In this paper, we present a variant of our previous research on multi-goal path finding problem, focusing on finding a feasible and closed path to visit a sequence of goals in an environment with obstacles. The newly proposed method, Segmentation & Regression v2 (S&Reg v2), employs multi-task learning networks to generate regions and estimates of lengths of local paths between pairwise goals. Importantly, the estimates are performed as weights for a complete graph to compute the visiting sequence. Subsequently, the path-finding process is executed following the sequence, and the predicted region works as a sampling domain to enhance the search speed. A hybrid sampler is designed by combining a uniform domain with the region domain, ensuring successful samples, even if the region is disconnected. Besides, a selection rule is introduced to balance the sampling domain during different searching stages. A proof of probabilistic completeness of the S&Reg v2 method is given. Simulations verify the superior performance of the S&Reg v2 method, demonstrating a reduction in calculation time ranging from 3.9% to 13.0%. Furthermore, a practical scenario validates the reliability of S&Reg v2, achieving a 15.0% improvement in success rate and a 9.7% reduction in calculation time.