An adaptive three-stage fuzzy controller for signalized intersections using golden ratio based genetic algorithm: a comprehensive study

Transcription

1 An adaptive three-stage fuzzy controller for signalized intersections using golden ratio based genetic algorithm: a comprehensive study Word Count Abstract: Body:,0 Tables: 0 = 00 Figures: 0 =,00 Total:, By Wenchen YANG, Ph.D. candidate Key Laboratory of Road and Traffic Engineering of Ministry of Education, TONG JI University, Shanghai 00, P.R. China Tel: Fax: tongjiywc@gmail.com Lun ZHANG, Ph.D. Professor Key Laboratory of Road and Traffic Engineering of Ministry of Education, TONG JI University, Shanghai 00, P.R. China Tel: Fax: Lun_zhang@tongji.edu.cn Francesco CIARI, Ph.D. Institut für Verkehrsplanung und Transportsysteme (IVT) Swiss Federal institute of Technology Zurich, Zurich 0, Switzerland Tel: + Fax: + ciari@ivt.baug.ethz.ch Zhaocheng HE, Ph.D. Associate Professor Guangdong Provincial Key Laboratory of Intelligent Transportation System, Sun Yat-sen University, Guangzhou 0, P.R. China Tel: +-0- Fax: hezhch@mail.sysu.edu.cn Paper prepared for Transportation Research Board th Annual Meeting Transportation Research Board Washington, D.C. January, 0 Submitted for Presentation and Subsequent Publication: August, 0

2 Yang, Zhang, Ciari, and He 0 Abstract Traffic signal fuzzy control is perceived as one of the most promising solutions to the next-generation traffic signal control problems. However, most of the studies use two-stage fuzzy controllers, whereas the uncertainty of traffic flow at intersections, and functional disability of controller learning are largely unexplored. In this study, an adaptive three-stage fuzzy logic controller for traffic signals is presented. This controller is able to update phase structure, fuzzy membership functions and fuzzy rules according to real-time traffic conditions with following two critical features: () to quickly capture the uncertainty of traffic flows, the controller introduces overlap phases of conflict-free flows to develop the traffic signal three-stage fuzzy model; and () the rolling horizon based optimization framework is designed to optimize fuzzy parameters with near-real-time online learning. Based on the observed second-by-second traffic data, a golden ratio based genetic algorithm is employed to efficiently yield the reliable solution of fuzzy parameters. Compared with five other traffic signal control approaches, extensive Paramics simulation experiments under different traffic conditions have demonstrated the potential of the developed controllers for adaptive traffic signal control at isolated intersections. Keywords: traffic signal; fuzzy logic; rolling horizon; golden ratio; genetic algorithm

