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978-1-5090-4601-0/17/$31.00 ©2017 IEEE
Improved Artificial Bee Colony Algorithm for
Solving Urban Traffic Light Scheduling Problem
Kaizhou Gao*, Yicheng Zhang, Ali Sadollah, Rong Su
School of Electrical and Electronic Engineering
Nanyang Technological University, 639798, Singapore
gaokaizh@aliyun.com, yzhang088@e.ntu.edu.sg, ali_sadollah@yahoo.com, rsu@ntu.edu.sg
Abstract
:
In this paper, a novel centralized traffic network model
is proposed to describe the urban traffic light scheduling problem
(UTLSP) in a traffic network. The objective is to minimize the
network-wise total delay time of all vehicles in a fixed time
window. To overcome the potentially high computational
complexity involved in UTLSP, an improved artificial bee colony
(IABC) algorithm is proposed. A new solution generating strategy
and three local search operators corresponding to different
neighbourhood structures of UTLSP are proposed to improve the
performance of IABC. Extensive computational experiments are
carried out using sixteen instances with different problem-scales.
The IABC with and without three local search operators are
evaluated and compared. The comparisons and discussions show
the competitiveness of IABC for solving UTLSP.
Keywords
:
Traffic light scheduling; artificial bee colony; Traffic
network; Local search
I. I
NTRODUCTION
An urban traffic network consists of a set of road links
connecting with each other via intersections. Each intersection
consists of a number of approaches and the crossing area. An
approach may have one or more lanes but has a unique,
independent queue. Approaches are used by corresponding
traffic streams (veh/h). Two compatible streams can safely cross
the intersection simultaneously, while antagonistic streams
cannot. In traditional traffic signal control, a signal cycle is one
repetition of the basic series of stages at an intersection, where
each stage consists of simultaneous traffic light signals allowing
a predefined compatible traffic streams to cross the intersection
simultaneously. The duration of a cycle is called cycle time [1-
4]. For safety reasons, constant lost (or inter-green) times of a
few seconds are necessarily inserted between consecutive
stages to avoid interference between antagonistic streams. For
each traffic light, the ratio of the green time and the red time
within one cycle is called the split, and the delay between
the starting times of green periods of two neighbouring
traffic lights along the same traffic route is called offset [5-6].
There are basically four types of characteristics that
distinguish different traffic signal control strategies, i.e., fixed
time strategies versus traffic responsive strategies, and
isolated strategies versus coordinated strategies. Notable
strategies proposed in the last few decades include, e.g.,
MAXBAND [7], TRANSYT [7], SCOOT [8], OPAC [9]),
PRODYN [10], CRONOS [11], and RHODES [12]. In this
paper we describe a traffic network by a flow dynamic model
similar to Daganzo’s cell transmission models (CTM) [13-14].
The novelty of our model is to describe each outgoing link flow
rate as a nonlinear mixed logical switching function, instead of
the traditional linear and saturated functions used in CTM, over
the source link’s density, the destination link’s density and
capacity, and the driver’s potential psychological response to the
past traffic light signals. The advantage of the outgoing flow rate
model is that it includes more detailed information gathered
from the traffic system, which makes our approach suitable to
both under-saturated and over-saturated situations. Besides, our
model considers drivers’ behaviours in response to the past
traffic light statuses in the traffic system. It is able to provide a
more realistic description of the dynamics of the real-world
urban traffic flow, making our traffic model more likely to lead
to proper traffic light control solutions for real-time applications.
Recently, meta-heuristics have been employed for solving
many optimization problems [15], e.g. traffic light scheduling
problems [16-20]. Some new meta-heuristics are proposed for
unconstrained and constrained optimization problems and these
meta-heuristics are applied to solve various optimization
problems [21-22]. Among different meta-heuristics, the artificial
bee colony (ABC) is a widely employed swarm intelligence
algorithm for continuous and discrete optimization problems.
