Hindawi Publishing Corporation
International Journal of Distributed Sensor Networks
Volume 2015, Article ID 271067, 10 pages
http://dx.doi.org/10.1155/2015/271067
Research Article
A Multimetric Ant Colony Optimization Algorithm for
Dynamic Path Planning in Vehicular Networks
Zhen Wang, Jianqing Li, Manlin Fang, and Yang Li
Faculty of Information Technology, Macau University of Science and Technology, Avenida Wai Long, Taipa, Macau
Correspondence should be addressed to Jianqing Li; jqli@must.edu.mo
Received 30 April 2015; Accepted 2 July 2015
Academic Editor: Shangguang Wang
Copyright © 2015 Zhen Wang et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
With the rapid growth in the number of vehicles, energy consumption and environmental pollution in urban transportation have
become a worldwide problem. Efforts to reduce urban congestion and provide green intelligent transport become a hot field of
research. In this paper, a multimetric ant colony optimization algorithm is presented to achieve real-time dynamic path planning
in complicated urban transportation. Firstly, four attributes are extracted from real urban traffic environment as the pheromone
values of ant colony optimization algorithm, which could achieve real-time path planning. Then Technique for Order Preference
by Similarity to Ideal Solution methods is adopted in forks to select the optimal road. Finally, a vehicular simulation network is set
up and many experiments were taken. The results show that the proposed method can achieve the real-time planning path more
accurately and quickly in vehicular networks with traffic congestion. At the same time it could effectively avoid local optimum
compared with the traditional algorithms.
1. Introduction
With the rapid development of green intelligent transportation, many intelligent transportation path planning algorithms were proposed, in order to achieve the optimal planning path with the least cost from a source to a destination
within a reasonable time. These algorithms focused on the
combination of swarm intelligent algorithm, such as artificial
bee colony algorithm [1], genetic algorithm [2], and ant
colony algorithm [3], to reduce energy consumption and
environmental pollution in urban transportation with traffic
congestion. Ant colony optimization algorithm (ACO) [4] is
an abstract evolution based on the observation of ant colonies
searching for food. Considering the similarity between a vehicle and an ant in searching for a path, ant colony optimization
algorithm is widely used in the research and application
of intelligent transportation. Many scholars have proposed
different optimization models of the ant colony optimization
algorithm, based on different research objects and in different application fields. Narasimha and Kumar proposed an
improved ant colony optimization algorithm based on solving the min-max Single Depot Vehicle Routing Problem [5]
and min-max Multidepot Vehicle Routing Problem [6] but
did not mention real-time path planning. Li et al. [7]
studied the Travelling Salesman Problem (TSP) with the ant
colony optimization algorithm and proposed a new multipath
routing algorithm based on improved ant colony algorithm.
In the paper the ACO was improved in three aspects: add the
utilization ratio of router’s buffer queue into the criterion of
selection; update the global pheromone with the utilization
ratio of link; select multiple paths to transfer data. This
algorithm can achieve network loading balance and reduce
the likelihood of congestion, but unfortunately it did not
consider real-time traffic and routing planning. Zeng et al.
[8] proposed an improved ant colony optimization algorithm
by dynamically adjusting the number of ants to solve the
Chinese Traveling Salesmen Problem. The algorithm only
considered how to get the global best result easily but failed
to consider multifactors of road and real-time navigation.
Moghaddam et al. [9] proposed an advanced particle swarm
algorithm to solve uncertain vehicle routing problems in
which the customers’ demands are supposed to be uncertain with unknown distributions. Lee et al. [10] investigated the vehicle routing problem with deadlines, to satisfy
2
the requirements of a given number of customers with
minimum travel distances, while respecting both uncertain
customer demands and travel times. At the same time, Philip
Chen et al. [11] used the algorithm of Multiple Attribute
Decision Making and Technique for Order Preference by
Similarity to Ideal Solution (TOPSIS) method, to calculate
the best path with the assumption that the road and vehicles
are equipped with Internet of Things sensor device, to obtain
instant traffic information. But the algorithm is similar to the
Dijkstra algorithm [12] to a certain degree; it can only produce
partial optimal results.
The above-mentioned papers have explored intelligent
path planning problems, but there are still some aspects
that need to be tackled, particularly in view of the existing
intelligent traffic navigation.
The existing path planning algorithms mainly focus on
the shortest path. Some of them can plan a better path in
urban areas with the comprehensive factors, such as path
length, driving speed, and road grade, and avoid the heavy
traffic path in the beginning of path planning. But for urban
traffic problems, especially during rush hours, it is obvious
that the shortest path is not always the fastest one, as the
traffic situation is a dynamic changing process. Once the
result is produced by the existing algorithms, they will not
be able to be changed. This means that they would fail to
dynamically adjust path planning according to the real-time
traffic situation.
Based on the wireless sensor network in the application of
intelligent transportation [13–15], A Multimetric Ant Colony
Optimization (MACO) algorithm is presented to deal with
intelligent traffic real-time path planning problems. The best
path is calculated automatically according to dynamic realtime traffic using this algorithm, which can be the shortest
distance, the shortest time, the best road condition, or the best
path of comprehensive situations according to customers’
requirements. The MACO contributes to not only planning
a best path with considering multiple factors of the road,
but also adjusting the path planning dynamically with the
real-time traffic situation. And, furthermore, the MACO can
contribute to the best average velocity with the least energy
consumption in green intelligent transportation. The rest of
this paper is organized as follows. The system model of an
intelligent transportation network is presented in Section 2.