3 Yang, Zhang, Ciari, and He INTRODUCTION Over the past decades, majorities of traffic signal control research has been mathematical-equation driven. Performance of these traditional models in practice are not usually satisfactory due to the uncertainty and disturbance of time-variant traffic flows []. Model-free research is expected to expand in the near future with significant advances in artificial intelligence and technologies, as well as the increasing data collected from sensors on urban network. Fuzzy logic-based controllers, first introduced into traffic signal control by Pappis [], is based on mathematical representation of human knowledge and experience. These controllers inference signal timings without precise multi-object mathematical models, and learn signal control knowledge in the uncertain traffic environment. They are widely used both in the research and in the practice of urban traffic signals []. The vast majority of these studies use two-stage fuzzy controllers. They improve the model performance by processing state variables dispersedly, and optimizing phase sequences via phase skipping [, ]. Though these measures can give priority to link flows with highest traffic intensity, the driver confusion induced by phase skipping brings potential safety hazards. The signal phase structure and the controller model are fixed once they are calibrated, resulting in insufficient use of capacities and weaker prediction of traffic states at intersections. Moreover, two-stage fuzzy controllers generally use empirical parameters preset by experts, and therefore do not possess learning ability. Aiming to address the issues above, three-stage fuzzy controller was developed to optimize signal phase structures []. The controller uses the four-phase signal as the basic phase structure, and gives red truncation to conflict-free approach flows by four overlap phases. Simulation results have shown that this controller has better performance in response to time-variant traffic flows due to flexible phase structure []. However, most of these studies select the candidate signal phase with the highest traffic intensity among red phases as the next green phase, and this criterion does not take all conflict-free approach flows at intersections into account, as well as its time-variant effect on drivers. Such unique fuzzy controllers are essentially two-stage fuzzy controllers with signal phase structure optimization. For the optimization of fuzzy parameters, genetic algorithms (GA) are probably the most widely employed method because they do not depend on gradient information and empirical knowledge and are able to find global optimum []. The works employing GA can be divided into three categories: optimizing parameters of fuzzy membership functions with empirical fuzzy rules [], optimizing parameters of fuzzy rules with empirical fuzzy membership functions [0], and simultaneously optimizing parameters of fuzzy membership functions and fuzzy rules []. The main limits of GA-based fuzzy controllers are the time efficiency and the solution quality of GA. Bionics mechanisms, such as simulated annealing, ant colony foraging and particle swarm prey [, ], are employed to improve local search of simple genetic algorithms. Though these improved hybrid genetic algorithms can search better solutions by integrating advantages of different algorithms, the structure is more complicated and a larger amount of calculations are needed, which results in low efficiency and poor portability of the algorithm. For performance evaluation, most current studies have employed numerical simulation of static traffic scenarios with Matlab or other similar software and they cannot simulate microscopic moving of vehicles along signalized intersections. More realistic microsimulation approaches are needed to evaluate the performance of the developed controllers []. Along the lines of previous studies, this paper presents an adaptive three-stage fuzzy control algorithm for traffic signals at isolated intersections. It offers an effective three-stage architecture

4 Yang, Zhang, Ciari, and He 0 to capture the uncertainty of time-variant traffic flows with overlapping signal phases. Based on the rolling horizon approach, a GA-based heuristic integrated with the golden ratio searching is developed to learn the optimal parameters of fuzzy controllers. Such a unique rolling optimization feature contribute to more effectively setting control variables in the overall optimization process. A Paramics-based online microscopic simulation platform has been used to test the performance of the controller on a major intersection in Shenzhen. THREE-STAGE FUZZY MODEL FOR TRAFFIC SIGNALS Structure of the three-stage fuzzy controller Continuous traffic flows in each lane of each approach at intersections are time-variant due to the non-uniform distribution of upstream arrival flows. To reduce the number of fuzzy rules effectively, this study has employed a multi-stage inference, that is, signal timings are optimized by multi stage instead of in one step as in single fuzzy controllers. To predict traffic states accurately, traffic intensities, the urgency of link flows to have the right of way, are used to describe traffic conditions at intersections. To capture the unexpected uncertainty of changing traffic flows adaptively, signal phase structures in fuzzy controllers are updated online. As shown in Figure, the three-stage fuzzy controller proposed here employs a signal phase optimization stage to account for traffic uncertainties at intersections. First stage: traffic intensity Third stage: green extension time 0 Vehicle detectors Traffic data of green phase Traffic data of red phase Green urgency evaluation controller Red urgency evaluation controller Green urgency Red urgency Two stage: signal phase optimization Signal phase optimization controller Red urgency Next phase Decesion controller g e (s) Traffic lights Three- stage fuzzy logic controller Real Traffic Environment 0 Figure Structure of a three-stage fuzzy controller for traffic signals In the first stage, arrival and departure inductive loop detectors, placed upstream and at the stop line of each lane of each approach respectively, are used to measure incoming flows and estimate queues. Then, the observed traffic data is used to estimate traffic intensities of green signal phase and red signal phases, denoted by green urgency and red urgency respectively. The second stage optimizes the next green signal phase among competing incoming flows with fuzzy inference. To respond quickly to the uncertainty of time-variant traffic flows, the signal phase structure is optimized by inserting overlap phases of conflict-free flows, instead of phase skipping. In the third stage, the green extension time of the current phase is inferred based on the intensities at stage I and on the next signal phase at stage II. The controllers in the first stage and the third stage have already been modeled in previous work [, ] and hence they are not included to avoid redundancy.

