Adaptive type-2 fuzzy traffic signal control with on-line optimization

Abstract

Traffic congestion has become a serious phenomenon in the cities. In order to achieve the effective control of intersections, multi-lane four-phase intersection is studied. The corresponding queue length model and vehicular delay model are established. Aiming at the dynamic uncertainty problem in the intersection, a type-2 fuzzy logic controller is designed. The green time of each phase is dynamically decided according to the real-time traffic information for purpose of achieving the smallest vehicular average delay, so as to enhance the traffic efficiency in the intersection. The excellent performance of the designed controller is confirmed through simulation experiments under different conditions. Finally, in view of the difficulty of parameter settings in type-2 fuzzy controller, DNA evolutionary algorithm is applied to online optimize and adjust the parameters of membership function. One group of parameters is difficult to fit all traffic situations, so on-line optimization and adjustment is necessary for reflecting the real-time change of traffic flow in time, which is of great significance for the practical application. The experimental results indicate that the online optimized type-2 fuzzy traffic control method has better effect.

Keywords

Type-2 fuzzy logic control traffic signal control optimization DNA evolutionary algorithm

1 Introduction

Traffic jam has become more and more serious due to the rapid growth of vehicle ownership in the cities, particularly in the rush hours. As a result, journey time, energy consumption, traffic accident, noise and environmental pollution seriously deteriorate. Obviously, the optimal regulation of traffic signal control has great signification with easing the traffic pressure and improving the efficiency of transportation. Transportation system is a large complex nonlinear dynamic system. Traditional controllers are usually restricted due to the influence caused by traffic environment, weather, driver selection, accident andso on.

The development of traffic signal control has experienced three stages, that are, fixed-time control, actuated control and adaptive traffic control. Webster [1] proposed a strategy for the optimal cycle length and green split with an objective to reduce the delay which was used as the standard of the fixed-time control. However, fixed-time control allocated green time according to historical data without capability of responding to short-term traffic demand and pattern changes. Actuated control [2] partially solved this problem by extending green response in allusion to real-time traffic arrivals, but such controllers only consider the situation of one phase with omitting the waiting vehicles in the other phases. To overcome this limitation, adaptive traffic control [3 –11] emerged in terms of the present and past information utilizing artificial intelligence techniques such as neural networks, fuzzy logic control, various evolutionary algorithms etc.

Traffic flow is usually controlled by rules, so the rule-based fuzzy control method would be more suitable for the study of traffic signal control system. Fuzzy logic has the capability to mimic human thinking and translate the expert knowledge into computable numerical data without the necessity to setup a precise mathematical model or define an exact relationship between input and output variables. It can be observed that a rapidly growing interest using fuzzy control in the field of traffic signal control [12 –15]. These proposed methods had improved the traffic efficiency to some extent, but traditional type-1 fuzzy logic theory has many limitations in treating large uncertainty factors and unexpected disturbances [16, 17], which is because type-1 fuzzy set only assigns a crisp value to the membership function discounting the fuzzy uncertainties. However, transportation system is such a large uncertainty nonlinear time-varying system. The collected traffic data is influenced by various factors such as the vehicle length, the environmental condition, the driver route selection and so on. So there are more uncertainties exist in traffic signal control system. Comparatively speaking, type-2 fuzzy system is a kind of nonlinear control system based on type-2 fuzzy set theory, and its own characteristic of three-dimensional fuzzy membership function provides a new degree of freedom to describe the uncertain behavior of system, which makes it more appropriate for research of traffic signal control system. Research has verified the better performance of type-2 fuzzy controller than type-1 one [18 –22].

However, the set of membership functions is extremely important and difficult for the fuzzy system [23]. Some intelligent algorithms like genetic algorithm (GA) were employed to optimize the parameters of the fuzzy logic controller [24 –28]. In these works, the parameters of fuzzy controller were adjusted and the corresponding simulation results demonstrated that the efficiency of fuzzy controller with optimization. Since Adleman [29] firstly introduced DNA computing to solve a computationally hard problem stems from the directed Hamiltonian path problem, in the last few years more researchers devote to the DNA algorithm research [30 –34]. DNA evolutionary algorithm is a kind of hybrid search algorithm based on biological molecules operation and brings in RNA molecule operation and DNA double-stranded structure characteristic of genetic information, which make it can overcome the drawbacks of standard genetic algorithm, such as weak local search capability and premature convergence. Compared with the standard genetic algorithm, DNA evolutionary algorithm has better search performance in solving complex optimization problems [31].

Based on the above analysis, a type-2 fuzzy logic traffic signal controller online optimized by DNA evolutionary algorithm is established in allusion to multi-lane four-phase intersection. The traffic evaluation index model is set up firstly, which includes vehicular average delay model and queue length model. Among that, the turning vehicles and multilane are taken into account. Then the membership functions’ parameters of type-2 fuzzy logic controller are optimized by DNA evolutionary algorithm. However, most of work adopted off-line optimization aiming at the controller. But if the arrival rate of the vehicles is flexible, one group of parameters is difficult to fit all traffic situations, so on-line optimization and adjustment is necessary for reflecting the real-time change of traffic flow in time, which is of great significance for the practical application. On account of this, this paper proposed an on-line optimization method. In view of the traffic volume on the road network usually does not have huge changes in the short time of several signal cycle time, a signal cycle time is counted as an optimization time period. The parameters after optimization are used in type-2 fuzzy controller to control the follow-up vehicles in the next cycle time.

The rest of this paper is organized as follows: Section 2 establishes the traffic evaluation index model. A type-2 fuzzy logic controller for a four-phase intersection is designed in Section 3. A simple introduction about DNA evolutionary algorithm and the corresponding optimization process of type-2 fuzzy controller are detailed in Section 4. Simulation experiments are set to compare with the benchmarks in Section 5. The discussion and conclusion are summarized in the last section.

