# Path Planning Optimization of the Load Transport Process Using Heuristic Algorithms
## 1 Introduction
Trajectory optimization is one of the most frequent topics in the study of load transport. Among the optimization methods used in these issues, heuristic methods are most often used, which include classical evolutionary algorithms or their modifications. The issues of trajectory optimization with the use of evolutionary algorithms have been described in detail in [16]. The authors, using the cuckoo search algorithm (CS), optimized the 3D trajectory of a body submerged in water. They compared their results with the two most popular algorithms: genetic algorithm and particle swarm optimization. The authors of the paper noticed that the CS algorithm is a more advantageous solution in the case of determining the trajectory of the body based on the minimum terminal error and maximum terminal velocity. In [17], GA and PSO were used to optimize the coverage of a large area by unmanned aerial vehicles. The authors solve the traveling salesman problem, a mathematical model that has been developed that allows for planning and optimizing the path of vehicles. The advantages of both algorithms were used to develop a method that allows for trouble-free exit from the local minimum while maintaining a better quality of solutions in computational time. The subject of trajectory optimization in various industries has been extensively described among others in review papers [18; 19; 20]. Heuristic algorithms, especially their hybrid combinations, are widely used not only in cargo transportation but also in other industries such as humanitarian logistics, e-commerce delivery, and distribution network management. These studies illustrate their effectiveness in solving complex optimization problems in different contexts. Reference [21] proposes a multi-objective model for the location and routing problem (LRP) in emergency logistics, which takes into account the urgency of delivering relief materials after disasters such as earthquakes or COVID-19. To solve this NP-hard problem, a hybrid metaheuristic algorithm combining Discrete Particle Swarm Optimization (DPSO) and Harris Hawks Optimization (HHO) is used, with additional improvement strategies, which allowed for improving the accuracy of the results and more effectively avoiding local minima. The optimization of takeaway food delivery, where a model combining drones and couriers in a common delivery network with multiple distribution centers, was developed in [22]. Using a two-stage algorithm based on clustering and an improved tabu algorithm, delivery routes were optimized, which contributed to reducing costs, reducing the number of couriers needed, and increasing customer satisfaction. Reference [23] focused on the optimization of the \"last mile\" in e-grocery using autonomous delivery vehicles (ADVs). A model of a two-tier distribution network with a mixed fleet of vehicles was developed, where traditional delivery vehicles serve the first tier and autonomous vehicles serve the second tier. The problem was solved using a hybrid GA-PSO algorithm, and the results showed significant reductions in transportation costs and emissions. In [24], the authors discussed the logistics of perishable products under uncertain demand conditions. A multi-period optimization model was used, including both forward and reverse logistics, with three main objectives: minimizing costs, environmental impact, and ensuring just-in-time delivery. The problem was solved using a hybrid GA-PSO algorithm supported by the CPLEX solver, and the study on the example of an enterprise in Shanghai confirmed the effectiveness of the proposed strategies. This work concerns the problem of optimizing the trajectory of the transported load using a rotary crane. This paper seeks to determine whether the Genetic Algorithm (GA) or Particle Swarm Optimization (PSO) is superior in terms of optimizing the crane's trajectory. A detailed comparison is made in terms of computation time, solution quality, and algorithmic convergence.