Multi objective Optimization in Traffic Signal Control DMU’s Interdisciplinary research Group in Intelligent Transport Systems, (DIGITS) Faculty of Computing, Engineering and Media Multi objective Opt[.]
Motivation
Transportation is vital for economic growth, social development, and enhancing human lifestyles, yet urban areas face significant challenges Congestion leads to increased fuel consumption and air pollution, adversely affecting economic progress Additionally, road traffic accidents result in approximately 1.35 million fatalities annually, particularly in low- and middle-income countries, highlighting the need for improved road safety The transportation sector also plays a crucial role in global warming, necessitating urgent action to reduce traffic exhaust emissions Solutions such as constructing new roads, expanding transport systems, and optimizing existing infrastructure are essential, but urban areas often lack space for new developments Consequently, upgrading and optimizing existing transport systems through Intelligent Transport Systems (ITS) has emerged as a promising trend in transportation research, aimed at enhancing the efficiency and performance of urban transport networks.
Chang (2014),Djalalov(2013), Hamza-Lup et al.(2008),Sanchez-Medina et al.(2010), Zhang et al (2011).
Intelligent Transportation Systems (ITS) integrate information and communication technologies into transportation infrastructure to enhance performance, efficiency, and safety By leveraging advanced technologies, ITS effectively tackles issues such as safety, traffic congestion, transport efficiency, and environmental protection, leading to the development of smarter roads Over the last decade, ITS has significantly improved transportation conditions and increased the capacity of road networks, while also reducing traffic congestion and exhaust emissions in urban areas globally.
The traffic signal control system is a vital and cost-effective tool for managing urban traffic, playing a crucial role in Intelligent Transportation Systems (ITS) It regulates the flow of traffic at intersections, determining which vehicles, pedestrians, and cyclists can proceed and which must stop The primary goal is to ensure safe and efficient movement for all users through intersections Consequently, the effective operation of traffic signal control is essential for the overall performance of urban transport networks, making it a fundamental component of ITS.
Traffic signal optimization plays a crucial role in enhancing the performance of traffic networks by focusing on key objectives such as minimizing delays, reducing the number of stops, and increasing overall network throughput and average speed This process involves determining essential parameters for signal-controlled street networks, including cycle time, green and red time splits, and offsets Effective traffic light signal optimization can improve one or all of these critical values, leading to a more efficient traffic flow.
Traffic signal timing optimization methods are primarily categorized into mathematical programming and simulation-based approaches Mathematical programming employs complex formulations to model traffic flow characteristics for traffic management optimization; however, these models often struggle to meet real-time requirements and fail to adequately represent the intricate interactions at complex intersections, such as queue spillback and lane blockages Furthermore, not all optimization challenges can be expressed through mathematical equations In contrast, simulation-based approaches focus on capturing the dynamic interactions of traffic characteristics, leading to a growing preference among researchers for these methods to enhance traffic signal timing efficiency.
Multi-objective Evolutionary Algorithms (MOEAs) are widely used to solve the multi- objective optimisation problem in transportation, Caraffini et al.(2013),Goodyer et al.
When optimizing transportation problems using Multi-Objective Evolutionary Algorithms (MOEAs), it is essential to conduct traffic simulations for evaluating solutions This process requires multiple evaluations, leading to significant processing time For instance, running a single simulation of the Andrea Costa traffic scenario takes approximately 25 seconds on a PC equipped with an Intel(R) Core(TM) i5-6500 CPU at 3.2GHz With a population size of 60 and 20 generations in the evolutionary process, the total number of simulations required for the optimization algorithm can be substantial, highlighting the computational demands of this approach.
The computation time for running simulations in traffic networks can reach approximately 8.3 hours, and this duration increases significantly with larger road networks and more vehicles While some research methods utilize advanced hardware to mitigate computation time, these solutions can be costly and impractical Therefore, there is a demand for optimization methods that deliver high-quality solutions efficiently, particularly in the early stages of the process Most optimization literature emphasizes the final quality of solutions, which may not be effective in scenarios where time or cost constraints limit function evaluations To address this, an indicator is needed to assess an algorithm's ability to generate good solutions throughout its operation This "anytime behavior" reflects the algorithm's capacity to continuously enhance solution quality as computation time progresses The hypervolume, a concept introduced by Zitzler and Thiele, quantifies the volume of the objective space dominated by a non-dominated set, with greater hypervolume indicating proximity to the Pareto-optimal front Thus, the hypervolume indicator serves as a valuable tool for comparing the anytime behavior of multi-objective optimization algorithms, making it particularly relevant for optimizing time-sensitive traffic signal control systems.
In transportation optimization, small population sizes are crucial for scenarios where limited processing capabilities necessitate quick response times This is especially true for local and distributed signal controllers, which have minimal processing power yet demand optimized signal timings within short timeframes Consequently, optimization algorithms that perform efficiently with small population sizes are highly desirable.
Integrating a local search with a global evolutionary algorithm can significantly enhance the convergence speed of the optimization process According to Espinoza et al (2003), the implementation of local search also contributes to a reduction in the population size of the optimization algorithm Thus, by selectively employing local search, the performance of an evolutionary algorithm can be improved, leading to increased efficiency in traffic signal optimization models.
Surrogate models are computational tools that estimate the objective values of candidate solutions more cost-effectively than traditional objective functions By minimizing the number of evaluations required by the original objective function, surrogates maintain a high quality of results, particularly in traffic simulations during evolutionary searches This allows for an increased number of generations within a limited evaluation budget, making surrogate-assisted Multi-Objective Evolutionary Algorithms (MOEAs) a promising approach to enhance the performance of traffic signal optimization algorithms.
This study introduces two innovative algorithms aimed at enhancing traffic signal timing: a multi-objective optimization algorithm based on local search (NS-LS) and a surrogate-assisted multi-objective optimization algorithm utilizing fuzzy distance and local search (SA-LS) These algorithms are designed to improve anytime behavior and demonstrate effective performance even with small population sizes A comparative analysis will be conducted against NSGA-II and MOEA/D across various population sizes, highlighting the superior effectiveness of the proposed methods.
Propositions
In this demanding field of intelligent transport systems, the following research proposi- tions have been set and studied:
Proposition 1: A local search method can be used to improve anytime behaviour of multi-objective optimization algorithms in traffic signal optimization problems.
Chapter 4 introduces an innovative local search algorithm designed to identify neighbors with promising fitness values This method enhances the algorithm's ability to predict effective search directions, increasing the likelihood of discovering superior neighbors early in the process As a result, the overall performance of the search algorithm can be significantly improved Experimental results, detailed in Chapter 6 and presented in Chapter 7, validate the effectiveness of this approach.
Proposition 2: A method based on an approximation model can be designed to evaluate candidate solutions in traffic signal optimization problems.