The path planning algorithm based on the ant colony optimization algorithm is discussed in Section 3. Section 4 shows
the simulation results. Finally, the conclusions are given in
Section 5.
2. System Model
2.1. Intelligent Transportation Network Settings. A vehicular
network is set up for intelligent transportation [15], which
includes two subnetworks. The first one is the basic road
network, which is deployed in the information node at the
intersection and relay nodes along the roads. The second
is the network of vehicle-mounted sensors. Figure 1 is a
schematic view of transport at an intersection, in which the
solid line arrows indicate the direction of traffic and the
dotted line arrows indicate the direction in which data is
International Journal of Distributed Sensor Networks
Figure 1: The model of road traffic network.
transferred. The main functions of these nodes are described
as follows.
(A) Information Nodes (as Solid Circles in Figure 1). They
are deployed at the intersections, to monitor and receive
data (including traffic flow and average velocity) from the
vehicles moving toward them in all directions, and transmit
the comprehensive traffic data to every direction.
(B) Relay Nodes (as Solid Squares in Figure 1). They are
deployed along both sides of the road and send the data
received from the information node in the opposite direction
of the traffic to subsequent vehicles to plan paths.
(C) Vehicle-Mounted Sensor Nodes. They are installed in
vehicles and can transfer data in two ways, that is, by
gathering data from relay nodes or the information nodes
along the road ahead. The optimal route can be identified
through calculation; meanwhile, data of the vehicle itself,
such as average velocity, average time, and path length, and
other information will be sent to the node, allowing for the
comprehensive integration of the information.
The three kinds of nodes form a wireless Internet of
Things for the transportation system. The vehicle-mounted
nodes receive data on the traffic ahead from the information
nodes and relay nodes to plan a path. Meanwhile, the vehicle
can also send its own driving data to relay nodes and
information node, for the traffic network to process data.
The information nodes can simultaneously receive data from
vehicles in all directions adjacent to the intersection and
then send back processed comprehensive traffic data in the
opposite direction and through relay nodes and spread such
data to a further distance. Since the traffic conditions are
constantly changing, it is necessary to put a timestamp on
all the information transferred. When the data is received by
the farther nodes overtime, the nodes will identify such data
International Journal of Distributed Sensor Networks
3
as non-real-time and invalid data and will simply discard the
data.
2.2. Parameters. Assume there are 𝐾 intersection nodes in
total in the vehicle network. The road segment is either a
one-way or two-way street. Based on the driving directions
of vehicles, the road network can be understood as a directed
graph 𝐺. For a vehicle on any segment, it must be driving
away from an intersection and at the same time towards
another intersection. For the road segment, the direction in
which vehicles drive away from an intersection is defined
as outdegree, and the direction in which the vehicles drive
toward the intersection is defined as indegree. So the vehicle
navigation problem can be the conversion of path planning
problem from 𝐴 to 𝐵 on the directed graph.
Suppose there are 𝑛 outdegrees at an intersection, that is,
𝑛 road segments leaving the intersection. For each outdegree,
it is defined that length is 𝐿, width 𝑊, road grade 𝐶 (based
on speed limits), and average driving speed 𝑉. For the
intersection node, comprehensive evaluation is applied to
each intersection outdegree.
Definition
Road Length 𝐿∗ . Suppose, in a directed graph 𝐺 abstracted
from an urban road network, there are 𝑛 outdegrees, with
lengths of (𝐿 1 , 𝐿 2 , 𝐿 3 , . . . , 𝐿 𝑛 ), respectively. 𝐿− is the road
segment with the shortest length (outdegree length). The
outdegree lengths are normalized as follows:
𝐿∗𝑖 =
𝐿−
.
𝐿𝑛
(1)
Road Width 𝑊. The width of the outdegree is based on traffic
lane. Supposing only one lane, then 𝑊𝑖 = 1 and the number
of 𝑖 indicates the 𝑖th outdegree of the intersection.
Road Grade 𝐶∗ . The road grade is calculated according to the
speed limits. To calculate simply, we suppose the maximum
speed limit of the city road is 120 km/h; the road grade is
normalized as follows:
𝐶𝑖∗
𝐶
= 𝑖 .
120
(2)
Average Velocity 𝑉∗ . Suppose 𝑚 vehicles pass a road segment
in a particular period; the average velocity of each vehicle is
𝐿𝑖
,
𝑉𝑖 =
𝑇end − 𝑇start
𝑉𝑘∗
=
(∑𝑖1 𝑉𝑖 )
120 ∗ 𝑛
;
(3)
𝑖 = 1, 2, . . . , 𝑛,
where 𝑉𝑖 denotes the average velocity of each vehicle, 𝐿 𝑖 the
length that the vehicle drives, 𝑇start the time the vehicle takes
to drive in, and 𝑇end the time the vehicle takes to drive out.
Thus 𝑉𝑘∗ is the average speed after normalizing all the vehicles
at a certain period.
3. Path Planning Algorithm
3.1. The Ant Colony Optimization Algorithm. Based on the
path planning problem in intelligent transportation and the
similarity of ant colony foraging and pathfinding, we can
use the ant colony optimization algorithm to implement the
path planning in intelligent transportation [13]. As in the
whole system, different vehicles have different destinations;
however, it is assumed that the vehicles share the same
route as the same group of ants in the same road segment.
When vehicles pass through a road segment, they transmit
integrated traffic data to the information node, which are
similar to the pheromones of the ant colony optimization
algorithm. When subsequent vehicles plan a path, they can
use these data as an important reference.
The parameters of ant colony optimization algorithm are
defined as shown in the following.