5 Yang, Zhang, Ciari, and He 0 0 Fuzzy controller of Signal phase optimization Structure of signal phase optimization The objective of phase optimization is to decrease traffic loss while ensuring traffic safety at signalized intersections. According to the inherent multi-objective nature of signal phase design, three basic principles in phase optimization should be followed: () Traffic safety is the primary goal of traffic signal control, and a reasonable signal phase structure has to satisfy the green conflict matrix to ensure traffic safety. () To better use the capability of signalized intersections and capture time-variant traffic flows, the signal controller should update signal phase structure according to real-time traffic intensities. () To ensure drivers smooth adaption to the changing signal control structures, the basic phase sequence should be adopted to improve traffic safety. Following the above critical principles, the basic four-phase signal structure (A-B-C-D) for balanced approach direction flows is used as a benchmark. It is assumed that drivers have good adaptability to weaving and merging vehicles from conflict-free direction flows. And by the objective of maximizing traffic capacity, the signal phase structure and phase sequence are optimized via eight overlap phases of conflict-free approach flows as shown in Figure []. The basic phase A-D is executed by a pre-assigned sequence, when it comes to phase A or C, the phase-switch fuzzy controller judge whether to employ one of the overlap phases. This brings the red signal forward to one of the straight flows with lower traffic intensity, and instead gives green signal priority to the conflict-free left-turn flows with the highest traffic intensity. Note that this study considers overlap phases as the optimization of the corresponding basic phase with red truncation. And hence the accumulated green time of the basic phase and its following overlap phase must fulfil the maximum green time constraint of the basic phase. Phase A Overlap Phase Phase B Phase C Overlap Phase Phase D OP OP OP OP OP OP OP OP Pedestrian Motor Vehicle 0 Figure Illustration of the optimization of signal phase Structure Inference rules In this study, the red urgency of a red signal phase i is denoted by I r (i) and the next signal phase by NG, where the linguistic value of the five fuzzy subsets of I r (i) are {very low, low, average, high, very high} abbreviated as {VL, L, A, H, VH}. According to the definition of signal phase evaluation controller, the input variable is I r (i), and the output variable is NG. It is considered that NG is strongly influenced by the traffic intensities of the candidate red phases and their phase-switch impact on driver behaviors. Thus, NG is optimized by inference rules between the candidate overlap phase with the highest red urgency (denoted by HOP) and the following red signal phase pre-assigned in the four-phase benchmark. Taking phase A as an

6 Yang, Zhang, Ciari, and He example, the candidate phase set of phase A is {OP, OP, OP, OP, B}, with I r (HOP) = max{ I r (OP), I r (OP), I r (OP), I r (OP)}. Inference rules for phase-switch optimization of phase A is shown in Table. For example, if I r (B) is VL and I r (HOP) is VH, NG is the HOP. Table Fuzzy rules of signal phase switch optimization Ir(HOP) I r (B) VL L A H VH VL B B HOP HOP HOP L B B B HOP HOP A B B B HOP HOP H B B B B HOP VH B B B B B DEVELOPMENT OF ADAPTIVE THREE-STAGE FUZZY CONTROLLER The rolling horizon approach The link between membership functions and fuzzy rules would be cut off if any of them is optimized separately []. To provides real-time and traffic-adaptive signal control, this study use a discrete time and rolling horizon process to optimize parameters of fuzzy controllers []. As illustrated in Figure -a: () The entire control time horizon (H) is decomposed into a series of control time intervals (T), and the parameters are optimized over each successive projection stage, but implemented only for the control interval T i (head section of each stage, including the implemented and optimized period). () At the optimization point (T 0 ) of each projection stage (L), the GA-based optimization module uses a genetic algorithm to search the optimal parameters of fuzzy membership functions and fuzzy rules as following steps. ) The population of candidate parameters is first generated using the genetic algorithm. ) According to the observed traffic data in the latest control interval, the evolution of traffic flows at signalized intersections is predicted second by second. Meanwhile, each fuzzy controller with each parameter individual are used to signalize the movement of the predicted traffic flows. The corresponding average delay at the intersection are calculated to evaluate the performance of each individual. ) The above steps are repeated until the termination criterion of GA is fulfilled. () Once the optimization process is finished, the parameters of the implemented fuzzy controller are updated by the optimal parameters. They hence map the latest traffic conditions. Then, the projection horizon shifted forward by one control interval, and the traffic state within urban network is updated with real-time measurements from the signal control system. The data acquisition time interval is one second, and the optimization process repeat again at the next T 0. The rolling horizon based optimization structure consists of four sub-modules as shown in Figure -b: the implemented three-stage fuzzy controller, the traffic flow emulator, the GA based parameter optimization module, and the historical database. To ensure the optimization efficiency, the implemented fuzzy controller is signalizing with the latest optimal parameters until the current optimization request is finished. Then, the optimization process is repeated if the up-to-date optimization request exists. And once the accumulated optimization time reach the maximum allowable optimization time T max, a decision is made to terminate the current optimization request immediately, and the optimization process for the up-to-date optimization

