**5. Review of trajectory-based metaheuristics for TSC**

This section surveys the previous works that applied trajectory-based metaheuristics techniques) for traffic signal control and optimization. As the name suggests, these algorithms form search trajectories in solution space and iteratively improve the single solution in its neighborhood. Their exploration process starts from a random initial solution generated by another algorithm. At each stage, the current solution is replaced by a better offspring population. Trajector-based metaheuristics are mainly characterized by their internal memory sorting the state of search, candidate solution generator, and selection policy for candidate movement through generations. **Table 3** summarizes the previous works that applied trajectory-based search metaheuristics, hybrid metaheuristics, and others for traffic signal control and optimization.

#### **5.1 Tabu search for signal control optimization**

Tabu Search (TS) is a metaheuristic introduced by Fred Glover in 1986 to overcome the local search (LS) problem of existing methods [123]. TS allows the LS heuristic to diversify the search for solution space outside the local optima [124]. One of the important features of TS is its memory function, which can restrict few search directions for a more detailed LS, thereby making it easier to avoid local optimum solutions. By combining the greedy concept and randomization, the TS algorithm could provide an efficient solution to many optimization problems. In literature, only a few studies have focused on the application of Tabu search for signal control optimization. Hu and Chen proposed traffic signal control based on a novel greedy randomized tabu search (GRTS) algorithm considering travel time as the primary optimization objective [118]. GRTS results were compared with a GA-based traffic control scheme using data from a real city network to demonstrate the benefits of the proposed method. Numerical simulation results revealed that over 25% reduction in travel time might be achieved under medium to high traffic demands. In another study, Karoonsoontawong and Woller applied reactive tabu search (RTS) for simultaneous solutions of traffic signal optimization and dynamic user equilibrium problems on two transport networks in a simulated environment [119]. Three different variants of RTS were investigated based on deterministic or probabilistic neighborhood definitions. The performance of all the RTS variants was evaluated using three criteria such as solution quality, CPU time, and convergence speed. Simulation results showed that the RTS approach could provide promising results in terms of improving the overall network performance.

In a recent study, Hao et al. proposed a hybrid tabu search-artificial bee colony (TS-ABC) algorithm for robust optimization of signal control parameters in undersaturated traffic conditions at isolated signalized intersections [68]. This study considered two performance indexes such as average delay and mean-square error of average delay. The proposed signal control optimizer was validated using field data from an intersection in the city of Zhangye, China. Numerical simulation results compared with GA showed that the proposed TS-ABC is better in reducing the traffic delay under varying and heterogeneous traffic conditions. Chentoufi and Ellaia also proposed a hybrid particle swarm and tabu search (PSO-TS) for adaptive

#### *Metaheuristics for Traffic Control and Optimization: Current Challenges and Prospects DOI: http://dx.doi.org/10.5772/intechopen.99395*


**Table 3.**

*Summary of previous studies on traffic signal optimization using trajectory-based metaheuristics, hybrid metaheuristics, and others.*

traffic lights timing optimization on real-time isolated signalized intersections in the context of Moroccan cities [120]. The authors also highlighted the significance of integrating the proposed PSO-TS model and VISSIM to achieve optimum average delay estimates. Simulation results demonstrated the superior efficiency of the PSO-TS technique against the traditional static models under oversaturated traffic conditions.

#### **5.2 Simulated annealing (SA)**

Simulated Annealing (SA), developed by Kirkpatrick et al. is inspired by the statistical mechanics of annealing in solids [125]. For understanding, consider a change in temperature, which causes a change in energy and movement of particles in solids. There is a sequence of decreasing temperature in annealing until criteria are met [126].

Li, Schonfeld [112] reported traffic signal time optimization using metaheuristic capabilities of SA with GA. It was concluded that SA-GA models outperform in optimization compared to individual SA and GA models. Similar results were reported by Song et al. in evaluating the optimized model for reducing traffic emissions on arterial roads [113]. Oda et al. [114] employed SA to optimize traffic signal timing and reported its improved performance as compared to traditional models.

## **6. Other metaheuristics for TSC**

This section reviews the previous works that applied some other metaheuristics for traffic signal control and optimization. These include the harmony search algorithm, water cycle algorithm, and Jaya algorithm. **Table 3** summarizes the previous works that applied trajectory-based search metaheuristics, hybrid metaheuristics, and others for traffic signal control and optimization.