Chapter 4 introduces a novel surrogate model utilizing an Artificial Neural Network to enhance traffic signal system optimization This model learns the correlation between input variables, specifically the duration of traffic signal phases, and output metrics, including traffic flow and delay, by leveraging solutions assessed by a traffic simulator from previous generations To improve approximation accuracy, the surrogate is continuously updated throughout the optimization process Additionally, it is integrated with a traffic simulator to evaluate the objective values of candidate solutions during each generation of the evolutionary search.
Proposition 3: A local search method can be combined with an approximation model to enhance anytime behaviour of evolutionary search in traffic signal optimization problems, especially in small population sizes.
Chapter 5 introduces a novel surrogate-assisted evolutionary algorithm designed for optimizing traffic signals This approach employs an approximation model to minimize the reliance on traffic simulator evaluations, while a local search method enhances the convergence rate of the evolutionary process Consequently, the proposed algorithm increases the number of iterations within the same evaluation limits set by the traffic simulator Additionally, an effective management model is suggested to optimize the use of the surrogate Experiments conducted in Chapter 5 assess the performance of this combination, focusing on improvements in anytime behavior for traffic signal optimization, with results detailed in Chapter 6.
Aims and objectives
This research aims to evaluate the effectiveness of integrating a surrogate-assisted evolutionary algorithm with a local search method to enhance the anytime behavior of traffic signal optimization systems, particularly with small population sizes Additionally, it seeks to assess the feasibility of using approximation models for evaluating candidate solutions in traffic signal optimization Another key focus is to explore how local search methods can improve the anytime behavior of multi-objective optimization algorithms in traffic signal optimization challenges.
The objectives of this study are:
1 To provide a comprehensive literature review of traffic signal optimization based on multi-objective evolutionary algorithms and traffic microscopic simulators.
2 To extend the knowledge of optimizing traffic signal control using surrogate-assisted evolutionary algorithms and local search.
3 To construct an optimization model for traffic signal control based on a local search method to improve anytime behaviour and this model can work effectively in small population sizes.
The development of a surrogate-assisted evolutionary algorithm aims to optimize multiple objectives in traffic signal control by employing a surrogate model to reduce the frequency of traffic simulator-based evaluations Additionally, the methodology incorporates a local search technique to enhance the convergence rate of the evolutionary search process.
5 To assess and compare the performance of the proposed models on traffic scenarios.
Major Contributions of the Thesis
Major contributions of the thesis are summarized as follows:
A new local search methodology has been introduced to identify superior neighbors within local areas This innovative approach enhances the ability to predict potential search directions, significantly increasing the likelihood of discovering better neighbors early in the process.
A novel multi-objective evolutionary algorithm incorporating local search is introduced to enhance anytime behavior in traffic signal timing By executing local search during the evolutionary algorithm's iteration process, the method swiftly identifies optimal solutions, thereby improving the convergence rate of the evolutionary search.
A surrogate model is developed to assess the fitness value of candidate solutions during optimization, effectively learning the correlation between signal timing phase durations and key traffic parameters like flow and time loss It leverages previously evaluated solutions from a traffic simulator to enhance its training, and is continuously updated throughout the optimization process to refine its approximation accuracy.
A novel surrogate-assisted multi-objective evolutionary optimization algorithm is proposed for managing traffic light signals at urban intersections This innovative approach employs a surrogate model to accurately estimate the fitness values of potential solutions, integrating both a traffic simulator and the surrogate during the fitness evaluation to avoid misleading optima Additionally, the algorithm incorporates local search techniques within its iterative process to enhance convergence speed The combination of local search and surrogate modeling significantly boosts the anytime performance of the evolutionary algorithm in optimizing traffic signal systems.
A proposed fitness evaluation scheme aims to effectively select between the surrogate model and the SUMO traffic simulator for estimating solution fitness values This scheme ensures the efficient utilization of the surrogate model by assessing the proximity of new solutions to those previously evaluated by the traffic simulator, as documented in the database used for constructing the surrogate, alongside the mean squared error (MSE) of the surrogate's approximation error.
Thesis structure
The thesis is organized as follows:
Chapter 2 delves into the foundational aspects of traffic signal control systems and road traffic simulators, highlighting their significance in transportation challenges It begins by defining key concepts related to traffic signal control systems, followed by an introduction to road traffic simulators, particularly the Simulation of Urban Mobility (SUMO) software The chapter further explores Multi-objective Evolutionary Algorithms (MOEAs), outlining their definitions, basic concepts, and general framework Finally, it discusses surrogate-assisted evolutionary algorithms and the techniques used for constructing surrogates, providing a comprehensive overview of these critical components in traffic management and optimization.
Chapter 3 provides a thorough literature review on multi-objective traffic signal optimization, emphasizing the use of Multi-Objective Evolutionary Algorithms (MOEAs) and local search-based MOEAs It examines the evaluation of candidate solutions through traffic simulators, highlighting the benefits and limitations of simulator-based MOEAs in traffic signal optimization Additionally, this chapter identifies gaps in previous research and includes discussions on the application of surrogate-assisted MOEAs for enhancing traffic signal optimization strategies.
Chapter 4 introduces the algorithms proposed in this study Firstly, the motivation and the flow of the local search strategy are provided Afterwards, this chapter presents NS-
The NS-LS algorithm is a multi-objective optimization approach designed to enhance the anytime behavior of traffic signal timing This article details the framework and flow of NS-LS, emphasizing the evolutionary search design It outlines the surrogate construction process, including model selection, training algorithms, error functions, hyperparameter tuning, and surrogate updates The surrogate works in conjunction with a traffic simulator to estimate the fitness values of candidate solutions, introducing an effective fitness evaluation scheme Additionally, the article presents SA-LS, a surrogate-assisted multi-objective traffic signal optimization algorithm that incorporates fuzzy distance and local search, along with an overview and discussion of its search flow.
Chapter 5 outlines the experimental setup for assessing the proposed algorithms' performance, introducing two benchmark test functions and two traffic scenarios It details the process of linking traffic scenarios with optimization models and describes the methods for extracting optimization objective values from SUMO outputs Additionally, the chapter discusses the performance indicators utilized in the thesis Finally, it presents the specifics of three experiments designed to evaluate the algorithms' effectiveness.
Chapter 6 presents the experimental results, evaluating the performance of the proposed algorithms against NSGA-II and MOEA/D using various performance indicators The optimization outcomes from three experiments are detailed to assess the validity of the propositions.
Chapter 7 wraps up the thesis by presenting conclusions, recommendations, and suggestions for future work, while reaffirming the propositions introduced in the opening chapter This section also offers a comprehensive summary of the key contributions made by the research.