7 Yang, Zhang, Ciari, and He request is conducted. Entire control time horizon H Length of Projecton Stage: L Stage Three-stage fuzzy controller Optimization point: T0 0 Roll Period Implemented period Optimized period Projected period Roll Period T0 Stage Roll Period T0 Stage Roll Period n T0 Control interval: T Control interval: T Control interval: T Control interval: Tn time a. rolling horizon framewrok b. adaptive three-stage fuzzy controller Stage n Detectors History database Traffic flow emulator GA based Optimization module Traffic inviroment Figure Rolling horizon optimization framework of three-stage fuzzy control Decoding parameters of three-stage fuzzy controllers All fuzzy controllers in this study have two input variables and one output variable, and all of them are divided into five fuzzy sets. To reduce the number of parameters of the controller, the base vertices of each triangle membership function are separately superposed to the centers of two adjacent membership functions (Fig. -a). And hence, only with the center of functions, its position and shape can be effectively determined. In addition, to improve the convergence speed of the optimization algorithm, a real-coded genetic algorithm is used to decrease the length of a chromosome. Traffic light 0 0 a. decoding membership functions b. individual decoding of three-stage fuzzy controller Figure Decoding an three-stage fuzzy controller For the fuzzy rules in each evaluation controller, the integer matrix R is defined as follows: R [ rij ], i [,], j [,], and r ij is an integer within [, ], which denotes the index value of the output of a fuzzy set. Then R can be converted into a row vector R line by line, and R can be used to denote the chromosome of fuzzy rules. To lessen driver confusion to the changing signal phase structure and further avoid hidden dangers in traffic safety at intersections, the inference rules in signal phase evaluation controller should be stable. For this reason, those rules are not updated online. The individual coding of the proposed controller is shown in Figure -b. Golden-ratio based hybrid genetic algorithm Golden ratio (GR), widely used in many fields [], is introduced here to improve the local search of the genetic algorithm. The golden ratio based hybrid genetic algorithm (GRGA) has been developed to obtain optimal solutions for each control interval of the entire optimization period. As shown in Figure, taking the best individuals in each generation of a real-coded

8 Yang, Zhang, Ciari, and He genetic algorithm as initial vectors [], the GRGA employs the opposite golden ratio to produce extra individuals with potentially better genes, and hence improves local searching. Start(Problems) Parameter initialization Population initialization G=G+ Meet the termination princilple? No Fitness calculation: Store-and-forward based delay model Selection Yes The best solution Output performance and results Crossing 0 0 Local optimization via GR Mutation Produce new individuals via GR state functions Calculate fitness value of new produced individuals Accept new individuals via Metropolis rule Figure Golden ratio based hybrid genetic algorithm End(improve or solve the practical issues) G: current generation number Gen:maximum generation number The performance of each fuzzy controller with each candidate parameters in individual X is evaluated by the average delay (d) at the intersection. To accelerate the optimization efficiency, the sore-and-forward macroscopic modelling is used to calculate the average delay together with predicting traffic evolution in the latest control interval []. Then the fitness value of X, denoted by f(x), is computed by: f( X) d () To increase population diversity, the best M s individuals of the existing population are first selected to generate the optimal subpopulation. Then two-thirds individuals in the subpopulation M s are randomly selected in turn, and every two selected individuals are considered as the adjacent neighbors. The new individuals set (NIS) with the golden ratio searching is calculated as follows: () As shown in equation, A and B are two adjacent individuals, and C is the potential local position determined by the golden ratio of A and B. This means, the ratio of the segment AC and AB is equal to the golden ratio (0.). The opposite golden ratio concept is used to determine the extra local position C. Specifically, the point C is rotated by 0 degrees, and the ratio of the segment C C and C B is equal to the golden ratio []. () Evaluate each new individual in the NIS by equation ; ()

