3.2 Objectives in Traffic Signal Optimization
3.2.1 Optimization Objectives in Traffic Signal Control
A. Reducing traffic delay is one of the most critical objectives in traffic management as it directly relates to travel time, fuel consumption and discomfort of drivers. Conse- quently, reducing delay at intersections is the main and fundamental objective in traffic signal optimization. The first signal timing optimization program was introduced for an isolated intersection by Webster and Cobbe (1966) to minimize the traffic delay using the Webster formulation. Guangwei et al. (2007) introduced a formula of the average delay of all vehicles travelled through the intersection. This formulation is based on the information of individual vehicles obtained from a microscopic traffic simulator. The
Table 3.2: Optimization objectives in traffic signal optimization using MOEAs.
No. References Optimization Objectives
Stops Flow Delay Emission Queue Time
1 Guangwei et al.(2007) √
2 Feng and Xiaoguang (2008) √ √ √
3 Fang and Elefteriadou(2008) √
4 Zhou et al.(2008) √ √
5 Qun (2009) √
6 Zhang et al.(2009) √
7 Ben et al.(2010) √
8 Sanchez-Medina et al.(2010) √ √ √
9 Kouvelas et al.(2011) √
10 Shen et al.(2011) √
11 Chin et al.(2011) √
12 Adacher(2012) √
13 Passow et al.(2012) √ √
14 Shen et al.(2013) √ √
15 Yan et al.(2013) √ √
16 Chen and Chang (2014) √ √
17 Kai et al.(2014) √
18 Abushehab et al.(2014) √
19 Tung et al.(2014) √
20 Zakariya and Rabia(2016) √
21 Gao et al.(2016) √
22 Sabar et al.(2017) √
23 Armas et al.(2017) √ √
24 Mihaita et al.(2018) √
weighting factor, which is assigned for transit vehicles, is taken into account when calcu- lating the average delay. Feng and Xiaoguang(2008) obtained desired objective values, such as overall delay, queue length, and travel time, by using the Cell Transmission Model (CTM). Webster delay model is adopted inQun(2009) to construct the function of the average delay per vehicle. After that, a formula of the total delay is derived and minimized. The total delay on each direction in Adacher (2012) is obtained from the TRANSYT and the proposed algorithm minimized the linear combination of the total delays in every direction. Shen et al. (2013) minimized both the average stop time and the average delay time. A macroscopic traffic simulation model is used in Chen
and Chang (2014) to formulate the total delay function and the total throughput of the traffic scenario. The total delay time in Kai et al. (2014) was derived from output files generated by SUMO and the optimization approach, proposed by the authors, min- imized the average vehicle delay, which is determined by the total delay time divided by the total vehicles. Two different formulas of the cycle length were proposed in Za- kariya and Rabia(2016) to minimize the delay of the intersection. The first cycle length formula is recalibrated from the Webster’s minimum delay cycle length formula which is introduced by Webster to estimate the optimal cycle length of an isolated signalized intersection. The second model is the exponential function of the non-linear regression model. Another way of calculating traffic delay was described in Sabar et al. (2017), which is the difference between the free-flow travel time and the estimated travel time needed to finish the route. The fitness function is, therefore, a time-dependent form derived from the travel time Davidson’s function which is used to predict travel time based on several parameters, for example, traffic volume, free flow travel time, and the capacity.
B. Reducing queue length is another major objective that has been used in traffic signal optimization approaches. How to calculate queue lengths in real-time at signalized intersections is a long-lasting problem and it becomes more difficult under over-saturated conditions,Wu and Yang(2013). The objective function inFang and Elefteriadou(2008) was the sum of average queues per lane for all approaches. Each approach is assigned a weight and its average queue length per lane is the sum of the initial queue at the beginning of the interval and the number of vehicles that arrived during the interval minus the number of discharged vehicles. InZhang et al.(2009), the sum of the vehicles waiting for leaving the queue which is derived from a real-time traffic flow model was minimized. The queue ratio maintenance optimization function inYan et al.(2013) was defined based on the average queue length per phase, which was derived from the output of the traffic scenario simulated by VISSIM.
C. Increasing traffic flow is one of the main objectives of traffic signal optimization systems. Traffic flow rate is a parameter of a traffic network. It is defined as the number of vehicles which passed a reference point in a given period of time. In Kouvelas et al.
(2011), traffic flow measurement was obtained from the traffic simulated scenario, which has available detectors installed on links. Both Sanchez-Medina et al.(2010) and Shen et al. (2011) simply defined the traffic flow as the total number of vehicles that left the
traffic network during the simulation and considered the traffic flow as the objective function. Yan et al. (2013) maximized the weighted vehicle number of the intersection.
Each movement is allocated a weight coefficient and its actual traffic flow is a function of cycle length, green time, and time. All these parameters are derived from the traffic simulator.
D. Reducing traffic exhaust emissions is becoming a critical criterion when designing traffic signal optimization systems because air pollution and other detrimental impacts on the environment from the transport sector have greatly impacted to the society. Pol- lution emissions from vehicles can be measured by emission models which are generally classified by macroscopic models and microscopic models. There have been a number of studies introduced optimization models for traffic signal control to mitigate the damage of vehicle emissions. Zhou et al.(2008) considered the total exhaust emission as the sum of the idle emission and the running emission of each entrance link of the intersection.
Traffic flow and length of links are included in the formula of the total emission. The idle emission is estimated based on the standard idle emission factor, traffic flow and the traffic delay of the link, which was calculated based on Webster delay model. Emis- sion value was calculated using the International Vehicle Emissions (IVE) model inBen et al. (2010). Air quality information in Passow et al. (2012) was obtained from mon- itors, models, and satellites. Although researchers often put the environmental targets after the traffic demand requirements but environment-related objectives are becoming a major concern of research of the transportation sector, especially in traffic signal control.
E. Reducing travel time is another objective in traffic signal optimization. Abushehab et al. (2014) carried out a number of experiments to determine algorithms and their corresponding parameters which are more suitable in traffic signal optimization to pro- duce the minimum total travel time. Sanchez-Medina et al. (2010) defined mean travel time as the average time which a vehicle takes to finish its route. Travel time in Zhou et al.(2008) was designed as the sum of the running time and the delay at intersections.
The running time function used by the author is the BRP function which is developed by Bureau of Public Road while the delay time is determined by the Webster model.
Average travel time for all vehicles to finish their routes was defined as the fitness value inTung et al.(2014).
Recently, studies in traffic signal optimization normally consider multiple objectives,
as a result, MOEAs are one of very promising algorithms to simultaneously optimize multiple objectives. In MOEAs, solutions are compared using their fitness value which is assigned based on the objective value. Consequently, objective calculation is very important. The next section introduces methods to calculate fitness value of candidate solutions.