2 Traffic evaluation index model

It is significant to establish an accurate traffic model for evaluating the advantages and disadvantages of control methods. However, in order to meet the needs of on-line real-time traffic control, traffic model have to make reasonable compromise between accuracy and computational complexity. Therefore, in the process of modeling, we make the following assumptions:

Vehicles must run along the same direction in a one-way lane.

Unidirectional lane is totally enclosed, namely, no vehicles out of or into the fork in the road.

Vehicular position in the motorcade is invariable, that is, no anchor or overtaking happens.

The vehicles that reach the intersection in all directions are random. The arriving of vehicles under the non-congested traffic flow obeys Poisson distribution, and the arriving of vehicles under the crowded traffic flow complies with the binomial distribution.

The most common multiple lanes single intersection is selected as study object, as shown in Fig. 1, which has universal practical significance for its research. Due to the right-turn vehicles have no conflict with the other directions’ vehicles, they don’t need waiting when across the intersection, thus the vehicle delay isn’t been produced, so the influence of the right-turn vehicles can be ignored.

Four-phase traffic signal control is adopted which is also the most common form in reality, as shown in Fig. 2.

Fig.1

Multi-lane single intersection.

Fig.2

Phase diagram of a four-phase signal.

It is supposed that no vehicle exists in the lanes before simulation, and new vehicles are generated from different directions depending on the pre-set arrival rate randomly during the simulation.

Suppose that the minimum successive time unit is 1 s, and two vehicles are not allowed to arrive at the same lane in a time unit. Let q (i) represent the number of arrived vehicles during a time unit, then $q (i) = {\begin{matrix} 1, & if a vehicle arrives during the i th time unit \\ 0, & otherwise \end{matrix}$ (1)

Suppose V_G denotes the number of waiting vehicles at the beginning of the green phase, and $V_{R}^{1}, V_{R}^{2}, V_{R}^{3}$ stand for the numbers of waiting vehicles at the beginning of the three red phases respectively. For multiple lanes, because drivers tend to switch to shorter queue while approaching the junction, the differences among the queue lengths of all lanes in the same direction are usually small. So the queue lengths of the green phase and the three red phases in the nth time unit can bedepicted as $Q_{Gn} = z * {⌈ (V_{G} + \sum_{i = 1}^{n} q_{i}) / p ⌉ - s * n}$ (2) $Q_{Rn}^{j} = ⌈ (V_{R}^{j} + \sum_{i = 1}^{n} q_{i}) / p ⌉, j = 1, 2, 3$ (3)

where p is the number of lanes; s is saturation flow rate, and s = 1 is supposed here; z = 1 if $⌈ (V_{G} + \sum_{i = 1}^{n} q_{i}) / p ⌉ - s * n \geq 0$ , otherwise z = 0.

Intersection’s vehicle delays can be expressed as the sum of vehicular queue length at each moment. Therefore, the vehicular delays of the current green phase and the three red phases can be expressed respectively as follows $D_{Gn} = \sum_{k = 1}^{n} z * (V_{G} + \sum_{i = 1}^{k} q_{i} - s * k * p)$ (4) $D_{Rn}^{j} = \sum_{k = 1}^{n} (V_{R}^{j} + \sum_{i = 1}^{k} q_{i}), j = 1, 2, 3$ (5)

In Formula (4), z = 1 if $V_{G} + \sum_{i = 1}^{k} q_{i} - s * k * p \geq 0$ , otherwise z = 0. Then the total delay of the current phase is $D = D_{Gn} + D_{Rn}^{1} + D_{Rn}^{2} + D_{Rn}^{3}$ (6)

For four-phase intersection, each cycle consists of four phase, so the total vehicular delay of each cycle is the sum of four phases’ delay. Therefore, the total delay time during the lth cycle is $D^{l} = \sum_{x = 1}^{4} D_{x}$ (7)

where D_x represents the total vehicular delay of the xth phase.

The total vehicular number of the current cycle is the sum of the number of waiting vehicles at the end of the last cycle and the vehicles that reach in this cycle. If q_l indicates the number of vehicles that arrive during the lth cycle, S_l stands for the number of waiting vehicles at the beginning of the lth cycle, then the average vehicular delay of the lth cycle can be expressed as $d_{l} = \frac{D^{l}}{q_{l} + S_{l}}$ (8)

3 Four-phase intersection type-2 fuzzy logic controller

The structure of a general type-2 fuzzy logic controller is depicted in Fig. 3, which is very similar to type-1 fuzzy logic controller. The major structural difference lies in the output processing block where defuzzifier in type-1 fuzzy logic controller is replaced by the type-reducer and defuzzifier in type-2 fuzzy logic controller.

Fig.3

Type-2 fuzzy logic controller.

In order to reduce computational complexity of the general type-2 fuzzy system lied in the fuzzy inference and type-reducer, interval type-2 fuzzy sets are adopted whose secondary memberships are either zero or one. Gaussian membership function’s curve shape is smooth. Its control characteristic is more gently. Studies have shown that it has good stability and it is a reasonable form to describe the fuzzy subset [35]. Thus interval type-2 Gaussian membership function with uncertain standard deviation is adopted in this paper, whose mathematical expression is: $μ_{\tilde{A}} (x) = exp (- \frac{(x - m)^{2}}{2 σ^{2}}), σ \in [σ_{1}, σ_{2}]$ (9)

Where m presents the center of the membership function, σ₁ and σ₂ are the two deviations of the membership function.

In order to reflect the effectiveness of type-2 fuzzy logic controller, the membership function adopts three linguistic partitions, namely “short (S)”, “medium (M)”, “long (L)”. let the universe of discourse be [0, 12]. According to the practical experience, the basic domain of QG (QR) is [0, 40], and the basic domain of T is [15, 65] for the straight phase and [15, 45] for the left-turn phase respectively. In addition, singleton fuzzification method is used to map the input variable in the fuzzifier block.

The preliminary rule base is given in Table 1 on the basis of daily experience and the expert knowledge of the traffic police.

