No abstract

No abstract

No abstract

Finding the shortest path of the traveling salesman problem (TSP) is a typical NP-hard problem and one of the basic optimization problems. TSP in three-dimensional space (3D-TSP) is an extension of TSP. It plays an important role in the fields of 3D path planning and UAV inspection, such as forest fire patrol path planning. Many existing studies have focused on the expected length of the shortest path of TSP in 2D space. The expected length of the shortest path in 3D space has not yet been studied. To fill this gap, this research focuses on developing models to estimate the expected length of the shortest path of 3D-TSP. First, different experimental scenarios are designed by combining different service areas and the number of demand points. Under each scenario, the specified number of demand points is randomly generated, and an improved genetic algorithm and Gurobi are used to find the shortest path. A total of 500 experiments are performed for each scenario, and the average length of the shortest path is calculated. The models to estimate the expected length of the shortest path are proposed. Model parameters are estimated and k-fold cross-validation is used to evaluate the goodness of fit. Results show that all the models fit the data well and the best model is selected. The developed models can be used to estimate the expected length of the shortest path of 3D-TSP and provide important references for many applications.

Shared bikes can help cities achieve carbon neutrality goals. Cleaning and disinfection are vital procedures of the maintenance of shared bikes, especially during the COVID-19 pandemic because shared bikes could be a transmission intermediary of viruses. This study proposes an optimization model of the cleaning and disinfection scheme of the dockless shared bikes. The disinfection is assumed to be performed at night, when the usage is lowest. By regarding the disinfection staff as traveling salesmen, the model is formulated as an extension of the Multidepot Multiple Traveling Salesman Problem (MDMTSP). The objective function is to minimize the total cost; which consists of the cost associated with the working time and per-capita cost of the disinfection staff. A heuristic algorithm combining k -means clustering and genetic algorithm (K-GA) is adopted to find the lower bound solution. Then, the K-GA-adjustment algorithm has been adopted to find the solutions that satisfy the constraints. To reduce the computing time needed, an approximate function for the lower bound of the optimal number of disinfection staff is obtained by constructing a Continuous Approximation (CA) model. A case study based on real location data of shared bikes in Chengdu, China, is performed to show how the maintenance department could adopt the optimization framework to design an efficient scheme to clean and disinfect the shared bikes.