Introduction
This chapter reviews essential components relevant to the evaluation of hypotheses from Chapter 1, focusing on traffic signal control systems, road traffic simulators, and optimization algorithms in transportation Section 2.2 defines traffic signal control systems, while Section 2.3 introduces road traffic simulators and the Simulation of Urban Mobility (SUMO) software In Section 2.4, Multi-objective Optimization Algorithms (MOEAs) are defined, along with their basic concepts and framework Section 2.5 distinguishes between surrogate-assisted evolutionary algorithms and traditional evolutionary algorithms, including techniques for constructing surrogate models The chapter concludes with a summary in Section 2.6.
Traffic Signal Control Systems
Introduction to Traffic Signal Control Systems
Transportation is an essential component of society, facilitating connections between regions and enabling seamless movement for individuals Innovations in transportation have transformed societal organization and dynamics.
Transportation significantly impacts civilization development, with a rapid population increase leading to a surge in registered vehicles The complexity of transport dynamics is rising, involving various drivers, pedestrians, bicyclists, and road infrastructure Urban traffic demand often surpasses transport capacity, necessitating the construction of new infrastructure or upgrades to existing roads However, space constraints in major cities hinder expansion, resulting in widespread traffic congestion that adversely affects both societal and economic aspects of regions A report by CE Delft highlights that the external costs of road traffic, including congestion, noise, and air pollution, account for 1 to 2% of GDP in the European Union.
The transportation system is currently facing significant challenges, including the need to reduce travel time, minimize delays, enhance passenger safety, and lower traffic exhaust emissions To address these issues, Intelligent Transportation Systems (ITSs) have been developed in various cities globally Over the past decade, these systems have significantly improved transportation conditions, increased road network capacity, and reduced traffic congestion and emissions in urban areas.
Traffic Signal Control (TSC) Systems are essential Intelligent Transportation Systems (ITS) used globally to manage traffic flow at intersections, ensuring safe and efficient movement for vehicles, pedestrians, and bicyclists These systems regulate conflicting traffic movements, determining which streams can proceed and which must stop, ultimately aiming to reduce congestion and emissions Inefficient operation at intersections is a major contributor to traffic delays, with studies indicating that 50-80% of traffic issues occur in these areas, consuming a significant portion of travel and waiting time Therefore, effective TSC systems are crucial for enhancing the overall performance of transportation networks, with most control strategies focused on increasing traffic flow and minimizing delays to prevent congestion.
Fundamental Definitions of Traffic Signal Control Systems
A traffic signal control system is essential for managing vehicle and pedestrian movements at intersections and crossings In the UK and many other countries, this system typically features three lights: red for stopping, green for proceeding safely through the intersection, and an amber warning light indicating an impending red A green arrow allows for protected turns, while simultaneous red and amber lights signal that vehicles must stop completely For pedestrians, the system includes a red light for stopping and a green light for crossing the road safely.
The Traffic Signal Controller (TSC) at an intersection manages traffic signal timing to ensure the safe passage of vehicles, cyclists, pedestrians, and other road users This involves determining the sequence of movements and assigning green light duration to each group at a signalized intersection, while also considering the needs of pedestrians and cyclists in the design process An example of movements in a two-phase signal system at a four-legged intersection is illustrated in Figure 2.1, with a corresponding signal timing diagram shown in Figure 2.2 Key definitions related to signal timing are outlined by Kittelson & Associates.
(a) Phase 1 (b) Phase 2 Figure 2.1: Movements in a two-phase system.
Figure 2.2: A diagram of two-phase signal system (C is signal cycle length, x1 and x2 are green durations of phase one and phase two, L1 and L2 are inter-green durations).
A signal cycle is a complete sequence of all traffic movements at an intersection.
A signal cycle length refers to the total duration needed to complete one full signal cycle, which is calculated by adding together the green times of each stage, the yellow change intervals, and the all-red clearance intervals.
A phase is a portion of a signal cycle assigned to one set of movements and it is defined as the green, yellow or all-red clearance intervals.
Offset is the difference between two green initiation times for two successive in- tersections Offset helps vehicles moving through successive intersections without being stopped.
Green splits are a portion of total available green time in the cycle allocated to each phase at an intersection.
Inter-green time includes the yellow indication and, if applicable, the all-red indication within a single traffic signal cycle This period is essential for transitioning between traffic states to prevent collisions between different traffic movements.
Effective traffic signal timing offers several advantages, including enhancing safety by allowing vehicles to navigate intersections securely, increasing the capacity of signalized intersections to accommodate more vehicles, reducing congestion and delays, and ensuring that pedestrians and side street traffic can cross the intersection with adequate accessibility.
Overview of Traffic Signal Control Systems
Traffic control plays a crucial role in managing traffic flow, alleviating congestion, and minimizing emissions The advancement of traffic control relies heavily on information and computer technology (Wang et al., 2018) Recent developments in traffic management techniques have led to more flexible control strategies (Chow, 2010).
Numerous traffic signal control systems have been proposed and developed, yet less than 50% have been implemented in real-world scenarios (Board et al., 2010) Signal control strategies for signalized intersections can be categorized into distinct classifications (Wang et al., 2018).
Fixed-time signal control methods utilize predetermined traffic signal parameters, including operation sequences, splits, and offsets, making them ideal for consistent and stable traffic patterns These pre-timed strategies are developed offline through optimization techniques that analyze historical traffic data.
Traffic-responsive signal control methods utilize real-time data to adjust signal timing according to current traffic conditions This data is gathered from sensors and inductive loops installed along roadways By dynamically modifying traffic signal parameters based on recent conditions, real-time traffic signal control (TSC) offers an effective solution for managing complex and unpredictable urban traffic networks.
Signal control strategies can be classified by the number of intersections involved as shown as follows:
Isolated strategies focus on optimizing signal settings for individual intersections without taking into account nearby intersections or their signal timings As a result, these strategies do not significantly influence the performance of neighboring intersections, leading to configurations that are tailored solely for each specific intersection.
Coordinated traffic strategies optimize the flow of vehicles through multiple adjacent intersections, ensuring that cars can pass through successive signals without stopping at red lights This system is designed so that the green light at one junction begins after a calculated delay, corresponding to the time it takes for vehicles to travel between intersections under ideal, congestion-free conditions.
Traffic signal control relies on advancements in modern control theory, artificial intelligence, traffic information technology, and traffic engineering The rapid evolution of AI methods, such as agents, neural networks, fuzzy logic, and collective intelligence, significantly influences traffic control strategies (Papageorgiou et al., 2003).
TRANSYT is a prominent fixed-time coordinated traffic signal control system that utilizes a traffic model and initial signal settings, including splits, cycle length, offsets, and green duration for each signal stage It generates fixed-time signal plans for various times of the day, employing an optimization model to produce performance metrics based on input decision variables The system employs a hill-climbing algorithm to identify optimal solutions In contrast, the Split Cycle and Offset Optimization Technique (SCOOT) serves as the traffic-responsive variant of TRANSYT, focusing on minimizing average queues in the area Unlike TRANSYT, SCOOT gathers real-time data from vehicle detectors and continuously adjusts parameters through gradient optimization to assess the impact of changes in cycle length, offsets, and splits SCOOT has been successfully implemented in numerous cities across the UK and internationally.