Table 1

Basic control level fuzzy rule base

	S	M	L
S	S	M	L
M	S	M	L
L	S	S	M

Fuzzy inference is the key process in type-2 fuzzy control. There are two inputs and one output in the proposed controller, so the rules can be depicted as $R^{i} : If x_{1} is {\tilde{F}}_{1}^{i}, x_{2} is {\tilde{F}}_{2}^{i}, Then y^{i} is {\tilde{G}}^{i}, i = 1, \dots, M, M = 9$ . The possible value of ${\tilde{F}}_{j}^{i}, j = 1, 2$ and ${\tilde{G}}^{i}$ is S, M or L. The corresponding membership functions of jth input variable and output variable can be denoted by the way of $μ_{{\tilde{F}}_{j}^{i}} {(x}_{j})$ and $μ_{{\tilde{G}}^{i}} (y)$ . Due to the input variables adopt singleton fuzzification in this paper, the inference result of ith fired rule is depicted as: $μ_{{\tilde{B}}^{i}} (y) = μ_{{\tilde{G}}^{i}} (y) ⊓ {⊔_{x \in X} {μ_{{\tilde{F}}_{1}^{i}} {(x}_{1}) ⊓ μ_{{\tilde{F}}_{2}^{i}} {(x}_{2})}}$ (10)

Because the fuzzy sets are interval type-2 fuzzy sets, the inference of antecedents can be addressed as: ${\bar{f}}^{i} = {\bar{μ}}_{{\tilde{F}}_{1}^{i}} (x_{1}) ⊓ {\bar{μ}}_{{\tilde{F}}_{2}^{i}} (x_{2})$ (11) ${\underline{f}}^{i} = {\underline{μ}}_{{\tilde{F}}_{1}^{i}} (x 1) ⊓ μ_{{\tilde{F}}_{2}^{i}} (x 2)$ (12)

where $μ_{{\tilde{F}}_{j}^{i}} (x_{j})$ and ${\bar{μ}}_{{\tilde{F}}_{j}^{i}} (x_{j})$ are the lower and upper membership grades of $μ_{{\tilde{F}}_{j}^{i}} {(x}_{j})$ .

Then the inference result of ith fired rule is simplified as: $μ_{{\tilde{B}}^{i}} (y) = μ_{{\tilde{G}}^{i}} (y) ⊓ F^{i}, F^{i} = [{\underline{f}}^{i}, {\bar{f}}^{i}]$ (13)

Suppose that N rules are fired, then the final inference result of all fired rule in the rule base is described as: $μ_{\tilde{B}} (y) = ⊔_{i = 1}^{N} μ_{{\tilde{B}}^{i}} (y)$ (14)

After fuzzy inference, the result of the output is an interval type-2 fuzzy set. Type-reducer is necessary to convert interval type-2 fuzzy set into type-1 fuzzy set. Then the corresponding expression of the center-of-set type-reduction is: $\begin{matrix} Y_{cos} (Y^{1}, \dots, Y^{M}, F^{1}, \dots, F^{M}) = [y_{l}, y_{r}] \\ = \int_{y^{1}} \dots \int_{y^{M}} \int_{f^{1}} \dots \int_{f^{M}} 1 / - (\sum_{i = 1}^{M} f^{i} y^{i}) / (\sum_{i = 1}^{M} f^{i}) \end{matrix}$ (15)

where Y_cos is interval set determined by y_l and y_r, $f^{i} \in F^{i} = [{\underline{f}}^{i}, {\bar{f}}^{i}]$ , $y^{i} \in Y^{i} = [y_{l}^{i}, y_{r}^{i}]$ .

y_l and y_r can be represented as a fuzzy basis function expansion, i.e., $\begin{matrix} y_{l} = (\sum_{i = 1}^{M} f_{l}^{i} y_{l}^{i}) / (\sum_{i = 1}^{M} f_{l}^{i}) \\ y_{r} = (\sum_{i = 1}^{M} f_{r}^{i} y_{r}^{i}) / (\sum_{i = 1}^{M} f_{r}^{i}) \end{matrix}$ (16)

where $f_{l}^{i}$ denotes the firing strength membership grade contributing to the left-most point y_l; and $f_{r}^{i}$ denotes the firing strength membership grade contributing to the right-most point y_r.

After type-reduction, the results of the type-reducer can be applied to defuzzifier. Then the crisp output can be obtained as:

$f (x) = (y_{l} + y_{r}) / 2$ (17)

Based on the above analysis, the concrete steps to control four-phase intersection are as follows:

Step 1. Determine the values of the input variables QG and QR according the established traffic evaluation index model.

Step 2. Map the input variables QG (QR) to the universe of discourse in terms of X = k₁ * QG (QR) , k₁ = 3/10 .

Step 3. Set the membership functions of the input and output variables in type-2 fuzzy logic controller according to Formula (9).

Step 4. Proceed with type-2 fuzzy inference and type-reducer based on Formula (15), Formula (16) and the rule base, and the crisp output Y can be obtained through defuzzifier.

Step 5. Convert the universe of discourse of the output variable to the actual output value according to T = k₂ * Y + c, where c = 15, k₂ = 25/6 is for straight phase, and c = 15, k₂ = 5/2 is for left-turn phase.

Step 6. Apply the value of T to the traffic model, the corresponding vehicular average delay and queue length can be gotten. Then return Step 1 to continue execution until the pre-set simulation time has reached.

4 On-line optimization process with DNA evolutionary algorithm

4.1 DNA evolutionary algorithm and encoding principle

DNA evolutionary algorithm is a kind of hybrid search algorithm based on biological molecules operation. RNA molecule operation and DNA double-stranded structure characteristic of genetic information are introduced into the genetic algorithm. Compared with the traditional genetic algorithm, DNA evolutionary algorithm has better search performance in solving complex optimization problems [29 –34].