#### **6.1 Harmony search (HS)**

The metaheuristic harmony search (HS) algorithm simulates the natural musical improvisation process where the musicians aim to achieve a near-perfect state of harmony [127]. In the HS algorithm, the candidate solution population is known as harmony memory (HM), where every single solution in solution space is referred to as "harmony," which belongs to the "*n*"-dimensional vector. Though HS has been successfully used for numerous applications across diverse domains, its applications for signal control optimization are limited. In a recent study, Gao et al. applied to HS in addition to four others metaheuristics for traffic signal scheduling (TSS) problems [121]. Experiments were conducted on real-time data from signalized intersections in Singapore to examine the performance of proposed metaheuristics. The authors considered heterogeneous traffic conditions. Simulation results proved the adequacy of all algorithms; however, the hybrid algorithm (ABC-LS) outperformed other techniques in terms of solution quality.

In another study, Ceylan and Ceylan adopted a hybrid harmony search algorithm and TRANSYT hill-climbing algorithm (HSHC-TRANS) for solving stochastic equilibrium network design (SEQND) in the context of optimal traffic signal setting problems [128]. The effectiveness of HSHC-TRANS was evaluated against HS and GA in terms of network performance index (PI). Results showed that the proposed hybrid model yielded about 11% in the network's PI compared to the GA-based model. In another study, Gao et al. addressed the urban traffic signal scheduling problem (TSSP) using a discrete harmony search (DHS) with an ensemble

#### *Metaheuristics for Traffic Control and Optimization: Current Challenges and Prospects DOI: http://dx.doi.org/10.5772/intechopen.99395*

of local search [115]. The primary objective was to minimize the network-wide total delay under a pre-defined finite horizon. Extensive simulation experiments were carried out using traffic data from a partial transport network in Singapore. Comparative analysis showed that the HS algorithm as a meta-heuristic achieved better performance compared to fixed-cycle traffic signal control (FCSC). Dellorco et al. also investigated the applicability of HS for signal control optimization on the two-junction network with the fixed flow on the links [116]. A comparative analysis of HS with GA and HC algorithms showed that HS resulted in a better network's PI compared to its counterparts. Afterward, the validity of the proposed HS algorithm was assessed by applying it to a test network.

## **6.2 Jaya algorithm**

The Jaya algorithm is a recently proposed metaheuristic initially introduced by R.V. Rao [129]. The word Jaya comes from Sanskrit, which means "victory." In the Jaya algorithm, the search strategy always attempts to be victorious by reaching the optimal and best solution, and thus it is named "Jaya." It is arguably one of the simplest and easy-to-implement metaheuristics. The main benefit of Jaya for optimization problems lies in the fact that this algorithm requires only common controlling parameters such as population size and the number of iterations and does not require any additional algorithm-specific constraints/parameters. While this algorithm has been successfully used for several scheduling and optimization problems in recent years, its applications in the domain of traffic scheduling and management are relatively scarce.

A recent study conducted by Gao et al. compared the performance of Jaya algorithms with other metaheuristics (like water cycle algorithm (WCO), genetic algorithm (GA), artificial bee colony, and harmony search (HS), and hybrid ABC-LS) for solving traffic light scheduling problem [121]. Simulation results showed all the algorithms achieved competitive results; however, the hybrid algorithm attained better accuracy and convergence. The proposed models were also tested on real-time traffic and phase data from a network of intersections in the Jurong area of Singapore. In another study, the authors proposed an improved Jaya algorithm for solving traffic light optimization problems in the context of large-scale urban transport networks [122]. The chosen performance index was to minimize the network-wide total traffic delay within a given time horizon. To enhance the search performance in the local search space, a neighborhood search operator was proposed. Experiments were carried out using traffic data for a case study from the Singapore transport network. Study results demonstrated the robustness and better performance of proposed improved Jaya algorithms against standard Jaya algorithm and exiting traffic light control scheme. In another follow-up study, Gao et al. studied large-scale urban traffic lights scheduling problems using three different metaheuristics, namely Jaya, WCO, and HS [117]. The objective function was to optimize the delay time of all vehicles network-wise under a fixed time horizon. This study also proposed a feature search operator (FSO) to improve the search performance of proposed metaheuristics. To examine the efficacy of proposed methods, experiments were carried out using real-time traffic data. It was concluded that metaheuristic-based traffic control could significantly improve the network performance compared to existing traffic control strategies. Numerical simulation results showed that in comparison to feature-based search (FBS), operator for all algorithms improved the total vehicle delay time by more than 26% in their worst case scenarios.

**Figure 7a** depicts the relationships between total network delay time (sec) and sampling intervals for a typical urban traffic network with 100 junctions from the west Jurong area in Singapore [117]. Minimum (min.), average (avg.)