The Area Traffic Control Centre in Leicester, Leicestershire, and Rutland utilizes an intelligent transport system to manage daily traffic effectively This system oversees more than 800 traffic signal sets, adjusting their timings to enhance traffic flow Key data sources for the system include SCOOT and traffic cameras, ensuring optimal traffic management (Council, 2019).
Performance Measures of Traffic Signal Control Systems
Traffic signal control systems are assessed using various measures that focus on drivers' experiences at signalized intersections The primary indicators for evaluation include delay and queue length, which are crucial for understanding traffic flow and efficiency.
Delay is a crucial metric for evaluating the effectiveness of signalized intersections, as it directly impacts lost travel time, fuel consumption, and passenger comfort It is defined as the additional time a vehicle spends at an intersection compared to the time required for uninterrupted passage Total delay is categorized into three types: acceleration delay, deceleration delay, and stopped time delay Deceleration delay occurs when a vehicle slows down and stops due to a red signal or a queue at the start of the green phase Stopped delay refers to the duration a vehicle remains stationary in a queue, measured from the moment it stops until it begins to move again Acceleration delay starts when the vehicle accelerates at the onset of the green phase and concludes when it reaches normal travel speed without obstruction.
Accurate delay prediction is crucial yet complex due to the irregular arrival rates of vehicles Delay can be estimated through real traffic measurements, simulations, and analytical models, with the latter being popular for their simplicity in assessing delay at signalized intersections Various delay models, such as the HCM 2000 and Webster's delay model, have been developed to estimate the average delay experienced by vehicles However, these models rely on certain assumptions, including the premise that vehicles arrive at traffic lights following a Poisson process, which helps to simplify complex flow conditions into a quantifiable framework for delay approximation.
Delay calculations derived from theoretical models may lack accuracy, as these models do not fully account for the dynamic nature of actual traffic According to Mathew (2014) and Chen and Chang (2014), the characteristics of real-world traffic cannot be effectively represented by mathematical formulations.
Queue length serves as a vital metric for deciding whether to halt vehicle discharges from upstream intersections (Mathew, 2014) Numerous studies have focused on estimating average queue lengths at traffic signals, with methodologies generally categorized into two types (Liu et al., 2009) The first type relies on cumulative traffic input-output models, applicable only when the queue length is less than the distance between the intersection stop line and the road detector (Sharma et al., 2007; Webster, 1958) Conversely, the second type utilizes traffic shockwave behavior to analyze queuing processes (Ban et al., 2011; Liu et al., 2009; Stephanopoulos et al., 1979) Although shockwave theory effectively describes complex queuing dynamics, it assumes a known vehicle arrival rate, which may not hold true in congested scenarios.
In addition to traditional performance metrics, traffic signal control systems can be evaluated based on exhaust emissions, safety, and pedestrian level of service Recent research highlights the growing concern over vehicle-related air pollution among researchers and policymakers According to Tong et al (2000), transient driving modes, such as acceleration and deceleration, generate higher emissions compared to steady-speed driving modes.
Air pollution is notably more severe at signalized intersections, leading to vehicle emissions being a key factor in evaluating the effects of proposed traffic signal control systems Traffic safety at these intersections plays a crucial role in enhancing road safety in urban areas Various strategies and tools for safety assessment in urban traffic networks have been developed, as noted by HSM (2010) and Pirdavani et al (2010) The pedestrian level of service at a signalized intersection indicates how well it accommodates pedestrians, directly affecting their delay experience, safety, and comfort when crossing This measure is essential for understanding the pedestrian-friendliness of signalized intersections, with a comprehensive review available in Kadali and Vedagiri (2016).
Traffic simulation
Introduction
The rapid growth of Intelligent Transportation Systems (ITS) applications has led to a rising demand for tools that aid in the design and evaluation of proposed strategies Traffic simulators have emerged as cost-effective solutions to meet these needs, playing a crucial role in traffic research for several reasons.
Testing and evaluating traffic strategies in real-world networks can be costly and challenging, particularly when establishing expected traffic parameters for experimental setups Traffic simulators serve as an effective tool, enabling researchers to assess the validity and efficiency of proposed strategies prior to implementation, significantly reducing construction costs Additionally, these simulators allow for the comparison of various alternative strategies and improvement plans, making them a widely utilized method in the modeling, planning, and development of traffic networks and systems (Kotusevski and Hawick, 2009).
Traffic simulation software, including SUMO, VISSIM, MATSim, AIMSUN, and Paramics, can be categorized into three types based on their level of detail: microscopic, mesoscopic, and macroscopic simulators Macroscopic simulators analyze traffic at a high level of aggregation, focusing on overall traffic flow without detailing individual vehicles, making them suitable for traffic flow analysis In contrast, microscopic traffic models capture the dynamics of each vehicle for more granular simulations.
Figure 2.3: The structure of the node file of a traffic scenario simulated by SUMO,
Figure 2.4: The structure of the edge file of a traffic scenario simulated by SUMO,
Figure 2.5: The structure of the traffic light file of a traffic scenario simulated by
Krajzewicz et al (2019) explore the interactions between vehicles and their surrounding environment, highlighting the significance of understanding these dynamics Mesoscopic traffic models offer an intermediate level of detail by focusing on individual vehicles without delving into their interactions In contrast, microscopic traffic simulations have emerged as valuable tools for assessing the deployment of Intelligent Transportation Systems (ITS), as noted by B D Venter and Barcelo.
(2001) Comparative studies of traffic simulators can be found atPell et al (2017) andMustapha et al (2016).
Figure 2.6: The Netconvert command to generate a traffic network file of a scenario simulated by SUMO, Krajzewicz et al.(2019).
Figure 2.7: The structure of the route file of a traffic scenario simulated by SUMO,
Simulation of Urban Mobility (SUMO)
Simulation of Urban Mobility (SUMO) is a widely recognized microscopic traffic simulator, developed primarily by the Institute of Transportation Systems at the German Aerospace Centre since 2000 This open-source and highly portable tool is designed to accommodate large road networks, making it an invaluable resource for the traffic research community to implement and evaluate their studies SUMO's multi-modal capabilities allow for the simulation of not only car movements but also public transport systems, including bus and train networks, and its high portability enables use across various operating systems.