The double helix DNA molecular strand consists of four nucleotide bases: adenine (A), guanine (G), cytosine (C) and thymine (T). Based on Watson-Crick complementary principle, hydrogen bond occurs through the pairwise attraction of the bases, i.e., A bonds with T and G bonds with C. Inspired by this structure, we map four nucleotide bases C, G, A, T to integer 0, 1, 2 and 3 respectively for encoding in computer. An example of encoding method about segment of DNA strand is shown in Fig. 4. DNA evolutionary algorithm adopts the quaternary encoding, which can effectively avoid the hamming cliffs problem in binary system and the floating-point precision problem in decimal system.

The structure of DNA evolutionary algorithm is similar to the traditional genetic algorithm, including selection operation, crossover operation and mutation operation. Besides, DNA genetic algorithm also has several kinds of operators.

(1) Selection

Fig.4

DNA molecular chain encoding.

The purpose of selection operation is to choose excellent individuals from the current population. The roulette wheel selection strategy combined with elitism retention mechanism is currently the most widely used method. It is a kind of selection mode based on the probability to ensure that the current optimal individual which possesses the optimal fitness value can evolve to the next generation, thus guaranteeing the convergence of the algorithm.

(2) Crossover

In order to enhance the search performance, DNA evolutionary algorithm will use the translocation operation, transformation operation and permutation operation instead of traditional crossover operation in genetic algorithm.

Translocation operator: Make subsequence of DNA sequence transfer to the new location. For example, suppose that the original DNA sequence is X = X₅X₄X₃X₂X₁, where X_i (i = 1, ⋯, 5) is the subsequence of DNA sequence, if X₂ is moved to the position of X₄, then the new sequence after translocation operation becomes X′ = X₅X₂X₄X₃X₁.

Transformation operator: Let segment of DNA sequence exchange their locations. For example, suppose that the original DNA sequence is X = X₅X₄X₃X₂X₁, if X₂ and X₄ exchange the positions, and then the sequence X after transformation operation becomes X′ = X₅X₂X₃X₄X₁.

Permutation operator: One subsequence of DNA sequence is permutated by the other subsequence. For example, suppose that the original DNA sequence is X = X₅X₄X₃X₂X₁, when the subsequence X₂ is replaced by the other DNA sequence R₂, the new sequence is X′ = X₅X₄X₃R₂X₁.

(3) Mutation

Mutation operation plays an important role in maintaining the population diversity, which can prevent the algorithm trapped in local minimum, but to a certain extent affect the convergence of the algorithm. According to the literature [29], there are “hot spot” and “cold spot” existed in DNA sequences, and “cold spot” nucleotide variation is much slower than “hot spot” nucleotide variation. Using this feature, we employ the shifty probability in different evolution stage. The coding of each individual is divided into two parts, high coding and low coding. In the part of high coding, the initial stage of the algorithm requires a larger mutation probability to obtain larger search space, and along with the iteration increases, a small mutation probability is needed in order to prevent the loss of the optimal solution. Low coding part is just the opposite. The corresponding high coding and low coding mutation probability can be respectively as follows: $P_{mh} = a_{1} + \frac{b_{1}}{1 + exp [a (g - g_{0})]}$ (18) $P_{ml} = a_{1} + \frac{b_{1}}{1 + exp [- a (g - g_{0})]}$ (19)

where a₁, b₁, g, g₀ and a are denoted the initial mutation probability, the range of mutation probability, the evolution generation, the generation of mutation probability turning and the speed of change. The shifty probability with evolution generation of mutation operator is shown in Fig. 5.

Fig.5

The curve of P_ml and P_mh.

On basis of the DNA encoding principle and the corresponding genetic operators, the corresponding flow chart about implementation steps of DNA evolutionary algorithm is given in Fig. 6.

4.2 Controller’s parameters optimization based on DNA evolutionary algorithm

The control performance of fuzzy controller is determined by the set of membership functions and fuzzy rules. Especially for the complex systems, it is difficult to achieve control target of the system if using traditional parameter settings’ methods. Compared with the traditional type-1 fuzzy controller, the parameters of the designed type-2 fuzzy logic controller are much more complicated. In view of good search performance given by DNA evolutionary algorithm, it is adopted to optimize and adjust the parameters of the designed controller.

Fig.6

The flow chart of DNA evolutionary algorithm.

In the process of using DNA evolutionary algorithm to adjust the parameters of the controller, the first thing is to initialize the parameter values of the algorithm, as shown in Table 2. The parameters are encoded according to the range of the parameters, and the parameters to be optimized are turned into the unknown solution in the space. For the type-2 fuzzy logic controller in this paper, if fuzzy rules are determined, the relative parameters to be optimized are parameters of the membership functions of the input and output variables. Given interval type-2 Gaussian membership function with uncertain standard deviation, two input variables and one output variable with three linguistic partitions are encoded in a 27 real gens chromosome by using quaternary encoding method. Formula (9), it is observed that the membership functions are determined by center value m and two deviation values σ₁, σ₂, where m_S ∈ [0, 2], m_M ∈ [4, 8], m_L ∈ [10, 12] and σ₁ (σ₂) ∈ [0.5, 2.5].

Table 2

The parameter setting of DNA evolutionary algorithm

Parameters	Values
Population size N	20
Iterations G	50
Encoding length L	10
Permutation probability	1
Translocation probability	0.5
Transformation probability	0.5

In order to obtain the optimal parameter settings, the fitness function should be set up according to the characteristics of the controlled object. The optimization problem can be converted to solve multi-dimensional function optimal value problem. For traffic control problem, the vehicular average delay at intersection is often considered as an important index for traffic control effectiveness evaluation. According to the established vehicular average delay in Formula (8), the fitness function can be defined as: $fitness = min ((\sum_{l = 1}^{M} d_{l}) / M)$ (20)

where M is the total number of cycles during the simulation time.

In the traffic control system, the traffic volume in different period changes intricately. In order to reflect the real-time change of traffic flow in time, on-line optimization and adjustment is necessary, which is of great significance for the practical application of control method. In the short time of several signal cycle time, the traffic volume on the road network usually does not have huge changes. Based on this thought, when the type-2 fuzzy controller is optimized online, we use a signal cycle as an optimization time period. The parameters after optimization are used in type-2 fuzzy controller to control the follow-up vehicles in the following time period. The control process is carried out in turn like this.

