**1.5 Metaheuristics for TSC: the new frontier**

Metaheuristics techniques, including and swarm intelligence and evolutionary algorithms, have emerged as appealing alternatives to classical optimization methods for addressing signal control problems. They can be easily adapted for solving signal optimization problems with mixed types of continuous and discrete variables on large-scale transportation systems. Metaheuristics are based on approximate random methods and involve an iterative master process that can efficiently provide high-quality, acceptable solutions with relatively low computational efforts [20]. No prior information regarding the search space characteristics is required. In addition, metaheuristics do not rely on gradient information of the objective functions and the associated constraints with reference to signal timing variables. Further, the process of finding the optimal solution is simple and straightforward. Entailing less complexity than exact methods means that metaheuristics could be easily implemented to solve non-linear complex optimization problems. Furthermore, for many large-scale engineering problems that involve uncertainties (such as traffic flow), obtaining near-optimal solutions within a reasonable time is acceptable. Owing to these benefits, several metaheuristics techniques have been successfully applied for solving TSC optimization problems. Metaheuristics aim at obtaining the optimal values/ranges for various signal parameters that influence the performance of signalized intersections and include variables such as cycle length, green splits, phase sequence, offsets, change interval, etc. These parameters of interest are also known as decision variables. Constraints conditions for signal optimization include lower and upper cycle length, green splits thresholds, etc.

Metaheuristics have been widely applied to solve the TSC problems under a single objective framework known as mono-objective optimization. The single objective optimization can be classified into four main types: i) travel time

minimization, ii) delay minimization, iii) throughput maximization, and iv) fuel consumption and exhaust emissions (*CO, CO*2*, NO*x*, HC*s) minimization. Monoobjective optimization of traffic signals has some benefits; however, field traffic is highly complex, non-linear, and stochastic in nature, and quite often, the application of multi-objective optimization becomes inevitable. In the process of finding the optimal signal control parameters, traffic engineers usually deal with multiple conflicting objectives. They are seldom interested in knowing the single-objectivebased best solution without considering the other objectives. It is quite possible that an indented improvement in one of the objectives may lead to the deterioration of others. Therefore, it is essential to obtain a reasonable trade-off among various clashing objectives while optimizing the signal timing parameters. To address this issue, researchers have proposed bi-objective or multi-objective metaheuristic frameworks which involve more than one objective function to be optimized concurrently. Adoption of multi-criteria/objectives metaheuristics for signal optimization is rational as well as more beneficial.

## **1.6 Study objectives**

This study provides a comprehensive review of metaheuristics techniques applied to signal control optimization. The surveyed literature is categorized based on the types of metaheuristics used, i.e., evolutionary algorithms and swarm intelligence techniques. A total of over 15 metaheuristics optimization techniques in traffic signal control and optimization are presented. Literature is summarized based on classification of techniques, considered optimization objectives, decision variables, and constraints conditions. Finally, based on the identified literature gaps, major challenges and prospects for future research are also proposed.

## **1.7 Paper organization**

The remainder of this work is organized as follows. Section 2 provides research methods and publication analysis of signal control optimization using metaheuristics. Section 3 reviews evolutionary algorithms' metaheuristics for signal optimization. Section 4 provides a summary of swarm intelligence techniques in the context of the subject domain. Section 5 and 6 presents surveys of trajectory-based metaheuristics and few others for TSC optimization. Finally, Section 7 presents the review conclusions and outlines the current challenges and recommendations for future research.