To construct a traffic simulation using SUMO, two key components are essential: road network representation and traffic demand The road networks are modeled as directed graphs in XML files, where intersections and roads are represented by nodes and edges, respectively Nodes are detailed in a node file, while edges include attributes such as position, shape, and speed limits, as illustrated in accompanying figures Additionally, a SUMO network can incorporate traffic lights, roundabouts, and other transportation elements, with an example of a traffic light file also provided.
Figure 2.8: The structure of the configuration file of a traffic scenario simulated by
All the information about road network are described in the net.xml file SUMO road networks can be either generated from XML files or converted from other input data.
Netconvert is a tool designed for importing road networks from various traffic simulators like Vissim, MATSim, and VISUM, enabling the creation of compatible road networks for use in SUMO, as noted by Krajzewicz et al (2019) Additionally, SUMO supports other formats, including OpenStreetMap Users can modify existing road network files with the NETEDIT tool, as highlighted by Krajzewicz et al (2019).
In SUMO scenarios, traffic demand is a crucial element that defines vehicle routes, as illustrated in Figure 2.7 Routes can be generated by converting existing origin/destination (O/D) matrices into route descriptions or by manual specification The former method is commonly used in traffic science for large-scale real-world scenarios, while the latter allows researchers to customize traffic movements according to their preferences (Krajzewicz et al., 2012) Additionally, SUMO can import routes from other simulations, and supplementary information, such as traffic light timing data, can be incorporated into the traffic simulation through additional files.
Once the network and route files are created, a configuration file is generated to integrate all components, allowing the simulation scenario to be visualized in the SUMO-GUI The structure of this configuration file for a traffic scenario simulated by SUMO is illustrated in Figure 2.8.
SUMO generates extensive measurements for each simulation run, offering both unaggregated vehicle-based data like positions and speeds at every step, as well as aggregated journey information Additionally, it provides insights into simulated detectors, traffic lights, and lane or edge values Beyond standard traffic metrics, SUMO also includes critical environmental measures such as noise and pollutant emissions, along with fuel consumption statistics (Behrisch et al., 2011).
Multi-objective evolutionary algorithms
Definition of Multi-objective Optimization Problems and Basic
Optimization involves maximizing or minimizing functions to identify feasible solutions that align with optimal values for one or more objectives It can be categorized into single-objective optimization, which focuses on one objective function, and multi-objective optimization problems (MOOPs), which involve multiple objective functions The primary aim of single-objective optimization is to determine the best solution that achieves either the minimum or maximum value, depending on the objective In contrast, MOOPs often yield multiple optimal solutions, complicating the decision-making process as one must select the best option based on higher-level criteria Typically, real-world optimization challenges feature conflicting objectives, constraints, and numerous Pareto solutions, with the goal of identifying trade-off solutions that deliver satisfactory performance across all objectives.
MOOPs have a number of objectives needed to be either minimized or maximized si- multaneously while satisfying the constraints Deb (2008) states the overall form of a MOOP as follows:
In an optimization problem with J equality constraints and K inequality constraints, there are M objective functions that can be continuous or discrete, as well as linear or non-linear The decision vector x consists of n decision variables x(i), where i ranges from 1 to n, each bounded by lower limits x(i)L and upper limits x(i)U These decision variables can also be either continuous or discrete A feasible solution is defined as one that meets all the specified constraints and adheres to the variable bounds.
Here are the fundamental concepts in MOOPs, which are defined as follows,Deb(2008):
Decision variable space or decision space of a problem is its feasible space with all possible numerical amount that can be allocated to decision variablesx i of MOOPs.
Objective space is the space including all possible values produced by the objective functions of a MOOP.
In multi-objective optimization problems (MOOPs), the concept of domination is essential for comparing solutions A solution \( x(u) \) is said to dominate another solution \( x(v) \) if it is strictly better in at least one objective while being equal to or better in all other objectives This relationship can be mathematically expressed as \( x(u) \prec x(v) \) if and only if \( x(u)_i \leq x(v)_i \) for all objectives \( i \) and there exists at least one objective \( i \) where \( x(u)_i < x(v)_i \).
Strong dominance: x (u) strongly dominatesx (v) (orx (u) ≺x (v) ) ifx (u) is strictly better thanx (v) in all objectives. x (u) ≺x (v) if and only if ∀i∈[1, n] :x (u) i < x (v) i (2.3)
Weak dominance: x (u) weakly dominates x (v) if x (u) is better or equal to x (v) in all objectives.
Non-dominated set: the non-dominated set Q 0 of a given set of solutions Q is a set including solutions that are not dominated by any solution in Q.
Pareto optimal solution: in the decision spaceX, a solutionx (i) is named Pareto optimal if and only if there exists no solutionx (j) thatx (j) dominates x (i)
The Pareto-optimal set, denoted as P0, refers to the collection of non-dominated solutions within the feasible search space P of a multi-objective optimization problem (MOOP) f(x) This set, Q0, represents solutions where no objective can be improved without sacrificing another, highlighting the trade-offs between competing objectives.
The Pareto front, denoted as PF₀, represents the objective vectors associated with the Pareto-optimal set in a multi-objective optimization problem (MOOP) This front illustrates the trade-offs between competing objectives, highlighting the optimal solutions that cannot be improved in one objective without worsening another.
In Multi-Objective Optimization Problems (MOOPs), the objective is to identify a set of solutions that closely approximates the Pareto-optimal set Many real-world challenges make it difficult for decision-makers to fully and accurately define these problems Additionally, finding all efficient solutions within a reasonable timeframe is often unfeasible As a result, decision-makers frequently resort to using approximated solutions in these scenarios (Sanghamitra Bandyopadhyay, 2013).
General Framework of Multi-objective Evolutionary Algorithms
Multi-objective Evolutionary Algorithms (MOEAs) replicate natural evolutionary processes such as reproduction, mutation, recombination, and selection to identify multiple acceptable solutions These algorithms have been effectively applied to Multi-Objective Optimization Problems (MOOPs) for over a decade, as noted by Zitzler et al (2004) A key distinction between traditional search methods and MOEAs is that the latter employs a population of potential solutions during each iteration, rather than focusing on a single solution This population undergoes transformation through selection, which reflects natural competition for reproduction, and variation, which simulates the changes that occur in nature.
Algorithm 1 Principal steps of a MOEA framework
2: Whiletermination conditions are not satisfied
6: Step 4: Check the termination conditions
7: ReturnNon-dominated set of solutions the natural ability to create “new” living beings using recombination and mutation Al- though their working mechanisms are simple, MOEAs are proven to be robust, general, and powerful search approaches.
Multi-Objective Evolutionary Algorithms (MOEAs) utilize the principle of survival of the fittest to enhance solution quality over generations Initially, a random population of solutions, known as individuals, is created Through iterative processes, MOEAs focus on improving these solutions and guiding them towards the Pareto front Each iteration, termed a generation, continues until a pre-defined maximum number of iterations is reached, serving as the termination condition The fundamental steps of the MOEA framework are detailed in Algorithm 1 and further elaborated in subsequent sections (Cheshmehgaz et al., 2015).