Summarize the above description, the procedure to optimize the type-2 fuzzy logic controller using DNA evolutionary algorithm is addressed as follows:

Step 1. Determine two input variables of the type-2 fuzzy logic controller according to the previous description in Section 3;

Step 2. Initialize encoding for the corresponding membership functions based on the range of each parameter;

Step 3. Calculate the fitness function value of each individual;

Step 4. Carry out the corresponding operations of DNA evolutionary algorithm and produce new population;

Step 5. Judge whether meet the termination conditions, if satisfied, then stop the iteration algorithm and decode the individual which possesses minimize fitness function value. The optimal parameters are applied to the type-2 fuzzy controller to control the vehicles in the following time period; otherwise, return to Step 3.

5 Simulation

5.1 Simulation conditions

Aiming at the four-phase single intersection as shown in Fig. 1, simulation experiments are set to test different levels of congestion in real traffic situation. In order to verify the efficiency of type-2 fuzzy control method, several methods are simulated which include fixed-time control (FTC), the traditional type-1 fuzzy control (T1) [14] and the type-2 fuzzy control in this paper (T2). The vehicular average delay and queue length under different methods are compared. Furthermore, in order to illustrate the importance of fuzzy controller’s parameter setting, we further compare T2, type-1 fuzzy control optimized by DNA evolutionary algorithm (DNAT1) and type-2 fuzzy control optimized by DNA evolutionary algorithm (DNAT2). Simulation experiments are set under the following six different arrival rates:

Table 3
Comparision of vehicular average delay

Arrival rate of the straight phase(veh / s) Arrival rate of the left-turn phase(veh / s) Vehicular average delay(s/veh) Improvement compared with FTC

FTC T1 T2 DNAT1 DNAT2

0.1 0.1 36.39 24.32 19.89 13.41 12.39 65.95%

0.2 0.1 37.25 32.44 24.17 16.85 15.66 57.96%

0.3 0.1 41.10 40.19 31.37 26.74 22.65 44.89%

0.4 0.1 114.67 91.87 67.58 60.37 50.88 55.63%

0.5 0.2 194.31 190.29 185.43 184.16 176.78 9.02%

Rate1 Rate2 73.17 67.15 61.95 53.59 43.58 40.44%

Arrival rate of the straight phase(veh / s)	Arrival rate of the left-turn phase(veh / s)	Vehicular average delay(s/veh)	Improvement compared with FTC
0.1	0.1	36.39	24.32	19.89	13.41	12.39	65.95%
0.2	0.1	37.25	32.44	24.17	16.85	15.66	57.96%
0.3	0.1	41.10	40.19	31.37	26.74	22.65	44.89%
0.4	0.1	114.67	91.87	67.58	60.37	50.88	55.63%
0.5	0.2	194.31	190.29	185.43	184.16	176.78	9.02%
Rate1	Rate2	73.17	67.15	61.95	53.59	43.58	40.44%

Case 1, the arrival rate of straight vehicles is 0.1veh/s, and the arrival rate of left-turn vehicles is 0.1veh/s.

Case 2, the arrival rate of straight vehicles is 0.2veh/s, and the arrival rate of left-turn vehicles is 0.1veh/s.

Case 3, the arrival rate of straight vehicles is 0.3veh/s, and the arrival rate of left-turn vehicles is 0.1veh/s.

Case 4, the arrival rate of straight vehicles is 0.4veh/s, and the arrival rate of left-turn vehicles is 0.1veh/s.

Case 5, the arrival rate of straight vehicles is 0.5veh/s, and the arrival rate of left-turn vehicles is 0.2veh/s.

Case 6, dynamical situation: the arrival rates of straight and left-turn vehicles are given by the normal distribution, as shown in the following formula.

$Rate = ρ * exp (- \frac{(t - c)^{2}}{2 σ^{2}})$ (21)

where ρ is the upper limitation of the maximum arrival rate, c and σ are the corresponding center and deviation. If the simulation time is 1200 s, then the parameter settings of the straight vehicles’ arrival rate Rate1 are ρ = 0.4, c = 600, σ = 300, and the parameter settings of the left-turn vehicles’ arrival rate Rate2 are ρ = 0.2, c = 600, σ = 300.

We can see that under various static arrival rates, Case1-Case3 belong to non-congestion situation, Case 4 is slightly crowded state, and Case 5 belongs to congestion condition. Simulation experiments are implemented through MATLAB simulation platform by using S-Function to code the traffic module and control module. In fixed-time control module, the green times of the straight phase and the left-turn phase are set 40 s and 20 s separately. The set of type-1 fuzzy control module is based on Reference [14], whose membership functions of the linguistic divisions and fuzzy rules are same with that in type-2 fuzzy control module to be fair. Type-2 fuzzy control module is set according to the design procedure detailed in Section 3. The initial green time is 15 seconds. Four-phase traffic model module is divided into two parts that are vehicular queue length and delay calculation. Vehicular queue length and average delay of green phase and red phases are outputted through this module.

5.2 Simulation results and analysis

In the above several simulation cases, the comparison results of vehicular average delay under different methods are shown inTable 3.

From Table 3, we can see that the vehicular average delays under different methods also increase as the vehicular arrival rate increases in the case of various static arrival rates. By comparing the vehicular average delays under the same arrival rate among these methods, we can see that fuzzy control method is better than fixed-time control method, T2 method is better than T1 method, the optimized T1/T2 method using DNA evolutionary algorithm is always better than T1/T2 method without optimization, which illustrates the advantage of T2 method and the necessity of parameters optimization. The effect of the proposed DNAT2 method is the best. When vehicular arrival rate is low (Case1-Case 3), and under slightly crowded state (Case 4) and dynamic arrival rate (Case 6), the improvement of DNAT2 can reach about 50% compared with the fixed-time control. In traffic extremely congestion state (Case 5), vehicles have been far beyond the processing capacity of intersection, so if only by improving the control method at this time, the space to improve is not large, only at 9.02% . But even in this kind of condition, the proposed DNAT2 method is also the most effective compared with other methods.