The Description of Parameters
𝑚: the number of ants (vehicles),
𝑑𝑖𝑗 : the distance between element (intersection) 𝑖 and
element (intersection) 𝑗,
𝜏𝑖𝑗 (𝑡): at 𝑡 moment, the residual pheromone on the
path between element (intersection) 𝑖 and element
(intersection) 𝑗, and at initial time, all the residual
pheromones of paths which are precomputed,
𝑝𝑖𝑗𝑘 : the probability that ant 𝑘 chooses element 𝑗 from
element 𝑖,
tabu𝑘 : recording the element that the 𝑘th ant has gone
through,
allowed𝑘 = {0, 1, . . . , 𝑛 − 1} − tabu𝑘 : recording the
allowed element that ant may choose next time,
𝜂𝑖𝑗 : the expectations that ants go through from element 𝑖 to element 𝑗,
𝛼: determining the relative influence of the
pheromone trail,
𝛽: determining the relative influence,
𝜌: Pheromone evaporation rate,
Δ𝜏𝑖𝑗𝑘 (𝑡): the amount of pheromone ant 𝑘 deposits on
the path form element 𝑖 to element 𝑗 visited at 𝑡 time,
𝑄: the intensity coefficients of pheromone which are
increased,
𝐿 𝑘 : the length of the tour built by the 𝑘th ant.
Suppose there are 𝑚 ants (vehicles) in the system, every
ant has the following characters:
(A) To select the next intersection according to the probability function with the value of the pheromones
between intersections (suppose 𝜏𝑖𝑗 (𝑡) as pheromone
on edge 𝑒(𝑖, 𝑗) at that moment (𝑡)),
(B) To ensure walking along the legal path, the ants
being forbidden to access roads which they have
passed before except when there is no other route to
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International Journal of Distributed Sensor Networks
the destination which is controlled by the tabu table
(suppose tabu𝑘 represents the 𝑘th ant’s tabu table and
tabu𝑘 (𝑠) represents the 𝑠th element in tabu table),
(C) To update pheromones on every edge which it has
walked along when the journey is completed.
At beginning, the initial value of pheromone on every
path is unequal. Suppose 𝜏𝑖𝑗 (0) = 𝐶0 (𝐶0 as the precomputed
constant). 𝑝𝑖𝑗𝑘 (𝑡) presents ant 𝑘’s probability to be transferred
from 𝑖 to 𝑗 at 𝑡 time:
𝛽
𝜏𝑖𝑗𝛼 (𝑡) ⋅ 𝜂𝑖𝑗 (𝑡)
{
{
{
𝛽
𝑝𝑖𝑗𝑘 = { ∑
𝜏𝛼 ⋅ 𝜏 (𝑡)
{
{ 𝑠∈allowed 𝑖𝑗 𝑖𝑠
{0
if 𝑗 ∈ allowed𝑘
(4)
otherwise,
where allowed𝑘 = {0, 1, . . . , 𝑛 − 1} − tabu𝑘 denotes intersections permitted as the next step by ant 𝑘, tabu𝑘 (𝑘 =
1, 2, . . . , 𝑚) records the intersections ant 𝑘 walks through,
and the set of tabu𝑘 is adjusted dynamically with evolution
processing. The heuristic function of 𝜂𝑖𝑗 denotes the visibility
of edge(𝑖, 𝑗), calculated with some heuristic algorithms. Normally let 𝜂𝑖𝑗 = 1/𝑑𝑖𝑗 , where 𝑑𝑖𝑗 denotes the distance between
the nodes 𝑖 and 𝑗. For ant 𝑘, the smaller the 𝑑𝑖𝑗 , the bigger the
𝜂𝑖𝑗 and the greater the 𝑝𝑖𝑗𝑘 . Obviously, the heuristic function
denotes expectations of ants access node 𝑖 to node 𝑗. 𝛼 denotes
the importance of trajectory and 𝛽 denotes the importance of
visibility. After 𝑛 moments, the ant finishes one travel and the
pheromones have to be adjusted on each path as follows:
Decision Making (MADM). TOPSIS method is often used
for solving MADM problems [19, 20]. MADM problems can
have several solutions [21], in which the most ideal solution
is named the positive ideal solution and the worst solution
named the negative ideal solution. In the TOPSIS method,
the solution which is closest to the positive ideal solution
and farthest from the negative ideal solution is the optimal
solution [22].
3.2.1. Normalized Road Decision Matrix. Suppose each intersection contains 𝑚 outdegrees; each of outdegree contains 𝑛
attribute value in the road network; then the matrix below is
formed:
𝑎11 𝑎12 ⋅ ⋅ ⋅ 𝑎1𝑛
]
[𝑎
[ 21 𝑎21 ⋅ ⋅ ⋅ 𝑎2𝑛 ]
]
[
, (7)
𝐴 = (a1 , a2 , a3 , . . . , a𝑚 ) = [ .
..
.. ]
]
[ .
. ⋅⋅⋅ . ]
[ .
[𝑎𝑚1 𝑎𝑚1 ⋅ ⋅ ⋅ 𝑎𝑚𝑛 ]
where (a1𝑖 , a2𝑖 , . . . , a𝑚𝑖 ) represent different outdegrees section
of the same intersection; (a𝑖1 , a𝑖2 , . . . , a𝑖𝑛 ) represent different
parameters of the same section.