Mating selection in multi-objective evolutionary algorithms (MOEAs) involves two key stages: fitness assignment and sampling During the fitness assignment stage, solutions within the population are evaluated based on their objective functions and constraints, resulting in a fitness value that allows for comparison among solutions Fitness assignment strategies are typically categorized into Pareto-based, criterion-based, and aggregation-based methods (Konak et al., 2006) Following this, the sampling stage creates a mating pool using various mate-selection strategies Common methods include roulette wheel selection, which selects individuals based on their fitness proportionally, and binary tournament selection, where pairs of solutions are compared to choose the better one for the mating pool The roulette wheel method utilizes a spinning mechanism where the fittest solutions occupy larger segments, while binary tournament selection involves repeated random pairings until the mating pool is filled.
Recombination and mutation operators are essential in generating offspring within the mating pool The recombination operator merges segments from parent pairs to produce a specified number of children, guided by a crossover probability In contrast, the mutation operator alters one or more variables in a solution according to a set mutation rate, which helps maintain population diversity across generations As noted by Deb (2008), mutation is crucial for avoiding local minima by ensuring that solutions within the population remain distinct from one another.
Once offspring generation is complete, environmental selection determines which solutions from the population and the newly created offspring will contribute to the next generation's population Following this, termination conditions are evaluated, and if met, the process concludes If not, the cycle continues with the newly formed population.
Jones et al (2002) found that 90% of multi-objective optimization methods aim to approximate the optimal Pareto front, with 70% of meta-heuristic approaches relying on evolutionary techniques For in-depth reviews of Multi-Objective Evolutionary Algorithms (MOEAs), refer to the works of Zhou et al (2011) and Cheshmehgaz et al (2015).
Multi-Objective Evolutionary Algorithms (MOEAs) aim to achieve two primary objectives: to identify solutions that closely approximate the Pareto-optimal front and to ensure a diverse set of solutions The first objective, convergence speed, is influenced by mating selection strategies and fitness assignment methods, while the second objective focuses on maintaining diversity among non-dominated solutions through effective selection schemes A high density of individuals around a specific solution can reduce its selection probability Additionally, the elitism mechanism, which preserves the best solutions while generating new offspring, may inadvertently hinder population diversity in MOEAs.
Surrogate-assisted evolutionary algorithms
Strategies for managing surrogates
2.5.2.1 Model management: its roles and classification
Achieving high accuracy in approximations is challenging due to limited input data Jin (2005) highlights that relying solely on surrogate models for fitness value estimation can lead to convergence at a false optimum Therefore, it is crucial to integrate the approximation model with the actual objective function, which, while often costly to compute, is typically accessible Effective use of the original fitness function can help reduce computational costs, a process referred to as model management or evolution control Jin (2005) categorizes model management into three primary groups.
(1) No evolution control: the surrogate is assumed to be highly accurate and it com- pletely replaces the original objective function in the evolutionary computation.
Fixed evolution control involves a predetermined number of solutions, where their fitness values are assessed through an approximate model, while the remaining solutions are evaluated using the original objective function This control mechanism comprises three distinct approaches.
A Individual-based: in each generation, some of the individuals are evaluated by the real objective function and the others use the surrogate for fitness calculation.
B Generation-based: fitness values of solutions in some generations are estimated by surrogates while in the other iterations, the original fitness function is used.
C Population-based: there are more than one sub-population taking part in the evolution process Each sub-population use its own surrogates to approximate fitness values.
Adaptive evolution control involves managing the frequency of an approximation model's use based on its accuracy, allowing for flexibility during the optimization process The higher the fidelity of the surrogate model, the more often it is employed to assess the fitness value of potential solutions.
2.5.2.2 Criteria for choosing individuals for re-evaluation
When utilizing surrogates in optimization, it's crucial to determine which solutions should be estimated and which should be re-evaluated with the original objective function This decision is closely linked to how many solutions will undergo this re-evaluation, aiming to minimize fitness evaluations while maintaining optimization accuracy Proper selection of individuals for evaluation with the original fitness function enhances the surrogate's ability to learn the input-output relationships, leading to a quicker reduction in approximation error and a faster optimization process Various strategies exist for selecting individuals for re-evaluation, ensuring efficient and effective optimization.
Random strategy: individuals are selected randomly to be evaluated by original objective function Fonseca et al.(2012).
To effectively select solutions for re-evaluation, focus on those that are likely to yield a high fitness value According to L Graening (2005), utilizing a more precise approximation model allows for a greater number of individuals to be assessed using surrogate methods.
Uncertain strategy: choose individuals, which have large degrees of uncertainty in approximation, to be evaluated using original fitness functions, Branke and Schmidt
In the context of uncertain solutions, two key reasons for their re-evaluation are highlighted Firstly, a significant level of uncertainty in fitness value approximation indicates that the surrounding objective space has not been sufficiently modeled, presenting a valuable opportunity to discover improved solutions Secondly, re-assessing the most uncertain individuals can enhance the accuracy of the adaptive surrogate's approximations.
In the representative strategy, solutions are organized into distinct clusters, with representative solutions identified for evaluation These representatives may include the solution closest to the cluster center or the optimal solution within each cluster, as noted by L Graening (2005) The selected representatives are then assessed using the original objective function to determine their effectiveness.
Techniques for constructing surrogates
To create an effective surrogate model, a sufficient number of samples must be collected, as the accuracy of the approximation is influenced by both the quantity of samples in the search space and the choice of the appropriate approximation model Various models can be employed for this purpose, including polynomial approaches, commonly referred to as Response Surface Methodology, as well as Support Vector Machines.
(2016),Rosales-Perez et al.(2015), Kriging modelLiu et al.(2014),Pan and Das(2015), Zhou et al.(2007), and Artificial Neural NetworksBhattacharjee et al.(2016),Jin et al.
(2015), Sun et al (2013) An overview of techniques used for constructing surrogates in multi-objective evolutionary optimization can be found in Santana-Quintero et al.
Numerous studies, including those by Diaz-Manriquez et al (2016) and Jin et al (2001), have explored the effectiveness of various approximation models, yet no definitive superior model has emerged When selecting an approximation model, it is crucial to consider multiple factors such as accuracy, efficiency, computational cost, and complexity While specific guidelines for model selection are challenging to establish, it is advisable to start with a simple meta-model If the results are unsatisfactory, a more complex model may be warranted In cases where sample sizes are limited and the design space is highly dimensional, utilizing a neural network model is recommended (Jin, 2005) In transportation optimization problems, where traffic simulators evaluate candidate solutions, the number of samples for constructing surrogate models is often kept small due to the time-intensive nature of simulations, making artificial neural networks a promising option for building approximation models.