Accordingly, in the case of various arrival rates, the trend comparisons of vehicular average delay and average queue length under the fixed-time control, type-1 fuzzy control and type-2 fuzzy control are shown in Figs. 7–18. Each curve always gradually rises from zero, which is constant with the setting that no vehicle exists in the roads before the beginning of simulation.

Fig.7

Vehicular average delay comparison under Case 1.

Fig.8

Vehicular average queue length comparison under Case 1.

Fig.9

Vehicular average delay comparison under Case 2.

Fig.10

Vehicular average queue length comparison under Case 2.

Fig.11

Vehicular average delay comparison under Case 3.

Fig.12

Vehicular average queue length comparison under Case 3.

Fig.13

Vehicular average delay comparison under Case 4.

Fig.14

Vehicular average queue length comparison under Case 4.

Fig.15

Vehicular average delay comparison under Case 5.

Fig.16

Vehicular average queue length comparison under Case 5.

Fig.17

Vehicular average delay comparison under Case 6.

Fig.18

Vehicular average queue length comparison under Case 6.

(1) In the simulation results of non-congestion traffic situation (Case 1-Case 3), as shown in Figs. 7–12, the overall trends of the two evaluation indexes that are vehicular average delay and average queue length under the three control methods are basically stable. At this time vehicles can be smoothly to cross the intersection. By further observation, we can see that:

In terms of vehicular average delay, the average delay of fixed-time control is about 35–41 s/veh, and it is around 25–40 s/veh for type-1 fuzzy control, whereas the average delay is about 20–31 s/veh for type-2 fuzzy control.

In the aspect of average queue length, the average queue length of fixed-time control in each cycle is 3–11 vehicles, and it is about 1–11 vehicles for type-1 fuzzy control, while the average queue length of type-2 fuzzy control is 1–8 vehicles.

So in the case of non-congestion traffic situation, type-2 fuzzy control method shows a better control performance.

(2) In slightly crowded traffic state (Case 4), the simulation results (Figs. 13, 14) shows that vehicular average delay and queue length under the three control methods present a rising trend. In this case vehicles gradually gathered in the intersection, but the gaps among the three control methods are big. By further observation, we can see that:

In terms of vehicular average delay, the average delay of fixed-time control is 115 s/veh, and this value under type-1 fuzzy control is around 92 s/veh, whereas the maximum value of the average delay under type-2 fuzzy control is about 68 s/veh.

In the aspect of average queue length, the maximum average queue length of fixed-time control is up to 48 vehicles, and it continues to rise. The maximum average queue lengths of type-1 and type-2 fuzzy control are 32 vehicles and 24 vehicles respectively, and they gradually become steady.

By comparing, we can see that in the case of slightly crowded traffic condition, fixed-time control makes the traffic condition become worse and worse, but type-1 and type-2 fuzzy control method can make the traffic pressure off gradually. Moreover, compared with type-1 fuzzy control method, the performance of type-2 fuzzy control is better.

(3) In the simulation results of congestion traffic condition (Case 5), as shown in Figs. 15 and 16, vehicular average delay and queue length of the three control methods show a sharply rising trend. Vehicles gathered quickly in the intersection, and the three control methods just have a little difference. By further observation, we can see that:

In terms of vehicular average delay, the average delay of fixed-time control is up to 194 s/veh, and this value is around 190 s/veh for type-1 fuzzy control, while the average delay is about 185 s/veh for type-2 fuzzy control.

In the aspect of average queue length, the maximum average queue length of fixed-time control is 125 vehicles, and it is about 130 vehicles for type-1 fuzzy control, and the maximum average queue length of type-2 fuzzy control is about 120 vehicles.

It can be seen that in the case of congestion traffic condition, the gap of the three methods is not large. The reason is that the number of vehicles has gone beyond the withstanding capability of the intersection. At this time, only relying on improving control method can’t achieve good effect. But even in this situation, the effect of type-2 fuzzy control method is the best.

(4) In the dynamic traffic situation (Case 6), the simulation test results (Figs. 17, 18) show that the average queue length under the three control methods also present a trend similar to Gaussian distribution due to using dynamic vehicular arrival rate with Gaussian type. Further observation, we can see that:

In terms of vehicular average delay, type-2 fuzzy control method (62 s/veh) is superior to type-1 fuzzy control (67 s/veh) and fixed-time control (73 s/veh).

In the aspect of average queue length, when vehicular arrival rate increases from the initial value to the maximum value at 600 s, the three control methods all follow this trend and achieve the maximum average queue length at about 800 s. However, compared with the maximum average queue length of fixed-time control and type-1 fuzzy control method (27 vehicles), type-2 fuzzy control method we put forward shows good control effect (20 vehicles).

When vehicular arrival rate reduces gradually from the maximum value, compared with the other two kinds of control methods, the average queue length under type-2 fuzzy control decreases more significantly. Thus we can infer that type-2 fuzzy control can more efficiently dissipate overlong queuing problem caused by traffic jam.

To sum up, the type-2 fuzzy control method shows good control performance in the above several different traffic situations, which illustrates this method can distribute green time more reasonably, make the vehicular average delay and queue length decrease as far as possible, delay traffic congestion and relieve overlong queue length problem.

In order to further investigate the importance of type-2 fuzzy system’s parameter settings, aiming at the different traffic conditions, we use the optimization steps mentioned in Section 4 to online adjust the parameters of the controller so as to obtain better control performance. Type-2 fuzzy control method optimized by DNA evolutionary algorithm (DNAT2) is compared with type-2 fuzzy control method without optimization (T2) and type-1 fuzzy control method optimized by DNA evolutionary algorithm (DNAT1), the corresponding simulation results are shown in Figs. 19–30.

