“…C min ≤ C ≤ C max (8) 0 ≤ θ z ≤ C ∀z ∈ Z (9) g min ≤ g z,i ≤ g max ∀z ∈ Z ∀i ∈ I (10) g z,1 + g z,1 = g z,5 + g z,6 ∀z ∈ Z (11) g z,3 + g z,4 = g z,7 + g z,8 ∀z ∈ Z (12) where OF is the objective function of three decision variables including cycle period (C), green splits (g), and offsets (θ ), Z is the intersection set (each Z has 8 g), I is the signal set of an intersection (containing green, yellow, and red signals), and C max and C min are maximum and minimum cycle length for a complete period, g max and g min are the maximum and minimum of a green splits, respectively. Equations (11) and (12) are for the ring-barrier diagram strategy such that the east-west and north-south movements will not contradict each other. The signal timing problem used in this article is a road with four intersections (Z = 4), both of which are T-junctions, as shown in Fig.…”