Artificial Neural Networks
Artificial Neural Networks (ANNs) effectively learn the relationship between inputs and outputs, making them valuable for function approximation In particular, multilayer feed-forward perceptron networks have been extensively utilized for various approximation challenges.
A Multilayer feed-forward perceptrons (MLPs) are a class of multilayered feed-forward artificial neural network There are at least three layers of nodes in an MLP which are one input layer, one output layer, and one or more hidden layers Each connection between nodes has a weight, which is randomly initialized at the beginning and is adapted during the training process Each neuron takes the weighted sum of signals coming from the previous layer There are several critical points needed to be determined when building an ANN: the structure of the ANN including the number of layers and the number of nodes in each of these layers, the selection of input and output, and the training algorithm,Santana-Quintero et al (2010) The output of a neuron is: y=f( m
The equation y = Σ (wi * xi) + b represents the output of a neuron, where xi denotes the i-th input and wi signifies the weight of the connection between that input and the neuron A crucial component of this model is the activation function f, which is nonlinear; among the various activation functions, the sigmoid function is one of the most widely utilized.
B Overfitting and underfitting are common problems in machine learning, which can lead to an inefficient performance of approximation models Overfitting happens when the model learns the noise instead of the signal, which is the actual pattern expected to learn by the model from the samples Consequently, the approximation model will work unusually well on the training data but very poorly on unseen samples In contrast, an underfitting model refers to a model which can not model the training data as well as generalize the unseen data To limit overfitting and underfitting, a resampling technique is recommended to estimate model accuracy The most popular resampling technique is k-fold cross validation It is commonly applied in machine learning as it is easy to implement, and its results generally have lower bias than other methods,Rodriguez et al. (2010).
C Bias and Variance are sources of prediction errors for any machine learning algo- rithms Bias, which are assumptions made by a model, is used to simplify the target function and make it easier to learn Low bias means fewer assumptions and high bias means more assumptions about the form of the target function High bias can lead to the missing the relevant relations between the inputs and the outputs, which causes underfitting phenomenon Bias error is an error caused by erroneous assumptions On the other hand, variance is the amount of difference between the outputs of the ap- proximation model using different training data sets Variance suggests the degree of dependence of the approximation model to the training data sets If the variance is low, the estimate of the model does not change significantly when using different training dataset High variance means the estimation result is sensitive to the change of training data Ideally, the variance should not be high, meaning that the approximation model can learn the hidden underlying relationship between the inputs and the corresponding outputs The objective of supervised learning algorithms is to obtain low variance and low bias However, there is a trade-off between these two concerns as decreasing bias will increase the variance and vice versa, Geman et al.(1992).
D Fine-tunning hyperparameters: one of the difficulties when working with neural net- works is selecting an optimal architecture for a specific problem Hyperparameters are parameters which determine the overall architecture of a neural network and they are usually determined before starting the training process Some examples of hyperparam- eters are number of hidden layers, the learning rate, and the number of neurons in each hidden layer.
Hyperparameter optimization aims to identify the best set of hyperparameters for learning algorithms, with grid search being a commonly used technique This method involves an exhaustive search that evaluates all possible combinations of hyperparameters, making it simple and straightforward to implement (Pontes et al., 2016) While grid search may require more computational time compared to other techniques, its ability to be easily parallelized—since each combination is independent—makes it one of the most popular methods for hyperparameter optimization (Pontes et al., 2016; Zhang et al., 2009).
Tamura and Tateishi (1997) demonstrated that a feed-forward neural network with two hidden layers outperforms one with a single hidden layer in learning training data patterns Additionally, Heaton (2008) noted that a two-hidden-layer neural network can approximate any non-linear function effectively, eliminating the need for more layers The size of the hidden layers is crucial for determining the neural network's architecture; too few neurons may result in under-fitting, while too many can cause over-fitting Sheela and Deepa (2013) provide a survey of methods for defining the optimal number of hidden neurons in a neural network.
Surrogate-assisted evolutionary algorithms are effective for optimizing costly problems by utilizing surrogate models to reduce the fitness evaluation cost of candidate solutions This approach is particularly beneficial for traffic signal optimization A multilayer feedforward neural network serves as an efficient approximation model to predict the fitness values during the evolutionary process To ensure optimal performance and prevent overfitting or underfitting, the hyperparameters of the neural network are fine-tuned using grid search and k-fold cross-validation techniques, as highlighted by Fushiki (2011) and Rodriguez et al (2010).
Conclusion
Traffic light control systems are crucial for urban traffic management, significantly influencing the safety of road users and the efficiency of traffic operations Optimizing their performance is a primary objective in designing effective traffic signal control systems Chapter 1 outlines several hypotheses regarding traffic signal optimization and emphasizes the need for foundational knowledge about key components This chapter also offers an overview of traffic signal control systems, traffic simulators, and computational intelligence techniques—such as multi-objective evolutionary algorithms and surrogate-assisted evolutionary algorithms—used to enhance traffic signal performance.
Multi-objective Traffic Signal Optimization
Introduction
Traffic signal control plays a vital role in urban traffic management, directly impacting the efficiency of the overall traffic system Recent advancements in optimization techniques have been applied to traffic control models to enhance the performance of signal systems The primary goal of traffic signal optimization is to improve intersection performance by reducing delays, queue lengths, and the number of stops, while also minimizing emissions and maximizing traffic flow and average speeds Effective traffic signal timing in a controlled street network requires determining cycle times, green time splits, and offsets, with optimization potentially targeting one or all of these variables based on observed traffic parameters like flow and queue length Traffic signal optimization models can involve single or multiple objectives to achieve optimal results.
Multi-Objective Evolutionary Algorithms (MOEAs) are more efficient and robust than traditional search methods like random search and hill-climbing, making them a popular choice for tackling multi-objective optimization problems (Guangwei et al., 2007) Their effectiveness has led to widespread application in traffic signal optimization, with notable implementations including the Non-dominated Sorting Algorithm II (Nguyen et al., 2016; Shen et al., 2013; Yan et al., 2013) and Genetic Algorithms (Abushehab et al.).
(2014),Ben et al.(2010),Chen and Chang(2014),Tung et al.(2014), and Particle Swarm Optimization, Abushehab et al.(2014),Dong et al.(2010), Kai et al.(2014).
The primary goal of local search methods is to identify a local optimum by making iterative adjustments from an initial solution within its neighborhood, thereby enhancing the quality of solutions based on objective values until a local optimum is achieved (Mladenovic and Hansen, 1997) Numerous studies have applied local search-based Multi-Objective Evolutionary Algorithms (MOEAs) to optimize urban traffic signal control problems (Gao et al., 2016; Sabar et al., 2017).