Fig.19

Vehicular average delay comparison before and after optimization under Case 1.

In the case of non-congestion situation (Case 1-Case 3), the simulation results (Figs. 19–24) show that the vehicle is still running well, the vehicular average delay of DNAT2 is about 12–22 s/veh, and the average queue length of DNAT2 is around 0.5–7 vehicles. Compared with T2 and DNAT1, DNAT2 has greatly improved.

In slightly crowded state (Case 4), the simulation results (Figs. 25, 26) indicate that the average queue length of the intersection still gradually increases slowly, but the optimized type-1/type-2 fuzzy control method is more smoothly than fuzzy control method without optimization. Vehicular average delay and queue length under DNAT2 method have a certain degree of reduction, and the effect is better than that under DNAT1.

In the case of congestion condition (Case 5), the simulation results (Figs. 27, 28) illustrate that DNAT2 don’t get effective improvement in terms of vehicular average delay and average queue length. Its main reason is the excessive vehicular arrival rate makes the congested intersection more congested. At this time, it can’t solve the problem of traffic congestion only optimizing the control method.

In dynamic traffic situation (Case 6), the simulation results (Figs. 29, 30) show that the maximum average queue length under DNAT2 method is 17 vehicles, compared with 27 vehicles under T2 and 23 vehicles under DNAT1, DNAT2 has a great improvement. In terms of vehicular average delay, the largest average delay under DNAT2 method is 43 s/veh, compared with 61 s/veh under T2 and 55 s/veh under DNAT1, the effect of DNAT2 method is enhanced a lot.

Fig.20

Vehicular average queue length comparison before and after optimization under Case 1.

Fig.21

Vehicular average delay comparison before and after optimization under Case 2.

Fig.22

Vehicular average queue length comparison before and after optimization under Case 2.

Fig.23

Vehicular average delay comparison before and after optimization under Case 3.

Fig.24

Vehicular average queue length comparison before and after optimization under Case 3.

Fig.25

Vehicular average delay comparison before and after optimization under Case 4.

Fig.26

Vehicular average queue length comparison before and after optimization under Case 4.

Fig.27

Vehicular average delay comparison before and after optimization under Case 5.

Fig.28

Vehicular average queue length comparison before and after optimization under Case 5.

Fig.29

Vehicular average delay comparison before and after optimization under Case 6.

Fig.30

Vehicular average queue length comparison before and after optimization under Case 6.

Through the above several kinds of traffic simulation tests, the performance of DNAT2 method is further improved, except in the case of extremely traffic congestion, and the improvement is bigger than DNAT1 method, which further confirms the validity of our proposed method.

6 Conclusion

In order to effectively manage the signal control of the intersections, aiming at the common multi-lane four-phase intersection, this paper established the corresponding traffic evaluation index model, and put forward a kind of traffic signal type-2 fuzzy logic control method based on type-2 fuzzy control theory. The green time of each phase is dynamically decided according to the real-time traffic information for purpose of achieving the smallest vehicular average delay, so as to enhance the traffic efficiency in the intersection. Type-2 FLC preserves the fuzziness and provides better approximation than type-1 FLC as its three-dimensional membership functions. This makes type-2 FLC more appropriate for traffic signal control. By comparing with fixed-time control method and traditional type-1 fuzzy control method, type-2 fuzzy control method had been proved the good control performance.

At the same time, in order to obtain better control effect and in terms of good search performance in solving complex optimization problems, DNA evolutionary algorithm is used to online optimize and adjust the membership functions of the type-2 fuzzy controller. For reflecting the real-time change of traffic flow in time, on-line optimization and adjustment is necessary, which is of great significance for the practical application of control method. The validity of the proposed method was verified by simulation experiments. From six kinds of cases, experimental results showed that the performance of the optimized type-2 fuzzy controller has been further improved on the basis of the original. The simulation experiments are based on single intersection in this paper, but the proposed method can be easily extended to a larger traffic network.

It is worth to mention that the established type-2 fuzzy control method online optimized by DNA evolutionary algorithm is also suitable for other complex nonlinear systems, such as power system, robot control, servo motor control, etc. According to the difference of the problem, the input and output variables and rule base of type-2 fuzzy controller are set accordingly, and the fitness function in the process of optimization will also be changed accordingly.

Footnotes

Acknowledgments

This work was supported by the National Key Technologies R&D Program of China (No.2014BAG01B03), National Natural Science Foundation of China (No.61374194, No.61373135, No.61672299, No.61503180), the Natural Science Foundation of Jiangsu Province (No.BK20160913), School-level Project of Nanjing Institute of Technology (No.YKJ201718, No.JCYJ201611, No.ZKJ201507, No.CKJA201305) and a Project Funded by the Priority Academic Development of Jiangsu Higher Education Institutions.

References

Webster

F.V.

, Traffic Signal Setting, Road Research Lab Tech Papers /UK/, 1958, 39, pp, 1–44.

Kronborg

and Davidsson

, MOVA and IHOVRA, traffic signal control for isolated intersections, Traffic Engineering and Control 34 (1993), 195–200.

Srinivasan

, Choy

M.C.

and Cheu

R.L.

, Neural networks for real-time traffic signal control, IEEE Transactions on Intelligent Transportation Systems 7(3) (2006), 261–272.

Wang

F.Y.

, Parallel control and management for intelligent transportation systems: Concepts, architectures and applications, IEEE Transactions on Intelligent Transportation Systems 11(3) (2010), 630–638.

Balaji

P.G.

and Srinivasan

, Distributed geometric fuzzy multiagent urban traffic signal control, IEEE Transactions on Intelligent Transportation Systems 11(3) (2010), 714–727.

Zhu

, Li

, Chen

and Xiong

, Parallel transportation management and control system and its applications in building smart cities, IEEE Transactions on Intelligent Transportation Systems 17(6) (2016), 1576–1585.