9 Yang, Zhang, Ciari, and He 0 0 () Select new individuals in the NIS by the metropolis principle and replace the worst individuals in the existing population. The acceptance probability of individual X, denoted by P(X), is calculated by: G f ( X ) ( ) P( X ) e Gen () In equation (), to approximate the best solution with faster convergence, P(X) increases with the evolutional generation number and fitness value of the individual X. Therefore, the GRGA select more local search positions of the GR later in the evolution process. is the coefficient parameter that determines the weight dependent on the generation number; CASE STUDY Case description A major intersection in Shenzhen City in the heart of financial district was used to test the model and the algorithm presented. It has high saturated flows in most of daytime, and the distribution of arrival traffic volumes at each ingoing link of the intersection is obviously unbalanced. The number and configuration of lanes on each approach in the real-world application are shown in Figure. The widely used optimal fixed time control is used in multi-timing zones (one channelized right turn lane without signals). Departure detectors are deployed respectively along each approach of the intersection, while arrival detectors are deployed at a distance of 0m upstream from tactical loops. Strategic loops Phase A Phase B Tactical loops Phase C Phase D 0 a. number and configuration of lanes on approaches b. phase sheme c. Paramics simulation model of test intersection Figure Test intersection in Shenzhen and its Paramics model Simulation scenarios Paramics was used as an mainstream tool for evaluating various signal control strategies. As in Figure -b, an online simulation platform of fuzzy logic control is developed to connect Paramics and the presented controllers []. Two simulation scenarios were designed as follows: () Scenario I: daily traffic scenario with no incident Simulation length is hours. The multi-timing zone is divided by the typical four traffic states at the intersection. The field-observed average traffic volume in a month (00.0) is used as the input OD of each timing zone (Table ). The Profile file in Paramics is used to simulate the short-time fluctuation of incoming flows. The traffic demand input over one hour is presented at -minute intervals in Paramics, consistently with the field survey data. () Scenario II: unexpected traffic scenario with traffic accident The traffic volume level and simulation parameters are the same as in Scenario I, except for peak time from 0:00 to :00 in the busy traffic state. During the time, a traffic accident is