Traffic Signal Optimization using MOEAs
Recent studies have increasingly focused on utilizing computational intelligence technologies to enhance traffic light signal control systems Research by Zhao et al (2012) and Araghi et al (2015) provides a comprehensive review of these methods Multi-Objective Evolutionary Algorithms (MOEAs) are recognized as effective optimization techniques in traffic signal optimization A summary of various studies and the evolutionary algorithms employed for optimization is presented in Table 3.1 Notably, the Non-dominated Sorting Algorithm II (NSGA-II) and the Genetic Algorithm (GA) emerge as the two most widely used algorithms in this domain.
In a study by Zhou et al (2008), a bi-level optimization model utilizing Genetic Algorithms (GA) was developed to enhance traffic quality and minimize emissions at intersections Following this, Qun (2009) introduced a signal control model for urban intersections also based on GA Additionally, Ben et al (2010) contributed further advancements in this area.
Genetic Algorithms (GA) can simultaneously optimize multiple objectives by aggregating them into a single objective function, calculated as the sum of various goals Each objective's significance is represented by a weighting factor, which indicates its importance in the overall optimization process For instance, Chin et al (2011) developed a traffic signal timing management system for coordinated intersections utilizing GA, showcasing its practical application in complex scenarios.
In 2014, a novel traffic light signal optimization method was developed for managing heavy mixed traffic flows on arterial roads, utilizing a genetic algorithm (GA) and a gauzy branch-and-bound technique This approach takes into account both link length and vehicle size, effectively addressing traffic evolution and queue formation to prevent queue spill-back.
Table 3.1: Evolutionary algorithms in traffic signal control systems.
Guangwei et al (2007),Zhou et al (2008), Qun
(2009),Ben et al.(2010),Shen et al (2011), Chin et al (2011),Passow et al (2012), Abushehab et al (2014),Chen and Chang
Sun et al.(2003), Feng and Xiaoguang(2008), Yan et al.(2013), Shen et al.(2013), Nguyen et al (2016), Armas et al.(2017),Mihaita et al.
Chen and Xu (2006),Dong et al.(2010), Kai et al (2014),Abushehab et al (2014)
4 Differential Algorithm Zhang et al (2009),Kai et al (2014)
5 Memetic Algorithm Sabar et al.(2017)
6 Harmony Search Gao et al.(2016)
Research demonstrates the effectiveness of the NSGA-II algorithm in optimizing traffic signal timing, showcasing its ability to achieve a well-distributed and rapidly converging optimal set (Sun et al., 2003) Feng and Xiaoguang (2008) enhanced urban intersection traffic signal control by integrating NSGA-II with a cell transmission model, outperforming traditional algorithms like Webster, Synchro, and TRANSYT by achieving lower mean delays Furthermore, Yan et al (2013) applied NSGA-II to manage traffic flow at isolated intersections under over-saturated conditions Additionally, Nguyen et al (2016) introduced a hybrid approach combining NSGA-II with local search techniques to enhance the anytime behavior of traffic signal optimization systems.
The Particle Swarm Algorithm (PSO) is a population-based stochastic optimization technique inspired by the social behaviors of fish and birds, sharing similarities with genetic algorithms PSO stands out among multi-objective evolutionary algorithms (MOEAs) due to its fewer adjustable parameters and ease of implementation Its effectiveness has been demonstrated across various research domains, particularly in optimizing traffic light signal timings Notably, Chen and Xu (2006) enhanced PSO by integrating fuzzy logic to address varying traffic demands, while Dong et al (2010) combined PSO with the Simulated Annealing algorithm for multi-objective optimization Additionally, Kai et al (2014) introduced a collaborative strategy that merges PSO with the Differential Algorithm, yielding superior results in reducing average delay times compared to traditional PSO methods.
The Differential Algorithm (DE), a multi-objective evolutionary algorithm (MOEA), has been effectively utilized for optimizing traffic signal control systems In a study by Zhang et al (2009), a real-time traffic flow control system was developed using a multi-objective discrete differential evolution algorithm, which demonstrated superior performance based on the experimental outcomes.
In Armas et al (2017), an optimization framework was developed for a large-scale traffic network, employing an evolutionary algorithm combined with clustering techniques The study introduced specialized mutation operators to identify coordinated signals with similar cycle lengths Additionally, varying mutation rates were applied to enhance the convergence speed of the evolutionary search process.
Mihaita et al (2018) proposed a multi-objective optimization method utilizing evolutionary algorithms to enhance urban intersections, specifically focusing on a reconstruction project in Nancy This approach includes an integrated framework that combines the optimization technique with a 3D mesoscopic traffic simulator, allowing for a comprehensive analysis of traffic flow and intersection efficiency.
NSGA-II is a highly effective multi-objective evolutionary algorithm, as demonstrated by Sun et al (2003), which highlights its superior performance compared to other algorithms in this category This exceptional capability is a key factor in its selection as the optimization algorithm in various research studies.
Multi-objective Traffic Signal Optimization using Local Search
Population-based computational intelligence algorithms, like NSGA-II and GA, outperform traditional methods but often face slow convergence, making them less suitable for real-time applications To tackle this challenge, Sabar et al (2017) developed an adaptive memetic algorithm for optimizing traffic signals, incorporating a local search to effectively navigate the solution space This algorithm uses GA to direct the search towards the Pareto-optimal front while the local search enhances the convergence rate, leading to higher quality solutions The local search operates on the principles of the simple descent method, continuously seeking improvements until specific termination criteria are met By systematically modifying the current solution with a neighbourhood operator, the algorithm replaces inferior solutions with better ones, ultimately demonstrating superiority over both GA and fixed-time signal control methods in experimental results.
In Gao et al (2016), a novel approach was introduced that combines three local search operators, each with distinct structures, to enhance the performance of the discrete harmony search (DHS) algorithm for urban traffic signal optimization These operators are categorized based on their focus: the first targets individual intersections, the second addresses coordinated intersections, and the third operates within a sub-region of the entire traffic network By integrating these operators into a local search strategy, the algorithm effectively identifies neighboring solutions, significantly improving the DHS's performance Comparative analysis shows that the local search-enhanced DHS outperforms the standard DHS in tackling urban traffic signal challenges.
Gao et al (2017) introduced a meta-heuristic algorithm that combines local-search operators to effectively minimize delays for both pedestrians and vehicles This approach employs the artificial bee colony algorithm to tackle the traffic light signal optimization problem The algorithm was evaluated using eight real-life database cases, demonstrating superior performance compared to NSGA-II in optimizing traffic signals.
In summary, integrating a local search with a global evolutionary algorithm can enhance the convergence speed of the search process Research by Espinoza et al (2003) indicates that local search techniques can also decrease the population size needed for optimization algorithms Consequently, combining an evolutionary algorithm with targeted local search strategies can significantly boost the efficiency of traffic signal optimization systems.