Talab

H.S.

and Mohammadkhani

, Design optimization traffic light timing using the fuzzy logic at a Diphasic’s Isolated intersection, Journal of Intelligent & Fuzzy Systems 27(4) (2014), 1609–1620.

Ding

, He

, Wu

and Fetzer

, Modeling traffic control agency decision behavior for multimodal manual signal control under event occurrences, IEEE Transactions on Intelligent Transportation Systems 16(5) (2015), 2467–2478.

Benhamza

and Seridi

, Adaptive traffic signal control in multiple intersections network, Journal of Intelligent & Fuzzy Systems 28(6) (2015), 2557–2567.

10.

Zhao

, Dai

and Zhang

, Computational intelligence in urban traffic signal control: A survey, IEEE Transactions on Systems, Man, and Cybernetics Part C: Applications and Reviews 42(4) (2012), 485–494.

11.

Zhao

, Gao

, Wang

and Wang

, A novel approach for traffic signal control: A recommendation perspective, IEEE Intelligent Transportations Systems Magazine 9(3) (2017), 127–135.

12.

Pappis

C.P.

and Mamdani

E.H.

, A fuzzy logic controller for a traffic junction, IEEE Transactions on Systems, Man and Cybernetics 7(10) (1977), 707–717.

13.

Murat

Y.S.

and Gedizlioglu

, A fuzzy logic multi-phased signal control model for isolated junctions, Transportation Research Part C: Emerging Technologies 13(1) (2005), 19–36.

14.

Rahman

S.M.

and Ratrout

N.T.

, Review of the fuzzy logic based approach in traffic signal control: Prospects in Saudi Arabia, Journal of Transportation Systems Engineering and Information Technology 9(5) (2009), 58–70.

15.

Talab

H.S.

, Mohammadkhani

and Haddadnia

, Controlling multi variable traffic light timing in an isolated intersection using a novel fuzzy algorithm, Journal of Intelligent & Fuzzy Systems 25(1) (2013), 103–116.

16.

Mendel

J.M.

, John

R.I.

and Liu

F.L.

, Interval type-2 fuzzy logic systems made simple, IEEE Transactions on Fuzzy Systems 14(6) (2006), 808–821.

17.

Wang

, A new look at type-2 fuzzy sets and type-2 fuzzy logic systems, IEEE Transactions on Fuzzy Systems 25(3) (2017), 693–706.

18.

Balaji

P.G.

and Srinivasan

, Type-2 fuzzy logic based urban traffic management, Engineering Applications of Artificial Intelligence 24(1) (2011), 12–22.

19.

Sabetghadam

, Shabaninia

, Vaziri

and Vadhava

, Type-2 fuzzy multiagent traffic signal control, In pp, Proceeding of the 13th IEEE International Conference on Information Reuse and Integration (2012), 509–512.

20.

, Srinivasan

, Lu

, Sun

and Zeng

, Type-2 fuzzy multi-intersection traffic signal control with differential evolution optimization, Expert Systems with Applications 41(16) (2014), 7338–7349.

21.

Chen

, Zhao

, Li

and Liu

, Intelligent traffic signal controller based on type-2 fuzzy logic and NSGAII, Journal of Intelligent & Fuzzy Systems 29(6) (2015), 2611–2618.

22.

Sambariya

and Prasad

, Design and small signal stability enhancement of power system using interval type-2 fuzzy, Journal of Intelligent & Fuzzy Systems 30(1) (2016), 597–612.

23.

S.K.

, Jang

H.J.

and Pedrycz

, A comparative experimental study of type-1/type-2 fuzzy cascade controller based on genetic algorithms and particle swarm optimization, Expert Systems with Applications 38(9) (2011), 11217–11229.

24.

Castillo

, Marroquin

R.M.

, Melin

, Valdez

and Soria

, Comparative study of bio-inspired algorithms applied to the optimization of type-1 and type-2 fuzzy controllers for an autonomous mobile robot, Information Science 192(1) (2012), 19–38.

25.

Hidalgo

, Melin

and Castillo

, An optimization method for designing type-2 fuzzy inference systems based on the footprint of uncertainty using genetic algorithms, Expert Systems with Applications 39(4) (2012), 4590–4598.

26.

Castillo

and Melin

, A review on the design and optimization of interval type-2 fuzzy controllers, Applied Soft Computing 12(4) (2012), 1267–1278.

27.

Gonzalez

, Melin

, Castro

, Castillo

and Mendoza

, Optimization of interval type-2 fuzzy systems for image edge detection, Applied Soft Computing 47 (2016), 631–643.

28.

, Zhang

, Yi

, Shang

and Gao

, A fast learning method for data-driven design of interval type-2 fuzzy logic system, Journal of Intelligent & Fuzzy Systems 32(3) (2017), 2705–2715.

29.

Adleman

L.M.

, Molecular computation of solutions to combinatorial problems, Science 266 (1994), 1021–1024.

30.

Lipton

, DNA solution of hard computational problems, Science 268 (1995), 542–545.

31.

Tao

J.L.

and Wang

, DNA computing based RNA genetic algorithm with applications in parameter estimation of chemical engineering processes, Computers & Chemical Engineering 31(12) (2007), 1602–1618.

32.

Chen

and Wang

, Optimization of short-time gasoline blending scheduling problem with a DNA based hybrid genetic algorithm, Chemical Engineering and Processing: Process Intensification 49(10) (2010), 1076–1083.

33.

Huang

C.H.

and Lin

C.L.

, Evolutionary neural networks and DNA computing algorithms for dual-axis motion control, Engineering Applications of Artificial Intelligence 24(7) (2011), 1263–1273.

34.

Sun

, Wang

and Bi

, Type-1/type-2 fuzzy logic systems optimization with RNA genetic algorithm for double inverted pendulum, Applied Mathematical Modelling 39(1) (2015), 70–85.

35.

Ahmad

, Razali

and Mohamed

, Fuzzy logic controller design for a robot grasping system with different membership functions, The 5th International Conference on Mechatronics (ICOM’13) 53 (2013), 1–9.