A stochastic simulation-based optimization method for equitable and efficient network-wide signal timing under uncertainties

The equity of right-of-way is an important topic in traffic management and control. With the balance consideration of traffic equity and efficiency, which are respectively evaluated by the Atkinson index and average travel time, this study proposes a bi-objective signal timing simulation-based optimization (SO) model under uncertainties, and solve it by a bi-objective stochastic simulation-based optimization (BOSSO) method. In this method, two types of surrogate models (i.e., regressing Kriging model and quadratic regression model) are used to capture the complicated mapping relationship between decision variables and bi-objectives, respectively in the whole variable domain and in the local trust-region. Meanwhile, the incorporation of the global regressing Kriging model and an adaptive selector helps to predict bi-objective values of untested samples and re-estimate simulated samples in the local trust-region, which can save great computational costs and smooth stochastic noises. Moreover, the non-interactive role of a decision maker is taken to generate more Pareto optimal solutions around his/her desired bi-objective values. Through the algorithm comparison for a benchmark bi-objective stochastic optimization problem, the proposed BOSSO method is validated to outperform three other counterparts (i.e., NSGA-II, BOTR and BOEGO) under the same simulation costs. In real-field experiments, an urban road network with 15 signalized and five non-signalized intersections in Changsha, China is modeled by VISSIM. After the well calibration of the microscopic traffic simulation model, the network-wide bi-objective signal timing stochastic SO problems with and without coordination are solved by BOSSO. Numerical results indicate that compared with the real-field case, the average travel time and Atkinson index are reduced respectively by at most 13.48% and 23.49% for optimized non-coordinated signal plans, and respectively by at most 25.58% and 2.83% for optimized coordinated ones. It is further validated that under variable traffic volumes, the non-coordinated signal plan can well improve both traffic efficiency and equity, and the coordinated one is capable to improve traffic efficiency at a larger degree but sacrifice traffic equity. Moreover, the balance analyses show the existence of competing relationship between bi-objectives, and BOSSO is confirmed to outperform NSGA-II, BOTR and BOEGO in searching the better Pareto optimal signal plans under the same budged simulations. In conclusion, BOSSO is promising to address bi-objective optimization problems characterized by costly evaluation, high dimensions and stochastic noises.