3.2.2. Calculating the Weight Vectors. Let 𝜔󸀠 = (𝜔1󸀠 , 𝜔2󸀠 ,
. . . , 𝜔𝑛󸀠 ) be the initialized weight value of attribute vector. It
needs to calculate weight vector 𝜔󸀠 maximizing all deviation
values for all the vectors. Formulate a nonlinear programming model:
𝑚
𝑚
Δ𝜏𝑖𝑗 = ∑ Δ𝜏𝑖𝑗𝑘 ,
𝑛
𝑖=1 𝑗=1 𝑙=1
(5)
𝑚
∑𝜔𝑗󸀠2
𝑗=1
Subject to
𝑘=1
where 𝜌 (𝜌 ⊂ [0, 1]) is the pheromone decay factor; (Δ𝜏𝑖𝑗𝑘 )
describes pheromones of ant 𝑘 left on the road segment 𝑒(𝑖𝑗)
of this travel; (Δ𝜏𝑖𝑗 ) describes pheromones of all ants left on
the road 𝑒(𝑖𝑗) of this travel:
𝑄
{
Δ𝜏𝑖𝑗𝑘 = { 𝐿 𝑘
{0
𝑛
𝐹 (𝜔󸀠 ) = ∑ ∑ ∑𝜔𝑗󸀠 𝑑 (𝑟𝑖𝑗 , 𝑟𝑙𝑗 ) ,
max
𝜏𝑖𝑗 (𝑡 + 𝑛) = (1 − 𝜌) ⋅ 𝜏𝑖𝑗 (𝑡) + Δ𝜏𝑖𝑗 ,
= 1,
0≤
(8)
𝜔𝑗󸀠
≤ 1,
where 𝑑(𝑟𝑖𝑗 , 𝑟𝑘𝑗 ) is the distance between different varieties
which belong to the same attribute. Set that
2
𝑑 (𝑟𝑖𝑗 , 𝑟𝑘𝑗 ) = (𝑟𝑖𝑗 − 𝑟𝑙𝑗 ) .
(9)
To solve formula (9), let
if 𝑘th ants access 𝑒 (𝑖, 𝑗) in this travel
(6)
otherwise.
3.2. The Pheromone Computation of MACO. The key part of
MACO is to determine parameter 𝑝𝑖𝑗𝑘 , namely, the probability
of ant 𝑘 transfer from node 𝑖 to node 𝑗 at time 𝑡, and firstly we
determine the initial value of pheromone 𝜏𝑖𝑗 (0).
Every intersection has some attribute values and every
attribute needs a different weight. This shows the important
grade, to calculate the pheromones in ant colony optimization
algorithm. So set a weight value for each attribute of each
outdegree of intersection as (𝜔1 , 𝜔2 , . . . , 𝜔𝑛 ), and calculate the
weight with the maximizing deviation method [16] and Technique for Order Preference by Similarity to Ideal Solution
(TOPSIS) method [17]. The maximum deviation method was
presented in [18] to solve the problem of Multiple Attribute
𝑚 𝑛 𝑛
𝑚
1
𝐻 (𝜔󸀠 , 𝜉) = ∑ ∑ ∑𝜔𝑗󸀠 𝑑 (𝑟𝑖𝑗 , 𝑟𝑙𝑗 ) − 𝜉 ( ∑ 𝜔𝑗󸀠 − 1) . (10)
2
𝑗=1 𝑖=1 𝑙=1
𝑗=1
The partial derivatives of formula (10) are computed as
𝜕𝐻 (𝜔󸀠 )
𝜕𝜔𝑗󸀠
𝜕𝐻 (𝜔󸀠 )
𝜕𝜉
𝑛
𝑛
= ∑ ∑𝑑 (𝑟𝑖𝑗 , 𝑟𝑖𝑙 ) − 𝜉𝜔𝑗󸀠 = 0,
1 ≤ 𝑗 ≤ 𝑚,
𝑖=1 𝑙=1
(11)
1 𝑚
= − ( ∑𝜉𝑗󸀠2 − 1) = 0,
2 𝑗=1
1 ≤ 𝑗 ≤ 𝑚.
From formula (11), get
𝜔𝑗󸀠 =
∑𝑛𝑖=1 ∑𝑛𝑙=1 𝑑 (𝑟𝑖𝑗 , 𝑟𝑙𝑗 )
2
𝑛
𝑛
√ ∑𝑚
𝑗=1 (∑𝑖=1 ∑𝑙=1 𝑑 (𝑟𝑖𝑗 , 𝑟𝑙𝑗 ))
,
1 ≤ 𝑗 ≤ 𝑚.
(12)
International Journal of Distributed Sensor Networks
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Normalizing the final weight from 𝜔𝑗󸀠 to 𝜔𝑗 , get
𝜔𝑗 =
𝜔𝑗󸀠
𝑚
∑𝑗=1 𝜔𝑗󸀠
=
∑𝑛𝑖=1 ∑𝑛𝑙=1 𝑑 (𝑟𝑖𝑗 , 𝑟𝑙𝑗 )
𝑛
𝑛
∑𝑚
𝑗=1 ∑𝑖=1 ∑𝑙=1 𝑑 (𝑟𝑖𝑗 , 𝑟𝑙𝑗 )
,
700
1 ≤ 𝑗 ≤ 𝑚. (13)
500
So we have the weights of different attributes, and then we
can obtain the data of every intersection.
3.2.3. Calculating the Positive and Negative Ideal Solutions.
According to the weight value determined from (13), we can
formulate the normalized decision matrix and obtain the
positive and the negative ideal solutions as follows:
𝜒𝑖𝑗 = 𝜔𝑗 𝑟𝑖𝑗,
(14)
𝜒− = [𝜒1− , 𝜒2− , . . . , 𝜒𝑛− ] ,
2
𝑝𝑖∗ = √ ∑𝑑 (𝜒𝑖𝑗 , 𝜒𝑗∗ ) ,
1 ≤ 𝑖 ≤ 𝑛,
𝑗=1
(15)
2
𝑝𝑖− = √ ∑𝑑 (𝜒𝑖𝑗 , 𝜒𝑗− ) ,
1 ≤ 𝑖 ≤ 𝑛.
