  In this paper, we propose a novel end-to-end approach for solving the
multi-goal path planning problem in obstacle environments. Our proposed model,
called S&Reg, integrates multi-task learning networks with a TSP solver and a
path planner to quickly compute a closed and feasible path visiting all goals.
Specifically, the model first predicts promising regions that potentially
contain the optimal paths connecting two goals as a segmentation task.
Simultaneously, estimations for pairwise distances between goals are conducted
as a regression task by the neural networks, while the results construct a
symmetric weight matrix for the TSP solver. Leveraging the TSP result, the path
planner efficiently explores feasible paths guided by promising regions. We
extensively evaluate the S&Reg model through simulations and compare it with
the other sampling-based algorithms. The results demonstrate that our proposed
model achieves superior performance in respect of computation time and solution
cost, making it an effective solution for multi-goal path planning in obstacle
environments. The proposed approach has the potential to be extended to other
sampling-based algorithms for multi-goal path planning.