#### **Figure 7.**

*(a) Results comparison with different sampling times for network of 100 junctions, (b) the % improvement of iJaya and iJaya+FBS with standard Jaya, (c) the % improvement IWCA and IWCA+FBS with standard Jaya, (d) the % improvement HS + FBS and standard HS. Ref. [117].*

and maximum (max.) total delay values each for 30 repeats and five sampling intervals (5, 10, 15, 20, and 30 sec) are reported. It is evident from the results that a sampling period of 15 seconds yielded the best results, which were then adopted for subsequent experiments. **Figure 7b** shows the relative percentage improvement in network performance (reduction in network delay) for standard Jaya algorithm with improved Jaya (iJaya), and Jaya with FBS operator (iJaya+FBS) for a sample 11 cases of traffic network from the same study [117]. Compared to standard Jaya, the iJaya yielded the improvements in range for 0–6% for min., avg., and max. Results, while iJaya+FBS algorithm resulted in corresponding improvement values between 9 and 11%. **Figure 7c** depicts the percentage improvement of IWCA and IWCA+FBS algorithms relative to standard WCA optimizer. The IWCA improved the standard WCA in terms of min., avg., and max. Results for 11 test cases in the range of 2–8%, while the corresponding improvement for IWCA+FBS algorithm is approximately 20–24%. **Figure 7d** shows the network performance improvement of standard HS and HS + FBS algorithms for the same network of traffic junctions [117]. The improvement for HS + FBS algorithm compared to standard HS optimizer are between 2 and 12% for min., avg., and max. Results for the considered cases.

**Figure 8** presents the graphical comparison among the three optimization algorithms (iJaya+FBS, IWCA+FBS, and HS + FBS) in terms of the average relative percentage deviation (ARPD) of the resulting network delay time values [117]. It is clear from the results that the IWCA+FBS algorithm with an average delay reduction of 28.54% outperformed the iJaya+FBS and HS + FBS having the corresponding values of 28.22% and 27.84%, respectively. Further, all the algorithms yielded an improvement of at least 26% in the worst-case scenarios.

*Metaheuristics for Traffic Control and Optimization: Current Challenges and Prospects DOI: http://dx.doi.org/10.5772/intechopen.99395*

#### **Figure 8.**

*ARPD improvements comparison for different optimizers. Reprinted with permission from Ref. [117] copyright (2021), Elsevier Ltd.*

#### **6.3 Water cycle algorithm (WCA)**

The water cycle algorithm (WCA) is another recently proposed metaheuristic whose search mechanism is inspired by the natural water cycle process, where streams and rivers flow down the hill to reach the sea [130]. The surface run-off model is imitated in WCA for updating the current candidate solutions and the generation of new offspring. The effectiveness of WCA has been explored for various applications such as truss structures, constrained and unconstrained engineering design problems [130–133]. However, very few studies have used WCO for traffic control, management, and optimization.

A recent study by Gao et al. proposed the application WCO for traffic signal scheduling and optimization based on actual traffic data from a case study in Singapore [121]. WCO was compared with four other metaheuristics and a hybrid algorithm (ABC-LS), considering the network delay as the main optimization objective. Numerical simulation results proved the benefits of adopting metaheuristic-based traffic control strategies instead of existing fixed traffic light schemes. In another study, Gao et al. compared WCO with the Jaya algorithm and Harmony search using the field traffic data from the same transportation network. The performance metric minimized the network-wide total traffic delay within a given time horizon [117]. The study proposed a neighborhood search operator to enhance the search performance of all the algorithms in the local search space. Study results showed that WCA, with an average better improvement of in network-wide delay (28.54%), outperformed HS (28.22%) and Jaya algorithm (27.84%).

#### **7. Conclusions, current challenges, and future research directions**

Traffic control and management using metaheuristics have emerged as an effective solution to mitigate urban congestion. This study provided a comprehensive review of state-of-art research on traffic signal optimization using different metaheuristics approaches. The surveyed literature is categorized based on the nature of applied metaheuristics, i.e., swarm intelligence (SI) techniques, evolutionary

algorithms, trajectory-based metaheuristics, and others. Although numerous metaheuristics have been employed for signal optimization, GA, PSO, ACO, and ABC algorithms have been widely explored. Various traffic signal parameters such as cycle length, green splits, offsets, and phasing sequence are considered decision variables to solve signal control optimization problems. Similarly, studies have considered several optimization objectives such as delay, number of stops, travel time, throughput, queue, fuel consumption, exhaust emissions to address the problem. Some studies have adopted single-objective optimization, while others have attempted to solve traffic signal control as a multi-objective optimization problem. However, little work has been done to understand the correlations between the conflicting objectives which is vital for traffic engineers and decision-makers to evaluate their relative importance. Based on the presented survey work, the following passages present key challenges, research gaps, and future research directions in this area.


statistical significance tests may be conducted to compare the performance among various metaheuristics in solving signal optimization problems.