ABC algorithm is a relatively new population-based meta-
heuristic approach that is based on the collective behaviour of
self-organized systems. It was first proposed to solve the multi-
variable and multi-modal continuous functions [23]. Many
comparative studies have shown that the performance of the
ABC algorithm is superior to other population-based algorithms
in the continuous space [25-28]. Due to this reason, the ABC
algorithm has received a significant amount of interests from
researchers in scheduling fields [29-32]. Zhang [33] proposed an
ABC algorithm for job shop scheduling problem with random
processing times. Wang [34-35] designed two effective ABC
algorithms for mono-objective and multi-objective flexible job
shop scheduling problem (FJSP). Thammano [36] designed a
hybrid ABC algorithm with local search to solve FJSP. GAO
[37-38] proposed a two-stage ABC algorithm for the fuzzy
flexible job shop scheduling problem with new job insertion. An
ensemble of local search operators was proposed in the study to
improve algorithm performance.
Existing models and approaches focused on many aspects of
traffic light scheduling problems. But there are some
insufficiencies. The first one is the limited problem scale and
few constraints. The second one is that most existing models and
approaches have limitations for practical traffic light scheduling
problems. The third one is that the most models are cycle
395
programs and the light periods are fixed. In our model, the
traditional concepts of cycles, splits and offsets are not adopted,
making UTLSP fall in the class of model-based optimization
problems, where each traffic light is assigned with a green light
period in a real-time manner by the network controller. Building
on the successful application of ABC for solving scheduling
problems, we propose an improved ABC (IABC) algorithm to
solve the UTLSP. The objective is to minimize the total
network-wise delay in a fixed time window.
The remainder of this paper is organized as follows. Section
2 describes the urban traffic light scheduling problem
formulation. In Section 3, the proposed IABC algorithm is
introduced. The experiment design, comparison and discussion
are provided in Section 4. Finally, we draw conclusions and list
a few future works in Section 5.
II. U
RBAN
T
RAFFIC
L
IGHT
S
CHEDULING
P
ROBLEM
A traffic network consists of a set of links and intersections.
For example, a simple unidirectional traffic network is depicted
in Fig. 1, where each intersection has only two antagonistic
traffic flows. We have proposed a discrete time model based on
the cell transmission. To simplify our technical discussions,
some key notations in urban traffic signal scheduling problem
formulation are listed as follows:
-----------------------------------------------------------------------
C
(k) The number of vehicle in link i in the time interval k.
f
(k) The exit flow rate from link i to link j in interval k.
Δ The sampling interval.
ℒ The set of all one-way links.
The set of all intersections.
Ω
The set of stages in intersection J, J∈.
ℱ
ℱ
⊆ℒ×ℒ, the set of all streams in intersection J, i.e.,
(i,j)∈ℱ
means that there exists a traffic stream from link i
to link j via intersection J.
h
:Ω
→2
ℱ
The association of each stage to relevant
compatible streams.
() The entrance flow rate of link in time interval .
() The exit flow rate of link in time interval .
() The speed category in time interval .
-----------------------------------------------------------------------
We make the following assumptions about a traffic network
[39], which is suitable for a deterministic analysis:
• No traffic demand is generated inside the network.
• The network entrance and exit models are known.
• The link turning ratios in the network are known.
• Each vehicle inside the network will leave the network,
delayed only by traffic signals.
• The vehicle speed in each link has a finite number of
known values.
In our traffic flow model we consider three types of
constraints, which are described as follows.
1) The Stage Status Constraints
At each time interval , there exists only one active stage for
an intersection , as captured by the following constraints:
∀∈Ω
()=0⇒∀(,)∈ℎ
()
,
()=0
(1a)
∑
()=1
∈
(1b)
∀∈Ω
(∀∈ℕ)
()∈{0,1} (1c)
where
()=0 and
()=1 denote the RED and GREEN
traffic lights associated with stage respectively, and ℕ
denotes the set of natural numbers. Condition (1a) means that if
the stage traffic signal is RED, then all compatible traffic
streams must bestopped, i.e., the relevant link flow rates must be
zero. Condition (1b) indicates that there can be only one GREEN
traffic stage at any time.