10 Yang, Zhang, Ciari, and He 0 0 assumed to happen at the straight lane of the southbound approach, and the inner lane is closed. Consequently, the straight capacity is reduced by /. The setting of key simulation parameters in two scenarios are as follows: i. The three-stage fuzzy controller switches green signals to the next signal phase once the green time extension is less than second. In the online optimization module, L is 0 minute, T 0 is minute for GRGA based fuzzy controllers, while T max is equal to the sum of L and T 0 ; The maximum allowable green time for phase A and phase C is 0s, while 0s for phase B and phase D, and 0s for overlap phases. The minimum green time for all phases is 0s. ii. The parameter setting of the GRGA is as follows: the population size (P) 00, the maximum generation number (Gen) is 0, the GR local search size (m) is 0, the optimal subpopulation size M s is m. is 0.. The crossrate and the mutation rate are adaptive to the generation number and fitness value of individuals []. The real-coded initial population is produced with fulfilling the signal timing constraints and individuals different from each other. iii. According to the design specification of urban roads [0], the through capacity per lane is 0 pcu/h and left-turn/right-turn capacity per lane is 0 pcu/h, the key simulation parameters, i.e., the mean driver reaction time and the mean headway time are calibrated respectively to.s and.s; iv. To overcome the stochastic nature of the simulation results, 0 simulation runs are performed for each signal strategy. The average delay (Delay, s) and the average number of queuing vehicles (Queue, pcu/s) at signalized links are used as the performance measures. Table Average traffic volume level under four traffic states in a month Timing period Traffic state ES*, WS EL*, WL NS, SS NL, SL ER*, WR, NR, SR :00-:00 Free,,,, 0, 0,, :00-:00 Busy,,,,,,, :00-:00 Congested,,, 0 0, 0,,, 0 0 Other Smooth 0, 0, 0,, 0,,, *ES, EL, and ER: the respective traffic volume of eastbound through, left turn, and right (pcu/h) Design of experiments The design of experiments reflect the investigation of the proposed two fuzzy controllers: ) the three-stage fuzzy controller (MultiSF) with signal phase optimization, ) the Golden-ratio genetic algorithm based three-stage fuzzy controller (GRMSF) as illustrated in the following two experiments: In experiment I: The performance of the widely used optimal fixed time control, actuated control and two-stage fuzzy control are used as benchmarks, and are compared to the MultiSF signal control in the designed simulation scenarios. The fixed time signal plans (Fixed) in the multi-timing zone are optimized using the Webster method []. The observed loops in the actuated controller (actuated) are 0m away from the stop lines and the unit extension time is second. The traffic intensity based two-stage fuzzy model (TFITSF) are used to perform fuzzy logic traffic signal control []. In experiments II: The majority of existing optimized fuzzy algorithms are developed for the two-stage fuzzy controller in specified traffic scenarios and hence not suitable for benchmarking. It is difficult to find a good benchmark for the GRMSF signal control. Simulated annealing is often used to improve local search of simple genetic algorithms. Many simulated

11 Yang, Zhang, Ciari, and He annealing based hybrid genetic algorithms (SAGA) have been applied in traffic signal controllers with promising results []. Here, the performance of the simulated-annealing genetic algorithm based three-stage fuzzy controller (SAMSF) is used as a benchmark and is compared to the presented GRMSF and MultiSF. EXPERIMENTAL RESULTS AND ANALYSIS The MultiSF signal control Daily traffic scenario with no incident Simulation results of the MultiSF signal control in the scenario I are shown in Figure -a. Throughout the whole simulation period, the performance of the MultiSF is consistently better that other types of control algorithms with smaller fluctuations. Compared with the Fixed, the Actuated and the TFITSF signal control, the MultiSF signal control obviously reduces the number of queuing vehicles by.pcu/s,.pcu/s, and.pcu/s, respectively, and reduces time delay by.0s,.s, and.s. Note that at five transition periods of traffic state changing, the MultiSF quickly respond to the changes in traffic demand and stabilizes faster. This indicates that the MultiSF has efficiently handled time-variant traffic flows by updating signal phase structures with overlap phases of competing approach flows. Unexpected traffic scenario with traffic accident Simulation results of the MultiSF signal control in the scenario II are shown in Figure -b. Compared with the TFITSF signal control, the performance of the MultiSF in the extremely congested condition is still outstanding with time delay and the number of queuing vehicles reduced by.s and.0pcu/s, respectively. During the traffic accident, the MultiSF quickly respond to unexpected changes of incoming flows with few sharp fluctuations. This indicates that the presented MultiSF adaptively adjusts the signal phase structure according to the changing traffic patterns caused by the uncertain incident. 0 a. in scenario I b. in scenario II Figure Time-varying control performance of the MultiSF signal control

