Delay estimation models for signalized intersections using differential evolution algorithm

Korkmaz, Ersin; Akgüngör, Ali Payıdar · 2017 · Crossref

DOI: 10.1016/s2307-1877(25)00840-5

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Summary

This study addresses the challenge of accurately estimating vehicle delay at signalized intersections, a critical parameter for optimizing traffic signals and determining the level of service. Existing analytical models, such as the Highway Capacity Manual (HCM) and Akçelik models, often rely on complex parameters or exhibit deficiencies under specific traffic conditions. To overcome these limitations, the authors developed new delay estimation models using the Differential Evolution (DE) algorithm, an artificial intelligence technique known for its efficiency in solving non-linear optimization problems. The primary objective was to create simple, practical models requiring fewer input parameters while maintaining high accuracy compared to established analytical methods. The researchers developed three types of Differential Evolution Delay Estimation Models (DEDEM): linear, exponential, and quadratic. These models utilized only two input parameters: the green ratio (effective green time to cycle length, ranging from 0.35 to 0.60) and the degree of saturation (volume to capacity ratio, ranging from 0.7 to 1.4). To generate reference data for model training and validation, the authors employed the TSIS-CORSIM microscopic traffic simulation software. They simulated a pre-timed, two-phase intersection with major and minor approaches, varying traffic volumes and control conditions. A total of 253 delay data points were collected from the major approaches; 209 were used for training the DE models to determine weighting factors, and 44 were reserved for testing. The DE algorithm was configured with specific control parameters, including a crossover probability of 0.95 and a mutation factor of 0.95, to optimize the fit between estimated and simulated delay values. The performance of the DEDEM models was evaluated against the HCM and Akçelik analytical models using Mean Absolute Error (MAE), Mean Square Error (MSE), and the coefficient of determination (R²). The results demonstrated that the quadratic DEDEM model outperformed all other models. For the test data, the quadratic model achieved an R² of 0.97, an MSE of 207.98, and an MAE of 12.12. In comparison, the Akçelik model, which performed better than the HCM model among the analytical approaches, yielded an MAE of 13.20 and an MSE of 269.08. The linear DEDEM model showed the lowest performance, while the exponential form was intermediate. Graphical comparisons confirmed that the quadratic model’s estimates were closest to the simulated delay values. The study concludes that the quadratic DEDEM model serves as a robust alternative for delay estimation at signalized intersections, offering high accuracy with minimal input parameters. The findings also validate the Differential Evolution algorithm as an effective model-fitting tool for transportation engineering problems. The authors suggest that future research should expand the model to include additional variables, test its applicability to vehicle-actuated signal controls, and validate the results using field data rather than simulation outputs.

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