## 1 Introduction  
Ant colony optimization (ACO) is a mainstream swarm intelligence algorithm inspired by the foraging behavior of real ant colonies [1; 2; 3]. In ACO, a colony of artificial ants constructs solutions guided by artificial pheromone trails and some heuristic information. ACO has been successfully applied in various complex optimization problems [4; 5; 6]. However, in most real-world applications, the optimization problem has a dynamic environment [7]. In particular, the environment of the optimization problem, including objective function, constraints, search space, input variables, and so on, may change over time.  
Major challenges occur when addressing dynamic optimization problems because repeated optimization of the changing optimum is required. The optimal solution in which the algorithm has converged to it before the dynamic change may not be the optimal solution after the dynamic change. Consequently, the optimization process needs to be restarted in order to search for a new optimal solution. However, it may not be very efficient to restart the optimization process from scratch in complex problems (e.g., \(\mathcal{NP}\)-hard combinatorial problems), as they require huge computational efforts and time [8].  
A more efficient way to address dynamic optimization problems is to use knowledge from previously optimized environments to speed up the re-optimization process [9]. With ACO algorithms, this knowledge can be transferred via the pheromone trails generated in the previous environments. However, the pheromone trails of the previous environment may contain information directing the search process to the previous optimal solution, which may represent a poor local optimum in the current environment [10]. Several strategies have been integrated to enhance the adaptation capabilities of ACO in dynamic optimization problems, such as the generation of new ants using immigrant schemes [11; 12], population-based pheromone update strategies [13], multiple ant colonies [14], and memetic computing [15].  
In this work, the traveling salesman problem (TSP) is used as the base optimization problem to generate dynamic test cases using the benchmark generator proposed in [10]. A conventional ACO [16] and a population-based ACO [13] that use pheromone evaporation and memory archive, respectively, to adapt to dynamic changes are applied to the generated dynamic TSP (DTSP) test cases.  
The most common method to evaluate the performance of ACO in dynamic environments is used in the experiments, that is, to obtain the mean and standard deviation (for multiple independent executions) for the generated DTSPs. Statistical tests are performed to compare the algorithms. In [17], it is argued that, for stochastic algorithms (e.g., ACO algorithms), this way of comparison may not be very informative. This is because the distribution of executing ACO algorithms multiple times may be asymmetrical and, hence, outlier values may affect the mean value. Consequently, inadequate information regarding the average performance of the algorithms may be provided. In contrast, quantiles of the distribution may address this issue with the use of median values as an average performance measurement.  
The rest of the paper is structured as follows. Section 2 provides a description of the TSP as well as a description of the generation of dynamic test cases. Section 3 describes the application of the ACO metaheuristic to the TSP. In addition, the pheromone update policies in dynamic environments for the two ACO algorithms used in the experiments are described. Section 4 presents the experimental setup and results. An analysis of the obtained results is provided. Section 5 concludes this work.