12 Yang, Zhang, Ciari, and He 0 0 The GRMSF signal control Daily traffic scenario with no incident Simulation results for the GRMSF signal control in Scenario I are shown in Figure -a. With online learning parameters of fuzzy controllers, both the GRMSF and the SAMSF signal control perform better in terms of delay and queuing vehicles. Compared with the MultiSF and the SAMSF signal control, the GRMSF decreases the number of queuing vehicles by 0.pcu/s, and 0.pcu/s respectively, and reduce delay by.s, and.0s. Moreover, the performance of the GRMSF in congested traffic state is obviously improved because of the better time efficiency (See. for computation time analysis), while in free and smooth traffic state, little difference is observed between the GRMSF and the GRMSF as both of them can timely update the fuzzy parameters. This indicates that the GRMSF have promising ability to find a better solution with the golden ratio based local searching. Unexpected traffic scenario with traffic accident Simulation results of the GRMSF signal control in the scenario II are shown in Figure -b. The GRMSF still get the better performance in delay and queuing vehicles because of the better optimization efficiency, while the SAMSF has small improvement as it is constrained by its poor optimization efficiency in highly and over saturated conditions. Compared to the MultiSF and the SAMSF signal control during the accident time, the GRMSF reduce the number of queuing vehicles by.pcu/s and.pcu/s, respectively, and reduces time delay by.s and 0.s. These results confirm that, by optimizing phase structure and learning parameters efficiently, time-space resources at the intersection are vastly saved, and hence traffic throughput is greatly improved. The GRMSF signal control has the potential of dealing with the uncertainty of time-variant traffic flows. a. in scenario I 0 b. in scenario II Figure Time-varying control performance of the GRMSF signal control

13 Yang, Zhang, Ciari, and He 0 Computation time of parameter optimization The average computation time of parameter optimization in the GRMSF and the SAMSF signal control in each control interval, is shown in Figure. The computation time is both increasing with the traffic intensity at the intersection. With the proposed GRGA, the GRMSF signal control consumes less computational time than the SAMSF, and updates fuzzy parameters in % of total control intervals. With the SAGA, most of the computation time in the SAMSF signal control exceeds the preset control interval of 0 minute in the congested conditions. This is because the simulated annealing approach is limited by huge computation and complicated convergence conditions compared with the golden ratio approach. Especially in the traffic incident period, there are a large number of queuing vehicles at the intersection, and each new arrival is added to the queue with the probability of 00%. Consequently, the computation time in the delay model sharply increases, and parameter updating of the SAMSF fails before the time window rolls to the next stage. 0 a. in Scenario I b. in Scenario II Figure Computation time of the GRMSF and the SAMSF signal control Signal phase sequencing The driver confusion to time-varying signal timings can be best illustrated by signal phase sequencing. Figure 0 shows the phase switch sequence by the MultiSF and the TFITSF signal control from :00 to :0 in Scenario I. The TFITSF uses phase skipping to optimize the sequence of signal phases, and the four basic signal phases are switching randomly. As a result, skipping phase are fluctuating intensely. All these may increase driver confusion and induce serious safety risks across the intersection. The MultiSF signal control uses overlap phases to optimize signal phase structures. By truncating straight flows and overlapping conflict-free left-turn flows, all candidate phases are organized in sequence and there is no phase skipping. For the studied case, the straight and left-turn traffic volumes in the southbound and eastbound approaches get higher in peak period and are reflected in overlap phases of OP and OP.

14 Yang, Zhang, Ciari, and He Figure 0 Illustration of phase switch sequencing of the MultiSF and the TFITSF Response time and cycle length variation The response time of the GRMSF signal control can be best illustrated with frequency of changes in the phase length. Figure -a displays the length of each phase of each cycle for the studied intersection by the GRMSF in scenario I, and Figure -b displays time-varying cycle length. The links having the right of way during the third phase have the highest traffic demand and is reflected in the phase timing, as well as in the overlap phase of OP. Apparently, the cycle time is lower in the non-peak period and dynamically varies with changing traffic patterns. And in the traffic state transition period, it responds quickly to the change of traffic patterns and optimize the length of each phase. However, because of the switch-off strategy with the green time extension, both cycle length and phase length in signal timings are frequently fluctuating. The signal timings with second as the maximum fluctuation range of cycle length are unstable. It indicates that the switch-off strategy in the GRMSF makes a large step optimization of signal timing, which may induce more potential traffic uncertainties at the intersection. Effect of convergence condition The performance of GRMSF signal control is vastly sensitive to convergence conditions of the proposed GRGA. Figure -c shows the variation of average delay experienced with varying the maximum generation number ( to 00) in scenario I, as well as the average computation time of parameter optimization. Due to the iterative optimization process in genetic algorithms, the average computation time in the GRMSF exponentially increases with the maximum generation number. By increasing the maximum generation number from to 0, the average delay values is reduced to around 0% compared to what was at the start of the initialization. This means that with the GRGA, up to 0 generations, the quality of the solutions increases as more generations are used. However, the results are not improving anymore, or only very little, after increasing the maximum generation number from 0 to 00. Indeed, there are few fluctuations of the average delay values. This happens because the iterative calculation of delays consumes a large amount of time with increasing generations. The performance of GRMSF with the newly optimized parameters is greatly weakened due to its serious hysteresis in real time optimization. In addition, at later stages of the optimization process, the difference between the best individuals of different generations becomes smaller.

