The vehicle routing problem with time windows (VRPTW) is a classical optimization problem. There have been many related studies in recent years. At present, many studies have generally analyzed this problem on the two-dimensional plane, and few studies have explored it on spherical surfaces. In order to carry out research related to the distribution of goods by unmanned vehicles and unmanned aerial vehicles, this study carries out research based on the situation of a three-dimensional sphere and proposes a three-dimensional spherical VRPTW model. All of the customer nodes in this problem were mapped to the three-dimensional sphere. The chimp optimization algorithm is an excellent intelligent optimization algorithm proposed recently, which has been successfully applied to solve various practical problems and has achieved good results. The chimp optimization algorithm (ChOA) is characterized by its excellent ability to balance exploration and exploitation in the optimization process so that the algorithm can search the solution space adaptively, which is closely related to its outstanding adaptive factors. However, the performance of the chimp optimization algorithm in solving discrete optimization problems still needs to be improved. Firstly, the convergence speed of the algorithm is fast at first, but it becomes slower and slower as the number of iterations increases. Therefore, this paper introduces the multiple-population strategy, genetic operators, and local search methods into the algorithm to improve its overall exploration ability and convergence speed so that the algorithm can quickly find solutions with higher accuracy. Secondly, the algorithm is not suitable for discrete problems. In conclusion, this paper proposes an improved chimp optimization algorithm (MG-ChOA) and applies it to solve the spherical VRPTW model. Finally, this paper analyzes the performance of this algorithm in a multi-dimensional way by comparing it with many excellent algorithms available at present. The experimental result shows that the proposed algorithm is effective and superior in solving the discrete problem of spherical VRPTW, and its performance is superior to that of other algorithms.

Based on the evaluation model of the gray correlation-TOPSIS method, this paper examines the index system of grass-roots water conservancy services in Hunan Province, China. This paper aims at the present situation of grassroots water conservancy in Hunan province, which assisted it in developing grassroots water conservancy services. The evaluation indicators include five criteria levels (institutional staffing, personnel quality, management level, public policy and service capacity) and twenty-four indicator levels. In this paper, the weight calculation method combined with an analytic hierarchy process and an entropy weight method, as well as quantitative and qualitative methods, was used to conduct an empirical study on the basic water conservancy service level of Hunan Province in 2020. The results classify grassroots water services in Hunan Province into three levels. By fitting the GDP of cities and prefectures with the comprehensive closeness, we conclude that there is considerable convergence between the grassroots water conservancy service level of Hunan Province and its local economic level. The more developed the economy, the higher the grassroots water conservancy service level. In addition, through obstacle factor analysis, the main constraints of grassroots water conservancy in various cities and prefectures are obtained. Therefore, the grassroots water conservancy service’s ability can be comprehensively improved from three aspects: serviceability, capital investment, and talent construction. This indicator system can promote the overall governance capacity of grassroots water conservancy in the future development of cities and prefectures, and it can also provide Hunan with experience and case examples for the implementation of rural revitalization.