100
10
4
11
5
12
6
13
7
14
8
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
63
64
57
0
Source
58
200
59
400
60
600
61
800
62
1000
1200
1400
Destination
Lane status
Multiattribute
According to the definition of TOPSIS method, the
nearer it is to the positive ideal solution the farther it is from
the negative one, the better the solution will be obtained. The
pheromones of each outdegree can be achieved as follows:
𝑝𝑖∗
,
𝑝𝑖− + 𝑝𝑖∗
1 ≤ 𝑖 ≤ 𝑛.
𝑇(𝑛) = 𝑂(𝑁 ⋅ 𝑛2 ⋅ 𝑚). And the real-time complexity of MACO
is lower than ACO because of distributed computing adopted
in MACO, which means the pheromones are computed in
information nodes and the MACO run in every vehicle to get
a very path for the vehicle itself. And next step we will study
the algorithm complexity furthermore.
4. Simulation
𝑗=1
(16)
Combining the experiment with the above algorithm,
several other parameters in the ant colony optimization
algorithm are determined as follows:
Δ𝜏𝑖𝑗 (0) = 𝑝𝑖 ,
𝑄
{
{
Δ𝜏𝑖𝑗𝑘 = { 𝐿 𝑖𝑗
{
0
{
200
9
3
Figure 2: The navigation path planning under different conditions.
3.2.4. Calculating the Pheromone Values of MACO. Euler
distance can be achieved with 𝑚 degrees on each intersection
node as follows:
𝑝𝑖 =
300
2
Travel distance
Travel time
subject to 𝜒∗ = [1], 𝜒− = [0].
𝑚
400
0
𝜒∗ = [𝜒1∗ , 𝜒2∗ , . . . , 𝜒𝑛∗ ] ,
𝑚
600
1
if the 𝑘th ant passed this 𝑒 (𝑖𝑗) in this travel (17)
else,
where 𝐿 𝑖𝑗 is the length of 𝑒(𝑖𝑗).
3.3. The Algorithm Complexity of MACO. The algorithm
complexity of MACO is similar to ACO according to MACO
based on ACO. We assume that 𝑚 ants have to traverse 𝑛
elements (intersections in this paper) after 𝑁 circulations
to get a solution of MACO. The effects of low power can
be neglected if 𝑛 is lager enough when calculating the
time complexity, and the time complexity of MACO is
We mainly pay attention to several different types in the
process of navigation algorithm: time priority, distance priority, road condition priority, and integrated priority. Time
priority refers to arriving at the destination with minimum
time, distance priority refers to arriving at the destination
with the shortest path, road condition priority refers to
arriving at the destination with the best intersection line, and
integrated priority preference refers to combining different
road properties and then arriving at the destination with the
least cost.
To illustrate conveniently, a road map measured with 8
by 8 squares is adopted to simulate road navigation. In the
designed grid map (Figure 2), each intersection represents a
road traffic intersection. Each node can adjoin the adjacent
nodes bidirectionally. To stimulate path planning under
different conditions, it is assumed that the path (49-56) and
path (2-58) have two-way four-lane widths and other roads
are of two-way two-lane width; here (𝑖-𝑗) represents the linear
connection from node 𝑖 to node 𝑗. Each of the horizontal
distances between the intersections is set at 200 meters;
the vertical distance between each intersection is set at 100
meters. At the same time, the average speed of road (57-64) is
set at 20 km/h, the average speed of road (49-56) is 30 km/h,
the average speed of roads (41-48) and (33-40) is 40 km/h, and
the average speed of the other roads is 60 km/h.
In the following, different navigation algorithms of
MACO and two famous algorithms (the Dijkstra algorithm
6
International Journal of Distributed Sensor Networks
Table 2: Statistics of three algorithms in normal situation.
B
A
C
The Dijkstra algorithm
The A∗ algorithm
The MACO algorithm
Figure 3: Normal traffic map in Zhuhai City.
Table 1: Different planning path ON 8 × 8 grid chart.
Navigation mode
Dijkstra navigation algorithm
A∗ algorithm
MACO
Distance priority
Road condition priority
Time priority
Integrated priority
Path length (m)
1400
2200
Time (s)
252
132
1400
1600
2200
1800
252
178
132
150
and the A∗ algorithm) are adopted to analyze the network.
First, the Dijkstra algorithm and MACO are adopted to plan
the shortest path and the result show that the planned paths
are the same one (57-64), with the length of 1400 meters
and time of 252 seconds. If MACO is only concerned with
the path length, the result obtained is consistent with the
Dijkstra algorithm. When only road width is considered, the
planned path by MACO is (57-49-56-64), with the length of
1600 meters and the time of 178 seconds. The path planned
by MACO is (57-25-32-64) with the length of 2200 meters
and 132 seconds if only the average velocity be cared about,
that is the same as the A∗ algorithm planned. When MACO
integrates road conditions such as path length, road width,
road grade, and average velocity for analysis, the optimal
planning path is (57-41-48-64), with the length of 1800 meters
and the time of 150 seconds. The simulation results of several
different ways of navigation are shown in Table 1.
