Results for the close-enough traveling salesman problem with a branch-and-bound algorithm

The Close-Enough Traveling Salesman Problem is a generalization of the Traveling Salesman Problem that requires a salesman to just get close enough to each customer instead of visiting the exact location of each customer. In this paper, we propose improvements to an existing branch-and-bound (B &B) algorithm for this problem that finds and proves optimality of solutions by examining partial sequences. The proposed improvements include a new search strategy, a simplified branching vertex selection scheme, a method to avoid unnecessary computation, a method to improve the quality of feasible solutions, and a method to reduce the space requirement of the algorithm. Numerical experiments show that the improved B &B algorithm proves optimality faster on some instances, finds good feasible solutions faster than the best known existing algorithm on instances that cannot be solved to optimality, and uses less space during the solving process.

Automated summary

The paper proposes improvements to an existing branch-and-bound algorithm for the Close-Enough Traveling Salesman Problem. The improvements include a new search strategy, simplified branching vertex selection scheme, methods to avoid unnecessary computation and improve the quality of feasible solutions, and a method to reduce space requirement. Numerical experiments demonstrate that the improved algorithm proves optimality faster, finds good feasible solutions faster, and uses less space.