15 Yang, Zhang, Ciari, and He a. Time-varying phase length of each cycle b. Time-varying cycle length c. Improvement with changing generation number Figure Performance of the GRMSF signal control in scenario I

16 Yang, Zhang, Ciari, and He CONCLUSIONS AND DISCUSSIONS This study has presented an adaptive three-stage fuzzy controller for the design of effective control strategies for urban traffic signals. Experimental tests on a typical isolated intersection under various traffic conditions have shown that: () The TFITSF signal control, optimizing phase sequence by phase skipping, causes intense fluctuations in phase structure, which may induce potential safety problems. The MultiSF signal control, optimizing phase structure by inserting overlap phased, can maintain consistent phase-switch sequence with better use of capacity at the intersection, as well as quickly respond to changing traffic pattern. Therefore, updating signal phase structure adaptively according to characteristics of time-varying traffic flows seems an effective decision for traffic signals. Phase skipping should be used carefully and rather reduced to the minimum level; () The entire system performance is largely sensitive to the performance of the proposed GRGA, affected by both local search and convergence condition. With less calculations and simpler convergence condition, the parameters of the GRMSF are updated in almost all of control intervals. But the SAMSF signal control mostly failed in high saturated conditions. The decision makers need to carefully trade-off between the quality of reliable solutions and optimization efficiency based on the scale of the implemented network and the characteristics of the proposed models so as to efficiently update the parameters of fuzzy controllers; () Though signal phase timings are fluctuating due to the switch-off strategy, with a proper optimization algorithm, the proposed model gets the better use of available intersection capacity with less delay time and queuing vehicles. And it responds quickly to changing traffic patterns. These have demonstrated the potential of the GRMSF in adaptive signal control for an isolated intersection. Limited by the hysteresis of rolling horizon and the optimization efficiency of GRGA, the proposed adaptive three-stage fuzzy controllers has the ability of the near-real-time optimization control. Even if it has promising performance at an isolated intersection, it is difficult to extend this method to control multiple intersections of an urban network. This is because parameters of the fuzzy controller are updated by using genetic algorithm to search in the efficient solution set. It can be seen that the computation time of fuzzy parameter optimization will exponentially grow with the number of intersections and with the complexity of the coordinated model in dynamic changing environments. The genetic algorithm based fuzzy controller for traffic signals will suffer form the curse of time-efficiency issue that arises because the optimization time is infinite. This approach will fallback to three stage fuzzy control without learning parameters. In addition, most of the state-of-practice signal controller are not able to support complicated signal control algorithms due to computational and processing limitations. Based on the discussion above, more extensive experiments or field tests will be conducted to assess the effectiveness of the proposed model applied for adaptive signal control at isolated intersections. And to extend the adaptive fuzzy logic controller into multiple intersections, there is a need to employ the model-free and self-learning algorithm, i.e., reinforcement learning, to optimize parameters of fuzzy controllers in real time, instead of genetic algorithm. ACKNOWLEDGEMENTS Thanks Prof. Kay W. AXHAUSEN for hosting me at the IVT of ETHz and letting me work with his team. I am grateful for his professional guidance and favorable conditions.thanks to ITS Research Center of Sun Yat-sen University for able assistance on Paramics works. This paper is

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