Fig. 1 A simple traffic network
2) The Link Volume Dynamic Constraints
Due to the conservation of vehicles, each link ∈ has the
following volume dynamics:
(+1)=
()+(
()−
())∆ (2a)
(∀∈ℕ)
()∈ℕ (2b)
()=∑
()
∈ℒ:(,)∈∪
∈
ℱ
(2c)
()=∑
()
∈ℒ:(,)∈∪
∈
ℱ
(2d)
3) The Flow Dynamic Constraints
For the example shown in Fig. 1,
()=
() and
()=
(). For each stage ∈Ω
and each stream (,)∈
ℎ
(), the exit flow
() is determined by the current
upstream link volume
(), the current remaining downstream
link capacity
−
(), where
is the maximum volume of
link , and the traffic light signals in the past +1 time intervals
(−),…,
(), i.e.,
()=
(
(),
−
(),
(−),…,
() (3)
where
(⋅) is a nonlinear function. The motivation of this
model is that if stage has been active for the past intervals,
then the drivers intend to keep a high speed as long as the
downstream link has sufficient capacity to receive the flow. The
following method is employed to define
(⋅). Assume that
there are +1 monotonically non-increasing speed categories:
C
i
(K)
f
ij
(K)
C
j
(K)
f
jr
(K)
C
r
(K)
C
α
(K)
f
αβ
(K)
C
β
(K)
396
≥
≥⋯≥
, which denotes speed ranges from high to
low. The actual speed category
is determined as follows:
()=∑
()
(4a)
∑
()
−
()=0 (4b)
(∀:0≤≤−1),1−
(−−1)∏
(−
)=1⟺
()=1 (4c)
∏
(−)
=1⟺
()=1 (4d)
(∀:0≤≤)
∈{0,1} (4e)
Condition (4b) indicates that if the traffic light of stage is
RED, i.e.,
()=0, then ∑
()
=0, which by
Condition (4a) means
()=0, i.e., the speed in the stage
must be zero. If the traffic light of stage is GREEN, i.e.
()=1, then by Condition (4a),
() can only choose one
speed category because of ∑
()
=1. Condition (4c)-(4d)
means that the actual speed category depends on the number of
consecutive green light intervals from backward in time, the
larger the number of consecutive green intervals, the higher the
speed category.
After
() being determined, the link flow rate
() is
given as follows:
()∆=min{
()
(),
()(
−
())} (5a)
()∆∈ℕ (5b)
Where ∙ denotes the floor element, i.e., the largest integer
not greater than input argument, and
() is the turning ratio
of vehicles in link towards link at time interval , which is
assumed to be known in advance. Condition (5a)-(5b) indicate
that the number of vehicles in one time interval,
()∆, is the
largest integer that is upper bounded by the upstream volume
()
() of link and the downstream remaining capacity
−
() weighted by the speed category
().
4) Objective Function
The total network-wise delay time within time intervals
can be estimated as follows:
∑∑
()1−
()
,
∆
∈
=∑∑
()−
∈
,
()∆ (6a)
Where ̅
() is the average speed of link in time interval ,
which can be approximated by the ratio of the exit flow rate
() and the average link density
()
⁄, where
is the
length of link , due to the assumption that vehicles in link are
uniformly distributed with identical speeds, i.e., the acceleration
step is negligible. Based on the Condition (2a)-(2b), the
following formula is used as objective function for the
scheduling purpose.
Min∑∑
()−
,
∑
()
∈ℒ:(,)∈∪
∈
ℱ
∆
∈
(6b)
In a standard mathematical programming formulation, the
aforementioned mixed logic constraints can be transformed into
a set of mixed integer linear constraints together with the mixed
integer cost function, which make our UTLSP become a large-
scale non-convex optimization problem that is difficult to solve
in a real-time manner.