Now we simulate with Zhuhai City map; as shown in
Figure 3, we choose the area with 60 road intersections as
coordinates. For each section between two adjacent intersections, we stimulate the path length, road width, road grade,
Algorithm
Starting point →
destination
Distance (meter)
Time
(second)
Dijkstra
algorithm
A→C
B→C
8870
10300
539
589
A∗ algorithm
A→C
B→C
9090
10300
467
589
MACO
A→C
B→C
9090
10300
467
589
and average velocity and then simulate MACO in SUMO
environment and then carry on the simulation under velocity
and time preference.
As shown in Figure 3, the Dijkstra algorithm, A∗ algorithm, and MACO apply to plan a path from point A to point
C and path from point B to point C separately; the results are
shown in Table 2. First of all, the algorithms are adopted and
make a comparison from point A to point C. The Dijkstra
algorithm chooses a path with distance of 8870 meters and
time 539 seconds; MACO chooses a path with distance of
9090 meters and time of 467 seconds, which is the same as the
A∗ algorithm. Then the algorithms are adopted to compare
from point B to point C, respectively. Path distance of all three
algorithms is 10300 meters, with the time of 589 seconds. The
results show that the path planned by the Dijkstra algorithm
is the shortest path and would not consider velocity and other
factors.
MACO can consider the comprehensive factors, so, from
point A to point C, although the path planned by MACO is
longer than the path planned by the Dijkstra algorithm, it
still saves time since the average velocity is higher, which is
the same as the A∗ algorithm planned. For the path whose
average path length and velocity are all optimal, MACO is
consistent with the result of the Dijkstra algorithm and the A∗
algorithm, such as from point B to point C, passes through the
distance of 10300 meters, using identical times of 589 seconds,
respectively.
Among the above, the left convergence curves of Figure 4
are based on time (velocity) priority; the right convergence
curves of Figure 4 are based on distance priority. On the left
of the Figure 4 there are two convergence curves and we get
the below convergence curve of travel time when we try to
get a planning path only considering the high velocity or
short travel time with MACO, and at same time we get the
convergence curve of travel distance accordingly as the above
one. And on the right of Figure 4 there are two convergence
curves, too. We get the above convergence curve of travel
distance when we try to get a planning path only considering
the shortest travel distance with MACO, and at the same time
we get the convergence curve of travel time accordingly as the
below one. We can see that all the curves can be converged
normally under two situations.
In order to further illustrate the advantages of MACO,
simulation is carried out with this map and path, but set
limited velocity in some sections as shown in the shadow
International Journal of Distributed Sensor Networks
7
20
Travel distance
Travel distance
20
15
10
5
0
0
20
40
60
80
15
10
5
0
100
0
20
40
Iterations
80
100
60
80
100
35
Travel time
Travel time
35
30
25
20
60
Iterations
0
20
40
80
60
100
30
25
20
0
20
Iterations
40
Iterations
(a) Time (velocity) priority convergence curves
(b) Distance priority convergence curves
Figure 4: Convergence curves of MACO.
Figure 5: Traffic map of congestion situation in Zhuhai.
Table 3: Statistics of three algorithms in congestion situation.
Algorithm
Starting point →
destination
Distance (meter)
Time
(second)
Dijkstra
algorithm
A→C
B→C
8870
10300
803
872
A∗ algorithm
A→C
B→C
10380
11290
591
663
MACO
A→C
B→C
10380
11290
591
663
part of Figure 5. Assuming that it is facing congestion, the
simulation results are shown in Table 3.
From Table 3 we can see that if we set the shadow part as a
traffic jam, the Dijkstra algorithm would not consider special
cases and the path planned is still consistent with the normal
circumstances, path length from point A to point C and point
B to point C is 8870 meters and 10300 meters, but the time
it takes increases to 803 and 872 seconds, respectively. And
MACO fully considers the congestion; the paths planned are
longer than normal and the path planned by the Dijkstra
algorithm increased to 10380 meters and 11290 meters from
point A to point C and point B to point C, but the time is less
than the Dijkstra obviously, as 591 seconds and 663 seconds,
which are consistent with the A∗ algorithm planned.
MACO not only considers the integrated traffic information according to the requirement of path planning, but also
can make path plans according to users’ requirements. Below
we still use Figure 5 traffic map and make analysis with only
focusing on the path length, road width, average velocity, and
comprehensive situation separately, as shown in Table 4.
According to Table 4, taking congestion into consideration, from point A to point C, the distance priority takes
the distance of 8870 meters but the longest time of 803
seconds; the road condition priority only considers the road
width which chooses the longest distance of 11600 meters and
takes 655 seconds; it is similar between time priority and the
integrated priority, the distance of 10380 meters, and takes 591
seconds. From point B to point C, the distance priority has the
shortest distance of 10300 meters but takes the longest time of
872 seconds; the road condition priority planned the longest
distance path for 12510 meters and takes 726 seconds in total;
compared to the comprehensive case, time priority planned a
longer distance path of 11530 meters and takes 647 seconds;
integrated priority has a distance of 11290 meters and takes
663 seconds. From the above it can be concluded that the
comprehensive situation, namely, integrated priority, takes
account of path length, road width, road grade, and average
velocity, so the distance and the time of the path planned
cannot be the best, but it provides the optimal comprehensive
solution.
The MACO has an important feature that it can plan path
in real time with the dynamic traffic situation. Using ring map
8
International Journal of Distributed Sensor Networks
A
A
C
C
B
B
The Dijkstra algorithm
The A∗ algorithm
The MACO algorithm
The Dijkstra algorithm
The A∗ algorithm
The MACO algorithm
(a) In the normal traffic situation
(b) In the heavy traffic situation
Figure 6: Map of Areia Preta in Macau.
