Lee J. Calculation of the shortest path sbyoptimal decomposition
IEEE Trans Syst Man Cybern 1982(3): 410
[12] A* .
, 2003 13(5) 335
[13]
. , 2003 23(1) 16
Two improved optimum path planning algorithms
LI Qing 1) , Song Dingli 2) , ZHANG Shuangjiang 1) , LI Zhe 3) , LIU Jianguang 4) , WANG Zhiliang 1)
1) Information Engineering School, University of Science and Technology Beijing, Beijing 100083, China
2) Hebei Polytechnic University, Tangshan 063009, China
3) Freight Section of Traffic Bureau Tangshan , Tangshan 063000, China
4) Gulf Science and Technology Corporation, Beijing 100102, China
ABSTRACT An improved Dijkstra's and an improved A* algorithm were proposed based on the analysis of their
drawbacks. In the traditional Dijkstra's algorithm, the distance between two unconnected nodes is infinite and some
relative calculations are useless. The improved Dijkstra's algorithm proposed that the connection between nodes
should be tested at first so that it can decrease the computing overhead to a great extent. When the traditional A* algorithm
is used in practice, its efficiency is not satisfied. The improved A* algorithm includes such steps as the following:
firstly, the original optimum path should be planned by the traditional A* algorithm; secondly the nodes in
the original optimum path; should be blocked in turn and the traditional A* algorithm is used again in order to look
for another new optimum path. finally, these new optimum paths should be compared with the original one so that
the final optimum path can be selected. Simulation results show that the improved Dijkstra's algorithm can enhance
the calculation efficiency and the improved A* algorithm can find the more optimum path.
KEY WORDS optimum path search; intelligent vehicle guidance and location; Dijkstra's algorithm; A* algorithm