III. A
RTIFICIAL BEE COLONY ALGORITHM FOR URBAN
TRAFFIC LIGHT SCHEDULING PROBLEM
Artificial bee colony (ABC) algorithm is a population-
based meta-heuristic proposed by Karaboga (Karaboga, 2005).
ABC is inspired from the foraging behaviour of a bee colony.
There are three kinds of bees, namely, employed bees, onlooker
bees and scout bees in the ABC algorithm. Each solution to the
problem under consideration is called a food source, whereas the
fitness of the solution corresponds to the amount of nectar of the
associated food source. The main steps of the basic ABC
algorithm are shown below.
a) Initialization of the parameters and population:
The parameters of ABC are the number of food sources (
SN
), the number of trials after which a food source is to be
abandoned (limit) and the termination criterion. The number of
food sources is equal to the number of employed bees or
onlooker bees. The initialization of population is to fill the
population with
SN
number of randomly generated food
sources, where each source is represented by an n-dimensional
real-valued vectors.
Let },...,,{
21 iniii
xxxX =represent the ith food source in the
population. The food sources are generated as follows:
rLBUBLBx
jjjij
×−+= )(
nj ,...,2,1=
,
SNi ,...,2,1=
(7)
where
r
is a uniform random number in the range [0, 1];
j
LB
and
j
UB
are the lower and upper bounds for the dimension
j
, respectively. The food sources are randomly assigned to
employed bees and the corresponding finesses are evaluated.
b) Employed bee phase:
In this phase, each employed bee
i
X
generates a new food
source
new
X
in the neighbourhood of its present position as
follows:
')(
)(
rxxxx
kjijijjnew
×−+=
(8)
where
ikSNk ≠∈ },,...,2,1{
and
},...,2,1{ nj ∈
are randomly
chosen indexes.
'
r
is a uniformly distributed real number in [-1,
1].
new
X
will be compared to
i
X
. If the fitness of
new
X
is equal
to or better than that of
i
X
,
new
X
will replace
i
X
as a new food
source; otherwise
i
X
is retained.
c) Onlooker bee phase:
An onlooker bee evaluates all the employed bees and selects
a food source
i
Xdepending on its probability value
i
p
calculated by the following expression:
397
=
=
SN
ii
i
i
f
f
p
1
(9)
where
i
f
is the nectar amount or the fitness value of the i
th
food source
i
X. The higher the
i
f
is, the higher the chance of
the i
th
food source is selected.
Once the food source
i
X
is selected, the onlooker bee will
execute the update
i
X
using equation (8). If the new food source
has equal or better fitness value than
i
X
, the new food source
will replace
i
X
as a new member in the population.
d) Scout bee phase
If a food source
i
X
can not be improved through a
predetermined number of trials limit, the food source is to be
abandoned and the corresponding employed bee becomes a
scout. The scout produces a new food source randomly as
follows:
rLBUBLBx jjjij ×−+= )(
for
nj ,...,2,1=
(10)
where
r
is a uniform random number in the range [0, 1].
e) Repeat steps 2)-4) until the termination criterion is
satisfied.
A. Solution representation
Fig. 2 shows a traffic network with nine intersections, where
traffic signals on every intersection are shown by the “Green”
color or the “Red” color. A vector is employed to represent the
traffic signals in one time interval and the values are shown in
Table I. Two binary bits are used to show the traffic lights on
different directions. For every intersection, “00” represents a red
light in the horizontal direction and a green light in the vertical
direction while “01” represents a red light in the horizontal
direction and a green light for turning left in the vertical
direction. “11” represents a green light in the horizontal
direction and a red light in the vertical direction while “10”
represents a green light for turning right in the horizontal
direction and a red right in the vertical direction.
Fig. 2 An example of traffic network and traffic light signals
123
456
789
Each intersection have only four status, “00”, “01”, “10”,
“11”. The vector in Table I is a traffic light assignment. For one
time interval, the length of solution vector is two times of the
intersection number. To evaluate total network-wise delay time
of time intervals, the length of vector would be 2 times of
the intersection number.