Table 4: Statistics under congestion situation using MACO.
Algorithm
A→C
B→C
Priority
Distance priority (as the Dijkstra algorithm)
Road condition priority
Time priority (as the A∗ algorithm)
Integrated priority
Distance priority (as the Dijkstra algorithm)
Road condition priority
Time priority (as the A∗ algorithm)
Integrated priority
of Areia Preta in Macau, for example, these further illustrate
the simulation results obtained by the algorithm as shown in
Figure 6.
Figure 6 shows two different situations in the urban traffic
of Macau. The left of the maps shows normal traffic situation
and that means there are no traffic jams. The right one of
the maps shows the dynamic traffic situation, meaning that
the traffic congestion is dynamically changing. The shadow
part of Figure 6 is the traffic jam with an average speed of
20 km/h; other sections are normal traffic roads. Bold line
shows two-way four-lane road with the average speed of
60 km/h and other roads indicate two-way two-lane roads
with the average speed of 50 km/h. The unidirectional road
segments are omitted for simplification. Simulation is carried
out with the path planning from point A to point B. Also the
Dijkstra algorithm, A∗ algorithm, and MACO are adopted to
make contrastive analysis, as shown in Table 5.
The obvious differences are shown among three algorithms from the planned path. In the normal traffic situation,
Distance (meter)
8870
11600
10380
10380
10300
12510
11530
11290
Time (second)
803
655
591
591
872
726
647
663
the Dijkstra algorithm plans a path whose travel distance is
1290 meters and the travel time is 104 seconds; it has the
shortest path but the longest travel time. MACO chooses a
path as good as the A∗ algorithm whose travel distance is
1406 meters and the travel time is 94 seconds. The path which
MACO chose is longer than that of the Dijkstra algorithm’s
but the time is shorter.
In order to describe the algorithms in detail, suppose
there are three cars travelling along the different paths
planned above. When they travel to point C, the congestion
happens in front of the path. Because they cannot plan
dynamically the path according to the traffic situation, the
cars adopt the planned path by the Dijkstra algorithm and
the A∗ algorithm toward destination with no change of
the route. They take 1290-meter travel distance with 142
seconds and 1406-meter travel distance with 216 seconds
finally, respectively. At the same time, the car which takes the
path planned (shown as red dotted line) by MACO changes
to a new route (shown as red solid line) which is planned
International Journal of Distributed Sensor Networks
9
Table 5: Statistics of Macau under the real-time traffic situation.
Traffic situation
Priority method
Dijkstra algorithm
A∗ algorithm
MACO algorithm
Dijkstra algorithm
A∗ algorithm
MACO algorithm
Normal traffic situation
Dynamic traffic situation
1500
1464
1450
1406 1406
1400
Time (second)
104
94
94
142
216
120
350000
303696
300000
1406
250000
200000
1350
1300
Distance (meter)
1290
1406
1406
1290
1406
1464
1290 1290
150000
183180
134160
175680
132164
132164
100000
1250
50000
1200
∗
Dijkstra
A
MACO
Normal traffic situation
Dynamic traffic situation
Figure 7: The distance cost comparison of two situations.
0
Dijkstra
A∗
MACO
Normal traffic situation
Dynamic traffic situation
Figure 9: The comprehensive cost comparison of two situations.
250
216
200
150
142
104
100
94
94
120
50
0
Dijkstra
A∗
MACO
Normal traffic situation
Dynamic traffic situation
Figure 8: The time cost comparison of two situations.
dynamically and has a travel distance of 1464 meters with
travel time of 120 seconds. The real paths they traveled are
shown in the right map of Figure 6.
From Figure 7, which shows the distance cost comparison
of normal traffic situation and dynamic traffic situation, we
can see that in two situations the Dijkstra algorithm and A∗
algorithm have no change of planning path. But for MACO
algorithm, the length of the planned path in dynamic traffic
situation is longer than that in normal traffic situation. Then
from Figure 8, which shows the time cost comparison of
three algorithms in normal traffic situation and dynamic
traffic situation, we can see that all the time costs of three
algorithms have increased, and the MACO algorithm has
the minor increase of time cost comparing with other two
algorithms. To further compare the three algorithms, we
construct comprehensive cost data using time cost to multiply
distance cost as shown in Figure 9. From normal traffic
situation to dynamic traffic situation, the comprehensive
costs of three algorithms are all increased. The cost of A∗
algorithm has increased drastically, the Dijkstra algorithm
is the second, and the MACO algorithm stands with least
increase. The results show that though it can give the same
planned path in normal traffic situation, MACO is better
than other algorithms, that is, the Dijkstra algorithm and A∗
algorithm, because MACO can adjust dynamically planning
path according to dynamic traffic situation and represent an
optimal path with integrating the path length, road width,
road grade, and average velocity with the least cost.
5. Conclusion
This paper has developed a novel multiple-metric ant colony
optimal algorithm for vehicle path planning, in which four
kinds of traffic attributes are considered, and some phases
of the algorithm are discussed. A new general metric has
been introduced as the pheromone value of ant colony optimization algorithm. Based on multiple traffic information
and planning requirements, the proposed algorithm selects
the most effective and suitable planning path. Simulation
results demonstrate that the presented algorithm could easily
achieve the suitable path according to different requirements,
including the shortest path planning and the shortest time
planning, in the real-time vehicular traffic networks. This
algorithm provides a potential solution for energy consumption and environmental pollution in increasingly complex
urban traffic environment, which could be used in intelligent
transportation system.
