**Commenced**in January 2007

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##### Offset Dependent Uniform Delay Mathematical Optimization Model for Signalized Traffic Network Using Differential Evolution Algorithm

**Authors:**
Tahseen Al-Shaikhli,
Halim Ceylan,
Jonathan Weaver,
Osman Nuri Çelik,
Onur Gungor Sahin

**Abstract:**

A concept of uniform delay offset dependent mathematical optimization problem is derived as the main objective for this study using a differential evolution algorithm. Furthermore, the objectives are to control the coordination problem which mainly depends on offset selection, and to estimate the uniform delay based on the offset choice at each signalized intersection. The assumption is the periodic sinusoidal function for arrival and departure patterns. The cycle time is optimized at the entry links and the optimized value is used in the non-entry links as a common cycle time. The offset optimization algorithm is used to calculate the uniform delay at each link. The results are illustrated by using a case study and compared with the canonical uniform delay model derived by Webster and the highway capacity manual’s model. The findings show that the derived model minimizes the total uniform delay to almost half compared to conventional models; the mathematical objective function is robust; the algorithm convergence time is fast.

**Keywords:**
Area traffic control,
differential evolution,
offset variable,
sinusoidal periodic function,
traffic flow,
uniform delay.

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