Vertical cylindrical storage tanks containing oil and gasoline require periodic inspections to prevent structural collapse due to corrosion and stress concentration caused by surface cracks. Wall-climbing robots have been increasingly utilized to overcome the limitations of manual inspection methods, which are often inefficient and struggle to accurately cover large areas. In practice, the tank surface is divided into multiple areas for inspection due to obstacles such as pipes and staircases, or due to the preference of inspectors to focus on specific regions rather than inspecting a continuous large surface. This division poses a significant challenge for optimizing the coverage path, as it requires the robot to efficiently traverse multiple discrete areas. In this study, we propose a global path-planning method to address this issue. The path-planning problem is formulated as an extended version of the well-known Traveling Salesman Problem (TSP) to optimize the route connecting multiple areas. An optimal line-sweep generation algorithm is then employed to generate the coverage path within each area. Finally, an Elitist Strategy Genetic Algorithm (ESGA) is proposed to solve the problem effectively. Computational experiments not only demonstrate the applicability but also the effectiveness of the proposed algorithm.