Conflict of Interests
The authors declare that there is no conflict of interests
regarding the publication of this paper.
10
International Journal of Distributed Sensor Networks
References
[1] A. Rekaby, A. A. Youssif, and A. Sharaf Eldin, “Introducing
Adaptive Artificial Bee Colony algorithm and using it in solving
traveling salesman problem,” in Proceedings of the Science and
Information Conference (SAI ’13), pp. 502–506, October 2013.
[2] N. Chaiyaratana and A. M. S. Zalzala, “Recent developments in
evolutionary and genetic algorithms: theory and applications,”
in Proceedings of the 2nd International Conference on Genetic
Algorithms in Engineering Systems: Innovations and Applications
(GALESIA ’97), vol. 446, pp. 270–277, Glasgow, Scotland,
September 1997.
[3] M. Dorigo, G. Di Caro, and L. M. Gambardella, “Ant algorithms
for discrete optimization,” Artificial Life, vol. 5, no. 2, pp. 137–
172, 1999.
[4] M. Dorigo, M. Birattari, and T. Stützle, “Ant colony optimization,” IEEE Computational Intelligence Magazine, vol. 1, no. 4,
pp. 28–39, 2006.
[5] K. S. V. Narasimha and M. Kumar, “Ant colony optimization
technique to solve the min-max single depot vehicle routing
problem,” in Proceedings of the American Control Conference
(ACC ’11), pp. 3257–3262, July 2011.
[6] K. S. V. Narasimha, E. Kivelevitch, and M. Kumar, “Ant Colony
optimization technique to Solve the min-max multi depot
vehicle routing problem,” in Proceedings of the American Control
Conference (ACC ’12), pp. 3980–3985, June 2012.
[7] L. Li, S. Ju, and Y. Zhang, “Improved ant colony optimization
for the traveling salesman problem,” in Proceedings of the
International Conference on Intelligent Computation Technology
and Automation (ICICTA ’08), pp. 76–80, IEEE, Hunan, China,
October 2008.
[8] D. Zeng, Q. He, B. Leng et al., “An improved ant colony
optimization algorithm based on dynamically adjusting ant
number,” in Proceedings of the IEEE International Conference
on Robotics and Biomimetics (ROBIO ’12), pp. 2039–2043,
December 2012.
[9] B. F. Moghaddam, R. Ruiz, and S. J. Sadjadi, “Vehicle routing
problem with uncertain demands: an advanced particle swarm
algorithm,” Computers & Industrial Engineering, vol. 62, no. 1,
pp. 306–317, 2012.
[10] C. Lee, K. Lee, and S. Park, “Robust vehicle routing problem
with deadlines and travel time/demand uncertainty,” Journal of
the Operational Research Society, vol. 63, no. 9, pp. 1294–1306,
2012.
[11] C. L. Philip Chen, J. Zhou, and W. Zhao, “A real-time vehicle
navigation algorithm in sensor network environments,” IEEE
Transactions on Intelligent Transportation Systems, vol. 13, no.
4, pp. 1657–1666, 2012.
[12] E. W. Dijkstra, “A note on two problems in connexion with
graphs,” Numerische Mathematik, vol. 1, pp. 269–271, 1959.
[13] E. Amiri, H. Keshavarz, M. Alizadeh, M. Zamani, and T. Khodadadi, “Energy efficient routing in wireless sensor networks
based on fuzzy ant colony optimization,” International Journal
of Distributed Sensor Networks, vol. 2014, Article ID 768936, 17
pages, 2014.
[14] Y. Liu, S. Zhang, J. Fan, and J. Jia, “A path planning algorithm
with a guaranteed distance cost in wireless sensor networks,”
International Journal of Distributed Sensor Networks, vol. 2012,
Article ID 715261, 12 pages, 2012.
[15] Y. Jo, J. Choi, and I. Jung, “Traffic information acquisition
system with ultrasonic sensors in wireless sensor networks,”
[16]
[17]
[18]
[19]
[20]
[21]
[22]
International Journal of Distributed Sensor Networks, vol. 2014,
Article ID 961073, 12 pages, 2014.
G.-W. Wei, “Maximizing deviation method for multiple
attribute decision making in intuitionistic fuzzy setting,”
Knowledge-Based Systems, vol. 21, no. 8, pp. 833–836, 2008.
D.-F. Li, “TOPSIS-based nonlinear-programming methodology
for multiattribute decision making with interval-valued intuitionistic fuzzy sets,” IEEE Transactions on Fuzzy Systems, vol.
18, no. 2, pp. 299–311, 2010.
Y. M. Wang, “Using the method of maximizing deviations
to make decision for multi-indices,” System Engineering and
Electronics, vol. 7, pp. 24–26, 1998.
M. Johnson and S. Silas, “Position aware and QoS based service
discovery using TOPSIS for vehicular network,” International
Journal of Engineering Science & Technology, vol. 5, pp. 576–582,
2013.
Ö. Bali, S. Gümüş, and M. Dağdeviren, “A group MADM
method for personnel selection problem using Delphi technique based on intuitionistic fuzzy sets,” Journal of Military and
Information Science, vol. 1, no. 1, pp. 1–13, 2013.
H. Zhang and L. Yu, “MADM method based on cross-entropy
and extended TOPSIS with interval-valued intuitionistic fuzzy
sets,” Knowledge-Based Systems, vol. 30, pp. 115–120, 2012.
G.-H. Tzeng and J.-J. Huang, Multiple Attribute Decision Making: Methods and Applications, CRC Press, Boca Raton, Fla,
USA, 2011.
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