TABLE I. Vector solution for one time interval
Inters. Num. 1 2 3 4 5 6 7 8 9
Traffic signal 00 11 11 10 01 00 11 00 10
B. Local search strategies
In UTLSP, one intersection links other intersections in
horizontal direction and vertical direction. Traffic light changing
at one intersection may alter the vehicle numbers on links and
affect traffic lights of neighbouring intersections, and even
significantly affect the objective function. For the same
intersection, traffic light changing in different time intervals will
also affect the objective function. Based on these characteristics
of UTLSP, three local search strategies are proposed to find
neighbouring solutions of existing solutions for better objective
values. The procedures of three local search strategies are
presented as follows.
---------------------------------------------------------------------------
Local search 1: Change signals for one intersection
Select one intersection in one solution .
For k=1 to N
Reverse the values of two binary bits for
().
End for
Get new solution′
Evaluate the objective value of ′
If ′ is better than
Replace using ′
Else
Remain X
End if
---------------------------------------------------------------------------
---------------------------------------------------------------------------
Local search 2: Change signals for a group intersections in
horizontal or vertical direction
Select one time interval in one solution .
Select connected intersections in horizontal or vertical
direction
For =1
Reverse the values of two binary bits for
().
End for
Get new solution′
Evaluate the objective value of ′
If ′ is better than
Replace using ′
Else
Remain X
End if
---------------------------------------------------------------------------
---------------------------------------------------------------------------
Local search 3: Change signals in sub-area of traffic network
Select one time interval in one solution .
Select connected intersections from line to line in
horizontal direction, <.
Select connected intersections from line to line in vertical
direction, <.
For =
For =
Reverse the values of two binary bits for
().
End for
End for
398
Get new solution′
Evaluate the objective value of ′
If ′ is better than
Replace using ′
Else
Remain X
End if
---------------------------------------------------------------------------
These three local search strategies are designed for three
neighbourhood structures of a traffic network. Local search 1 is
to search neighbourhoods of one selected intersection by
reversing the traffic lights of the intersection in time intervals.
Local search 2 is to search neighbourhoods of a group of selected
intersections by reversing the traffic lights of the intersections in
one time interval . Local search 3 is to search neighbourhoods
of a sub-region of the traffic network by reversing the traffic
lights of the intersections in the sub-region in one time interval
.
C. Employed bee phase
In this phase, employed bee
i
X
generates a new food source
new
X
. If the fitness of
new
X
is equal to or better than that of
i
X
,
new
X
will replace
i
X
as a new food source; otherwise,
i
X
is
retained.
To adapt UTLSP and the encoding rule of solutions, a novel
strategy for generating new food sources is shown as below:
---------------------------------------------------------------------------
Procedure: Generating new food source
If (r1<P1) //r1 is a random in [0,1], P1 is the probability to
generate new food source
Select two employed bee
p
X
and
q
X
,
iqp
XXX ≠≠
.
If (r2<P2) //r2 is a random in [0,1], P2 is the probability
to select a better food source
j
X
is equal to the better one between
p
X
and
q
X
.
Else
j
X
is equal to the worse one between
p
X
and
q
X
.
For k=1 to TI //TI is time interval times intersection
number
If (r3<P3) // r3 is a random in [0,1], P3 is the
probability to select element from
j
X
k
j
k
new
XX =
Else
k
i
k
new
XX =
Else
For k=1 to TI
If (r4<P4) // r4 is a random in [0,1], P4 is the
probability for local search
Local search 1 / 2 / 3
End
---------------------------------------------------------------------------
D. Onlooker phase
In the onlooker bee phase, the fitness of all the employed
bees are evaluated. A food source
i
X is selected depending on
its probability value
i
p calculated by expression (9). The
procedure to select a food source is shown as follows.
---------------------------------------------------------------------------
Procedure: Select a food source
Select two employed bee
p
X
and
q
X
,
qp
XX ≠
.
