TRABAJOS FUTUROS

To the best of our knowledge, traffic signal optimization using surrogate models is not common in the literature of current signal control approaches and there are few studies consider using surrogate in optimizing the traffic signal timing. Osorio and Bierlaire

(2009) introduces an approximate queuing network model to optimize congested urban road network networks. This study focuses on fixed-time signal control for coordinated intersections. The interaction between flows on upstream and downstream roads is taken into account. Roads are mapped into sets of queues and finite capacity queueing theory is utilized to capture the interaction between consecutive roads. A set of nonlinear equations is formulated to describe the correlation between decision variables, exogenous parameters, for example, the route choice decisions and total demand or the topology of traffic network, and endogenous variables such as the probability and the capacities of spillbacks. This approach assumes that exogenous variables are fixed, which are not practical since urban traffic is highly dynamic and uncertain.

A surrogate model was constructed in Gil et al. (2018) using a fuzzy model to define the optimal cycle length and the green duration ratios. The optimization objective, which is traffic delay, was obtained from the Intelligent Driver Model based microscopic traffic simulator, which was developed at the authors’ department. A fuzzy model was constructed to the model the relationship between objective values (total delay time in this case) and related traffic parameters, for example, the green time ratio, the cycle length and traffic flows. A number of simulation runs were implemented to collect data describing the total delay time and its influential parameters. The fuzzy model was created based on this data. The position of the fuzzy sets of the new rule was optimized using PSO. To optimize the objective function, any optimization technique can help and PSO would be a straightforward option. The accuracy of the approximation model mainly depends on the data collected from the traffic simulator. If the data does not cover all different types of traffic flows, and traffic light cycle’s type, the fuzzy surrogate model would not be able to adequately replicate the relationship between the total delay time and its related traffic parameters, as a result, the approximation error would be high. Furthermore, it is well-known in the literature of surrogate-assisted optimization that the surrogate model should be used together with the traffic simulator to avoid false

optima. Therefore, a management model should be introduced to decrease the negative impact of the approximation error.

In conclusion, surrogate-assisted MOEAs are promising to reduce computational cost in traffic signal optimization problems. However, the management model is needed to use surrogates properly and effectively.

3.4

Conclusion

Traffic signal control systems have a big impact on travel costs and the environment. Traffic signal optimization is an importation approach to increase the effectiveness of the control system. The optimization of parameters of signal timing is a computationally complex problem and the measurement of objective values, such as delay time, flow, and travel time is one of the fundamental issues in this research area. Different methods have been used to solve this task and traffic simulators is one of the most popular tools. Although estimating objective value by using traffic simulators has several advantages, such as higher accuracy and flexibility to capture the dynamic of transport, the simula- tion run is very time-consuming. Computational time rises rapidly as the scale of the traffic network increases.

Multi-objective evolutionary algorithms are superior to traditional searching approaches and they have been widely used to produce optimal signal timings. However, population- based MOEAs have slow convergence speed and the computational time would be a burden when population-based MOEAs are combined with traffic simulators to address the traffic signal optimization problems. Therefore, a simulation-based multi-objective evolutionary algorithm, which can produce good results with limited population size, a small number of generations or a few numbers of objective evaluations would be desirable in traffic signal optimization problems.

Combining a local search and a global may accelerate the search to optima. Further- more, local search also might help reduce the population size of evolutionary algorithms. Therefore, a hybrid of an evolutionary algorithm and a local search can improve the per- formance of traffic signal optimizations system.

Surrogates are approximate models which can be used to estimate objective values of solutions at a cheaper cost compared to original objective function. Surrogates has received increasingly interest in recent years. Surrogate-assisted MOEAs have been used for reducing computational cost of optimizing expensive problems. Consequently, surrogate-assisted MOEAs are promising for solving multi-objective traffic signal timing. Surrogate can be constructed using several approximation techniques. Surrogate should be combined with the original objective function, traffic simulators in case of traffic signal optimization problems, to reduce the computational cost while avoiding mislead the search to false optima.

Methodology

4.1

Introduction

Multi-objective Evolutionary Algorithms (MOEAs) have been widely utilized in the traffic signal optimization problems in order to provide effective control methods for urban traffic networks which are highly complex, uncertain and dynamic. However, running MOEAs on traffic optimization problems is time-consuming Shen et al.(2013). For example, with a small traffic simulation introduced in Bieker et al.(2015), it takes 25 seconds to run one simulation using a PC with Inter(R) Core(TM) i5-6500 CPU 3.2GHz. If the evolutionary process includes 20 generations and there are 60 solutions in the population, the number of solution evaluations needed is 1200 and therefore the traffic simulator has to run 1200 simulations. Consequently, the time to run simulations in the evolutionary process is about 8.3 hours. Furthermore, the computation time will rapidly rise as the scale of the traffic network increases, such as in road network size and number of vehicles. Consequently, in real-time traffic signal management where optimized solutions need to be provided in real time, optimization approaches which have the ability to provide good solutions at a reasonable processing time, especially at an early stage, is preferable. Anytime behavior of an algorithm is its ability to provide as good a solution as possible at any time during its execution and continuously im- proves the quality of the results as computation time increases. Therefore, optimization approaches for urban traffic signal control systems, which have good anytime behav- ior, are desirable. Moreover, in transportation optimisation, small population sizes are

inevitable for scenarios where processing capabilities are limited but require quick re- sponse times. Nevertheless, most existing algorithms are mainly focused on the quality of solutions at the end of the optimization process and population size has not been con- sidered as an indicator when evaluating the effectiveness of an optimization algorithm. Therefore, NS-LS has been introduced which is a multi-objective optimization strategy to improve anytime behavior and which can work effectively with various population sizes. Furthermore, local search is integrated into the evolutionary search to accelerate the convergence rate.

The multi-objective optimization for traffic signal control system using traffic simulators is computationally expensive. Therefore, a surrogate model is constructed to estimate the fitness value of candidate solutions and this model is used together with SUMO to eliminate the false optimum. SA-LS, which is an enhancement of NS-LS, is introduced for traffic signal optimization problems. The number of traffic simulator-based evaluations is reduced, as a result, the number of generations will be increased. Therefore, anytime behaviour of SA-LS would be improved.

This chapter is organized as follows: Section 4.2describes the motivation and the flow of the local search method while the framework and design of NS-LS are provided in Section 4.3. The construction process and updating rules of the surrogate model are shown in Section 4.4. Fitness evaluation scheme is introduced in Section 4.5. Details of SA-LS algorithm are provided in Section4.6 and Section4.7concludes the chapter.