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

Wenda Zhang (), Jason J. Sauppe () and Sheldon H. Jacobson ()
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Wenda Zhang: University of Illinois at Urbana-Champaign
Jason J. Sauppe: University of Wisconsin-La Crosse
Sheldon H. Jacobson: University of Illinois at Urbana-Champaign

Computational Optimization and Applications, 2023, vol. 85, issue 2, No 2, 369-407

Abstract: Abstract 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.

Keywords: Close-enough traveling salesman problem; Branch-and-bound algorithm; Combinatorial optimization; Computation (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10589-023-00474-3

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