If (r2<P2) //r2 is a random in [0,1], P2 is the probability to select
a better food source from
p
X
and
q
X
If the fitness of
p
X
is better than that of
q
X
,
pi XX =
;
else,
qi
XX =
.
Else
If the fitness of
p
X
is worse than that of
q
X
,
pi
XX =
;
else,
qi XX =
.
End
---------------------------------------------------------------------------
Once the food source
i
X
is selected, the onlooker bee will
update
i
X
using the Procedure in Section 4.3. If the new food
source
new
X
has a fitness value not worse than the fitness value
of
i
X
, the new food source
new
X
will replace
i
X
as a new
member in the population.
E. Procedure of Proposed IABC
Due to the characteristics of UTLSP, three local search
operators are proposed in the IABC algorithm. Novel and special
design are proposed to generating new food sources in employed
bee and onlooker bee phases. The aim of IABC is to balance the
exploration and exploitation by local search strategies and novel
new food source generating operators. The local search
operators are integrated in both the employed bee phase and the
onlooker bee phase. For one food source, the local search
operators can find a new food source with better performance in
local space. To show the steps of IABC algorithm in detail, the
procedure is presented as follows.
---------------------------------------------------------------------------
Procedure: IABC
Step1: Set parameters, population size, generation,
Limit
.
Step2: Initialize population, evaluate initial solutions and
obtain the best solution.
Step3: Perform the employed bee phase.
Step3.1 Generate new food sources.
Step3.2 Local search for better food sources.
Step3.3 Update the population and best solution.
Step4: Perform the onlooker bee phase.
Step4.1 Generate new food sources.
Step4.2 Local search for better food sources.
Step4.3 Update the population and best solution.
Step5: If
Limit
is met, perform the scout bee phase
Step6: Update the best solution.
Step7: If the stop criterion is not satisfied, go to Step 3; else,
output the best solution.
---------------------------------------------------------------------------
399
IV. E
XPERIMENT EVALUATION AND COMPARISONS
A. Experimental setup
To evaluate the performance of the proposed IABC
algorithm for the traffic light scheduling problem, two sets of
traffic light cases are evaluated. Comparisons and discussions
are conducted. In the two case sets, there are sixteen cases with
6 time intervals in a time window of 30 seconds and 60 seconds.
The time interval is set to 5 seconds. The sizes of cases are
ranging from 3×3 intersections to 10×10 intersections. The
proposed IABC algorithm and all compared algorithms are
coded in C++ and run on an Intel 3.40 GHz PC with 8 GB
memory. All experiments are carried out with 30 replications.
Besides the total delay time results of the whole traffic
network, we calculate the relative percentage deviation (RPD)
over the best solution and the average solution in 30 repeats for
each compared algorithm, which is shown as follows:
()=
×100 (11)
where
is the fitness value found by the kth compared
algorithm while is the optimal fitness found by all
compared algorithms. In the comparison results, we also
calculate the average relative percentage deviation (ARPD) of
each algorithm for the same cases. For all compared algorithms,
the smaller RPD value means the better algorithm performance.
B. Testing three local search strategies
To test the performance of three local search operators
proposed in Section 3.2, sixteen cases are evaluated by IABC
with no local search (IABC_No_LS), IABC with local search 1
(IABC_LS1), IABC with local search 2 (IABC_LS2) and IABC
with local search 3 (IABC_LS3). The RPD values of four
algorithms are counted for minimum (min) and average (ave)
results in 30 repeats. The ARPD values of each algorithm for all
cases are also counted. Both RPD and ARPD values are shown
in Table 2. It can be seen from Table 2 that IABC_No_LS
obtains RPD (min) values with “0.00” for 4 out of 16 cases and
RPD (ave) values with “0.00” for 6 out of 16 cases. IABC_LS1
algorithm gets RPD (min) values with “0.00” for 10 out of 16
cases and RPD (ave) values with “0.00” for 4 out of 16 cases.
