# Path Optimization Using Metaheuristic Techniques for a Surveillance Robot
## 2 Related Works
However, the implementation of path planning and trajectory tracking by autonomous robots generates a series of optimization problems that can be dealt with using various techniques [19]. In [PERSON] et al., stochastic trajectory optimization methods are used. The authors introduce the ergodicity metric as an objective in a sampling-based stochastic trajectory optimization framework for a mobile robot. In their approach, they construct a probability distribution over feasible trajectories and search for the optimal trajectory using the cross-entropy method [20]. A different approach consists of addressing these challenges with heuristic optimization techniques. In this work, we apply and compare three different heuristic optimization techniques to the CCPP problem, namely, GA, PS, and PSO. Briefly, their main characteristics regarding the path planning problem are as follows. GAs are computer programs that mimic the processes of biological evolution (selection, crossover, mutation) to solve problems and model evolutionary systems [21]. This feature makes them suitable for solving optimization problems that require an adaptive computer program. In the case of path planning, they allow researchers to easily introduce a fitness function with more than one objective that also maintains several possible solutions at the same time. In PSO, a group of simple entities called \"particles\" are positioned within the search space of a given problem or function. Each particle evaluates the objective function at its current location and determines its path through the search space by fusing certain aspects of its individual history, the location that has the best fitness, and those of one or more peers within the swarm [22]. The search approach used by this method is particularly suitable for the problem of optimizing a trajectory in a complex environment since it leads to the rapid identification of a solution, as shown in the results obtained in this problem. PS is an effective technique for exploring the minima of a function, even when that function is not differentiable, exhibits stochastic behavior, or is not necessarily continuous [23]. The PS algorithm explores a set of points surrounding the current location and actively searches for a point within this set where the value of the fitness function is less than at the current point. This feature makes this method suitable for finding routes as long as the initial route is close to a good solution. This suggests that this method will work effectively in small environments with few obstacles. Some other works have explored these techniques. For instance, the work in [24] proposes an hybrid PSO-SA algorithm for the optimization of AGV path planning. In [25], a comprehensive review of methodologies for path planning and optimization of mobile robots is provided. It includes not only the classic but state-of-the-art techniques such as artificial potential fields, GA, swarm intelligence, and machine learning-based methods. The paper by [PERSON] et al. focuses on the indoor AGV path-planning problem in large-scale, complex environments and proposes an efficient path-planning algorithm (IACO-DWA) that incorporates the ant colony algorithm (ACO) and dynamic window approach (DWA) to achieve multi-objective path optimization [26]. First, an improved ant colony algorithm (IACO) is proposed to plan a global path for AGVs that satisfies a shorter path and fewer turns. Then, local optimization is performed between adjacent key nodes by improving and extending the evaluation function of the traditional dynamic window method (IDWA), which further improves path security and smoothness. An overview of navigation strategies for mobile robots that utilize three classical approaches, roadmap (RM), cell decomposition (CD), and artificial potential fields (APF), in addition to eleven heuristic approaches, including GA, ACO, artificial bee colony (ABC), gray wolf optimization (GWO), etc., which may be used in various environmental situations is presented in [27].