The corresponding results by IABC_LS2 and IABC_LS3 are
worse than those of IABC and IABC_LS1 algorithms. Hence,
local search 1 is the best one among three local search strategies.
IABC with local search 1 gets smaller APRD values for
minimum and average results (0.39, 0.74) than those by the
IABC algorithm with no local search (1.81, 1.54). It is clear that
the IABC algorithm with local search 1 has the best values for
both minimum and average results among four algorithms.
Hence, local search 1 is employed to work together with the
IABC algorithm to solve all cases.
To further verify the IABC algorithm’s performance, Fig. 3
shows the optimal solution by IABC for the case 4 by 4 with 30
seconds time window. There are six sub-pictures for six time
intervals (k=1 to 6). In each sub-picture, the vehicle numbers on
all segments and traffic signals of all intersections are marked.
TABLE
II.
RPD
AND
ARPD
RESULTS OF FOUR ALGORITHMS
Case
IABC_No_LS IABC_LS1 IABC_LS2 IABC_LS3
min ave min ave min ave min ave
30s 3 by 3 0.00 0.26 0.00 0.00 0.00 0.35 0.00 0.18
30s 4 by 4 1.27 1.05 0.00 1.08 1.73 1.18 0.00 0.00
30s 5 by 5 0.72 0.51 0.00 0.11 2.38 1.37 1.11 0.00
30s 6 by 6 0.00 0.00 1.09 0.85 1.12 0.40 0.35 0.75
30s 7 by 7 0.00 0.00 0.20 0.23 0.98 1.92 0.61 0.74
30s 8 by 8 0.31 0.00 1.02 0.29 1.20 0.56 0.00 0.00
30s 9 by 9 0.65 0.57 0.00 0.00 0.49 0.85 0.24 0.48
30s 10 by
10 0.33 0.37 0.22 0.36 0.00 0.00 0.12 1.06
60s 3 by 3 0.00 0.00 2.89 2.33 2.89 2.64 2.89 4.55
60s 4 by 4 4.76 8.67 0.00 0.00 6.29 3.09 3.91 4.64
60s 5 by 5 0.55 2.52 0.00 2.34 0.29 0.00 2.98 4.02
60s 6 by 6 2.66 1.90 0.00 0.00 3.38 3.01 5.13 2.48
60s 7 by 7 6.77 5.94 0.00 2.28 0.25 0.00 0.78 0.98
60s 8 by 8 0.97 0.00 0.00 0.89 1.40 1.46 1.91 4.56
60s 9 by 9 8.87 2.83 0.00 0.08 4.46 0.00 5.77 0.78
60s 10 by
10 1.04 0.00 0.88 0.96 0.90 2.07 0.00 1.16
ARPD 1.81 1.54 0.39 0.74 1.74 1.18 1.61 1.65
Fig. 3 The optimal solution by IABC for the case 4 by 4
V. C
ONCLUSIONS AND FUTURE WORKS
In this study, we have discussed a centralized urban traffic
light scheduling problem (UTLSP). An Improved ABC
algorithm is proposed to minimize the total delay time of the
traffic network within a given period. To improve the algorithm
performance, we have proposed a novel new solution generation
method. In addition, we have proposed three local search
approaches to search neighbouring space of existing solutions.
In the experiment section, we have discussed parameter settings
of the IABC algorithm using the Taguchi method. Through
comparisons and discussions, the local search changing the
signals for one intersection has the best performance among
three strategies. The experiment results have shown that the
IABC algorithm is superior to four meta-heuristics and a
common MILP solver CPLEX.
400
In future, we will extend our work in the following
directions: 1) to improve our traffic network flow model by
considering more real-time constraints; 2) to explore more high
performance scheduling algorithms that are promising to
overcome not only high computational complexity but also
possible model uncertainties.
A
CKNOWLEDGEMENTS
This research is supported by the research grant S15-1105-
RF-LLF URBAN from the Economic Development Board,
Singapore, for the project of “Development of NTU/NXP Smart
Mobility Test-bed”.
R
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