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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Computing compatible tours for the traveling salesman problem
AU - Fortini, M
AU - Letchford, A N
AU - Lodi, A
AU - Wenger, K M
PY - 2011
Y1 - 2011
N2 - We consider the following natural heuristic for the Symmetric Traveling Salesman Problem: solve the subtour relaxation, yielding a solution x*, and then find the best tour x-bar that is 'compatible' with x*, where compatible means that every subtour elimination constraint that is satisfied at equality at x* is also satisfied at equality at x-bar. We prove that finding the best compatible tour is NP-hard and show that the tour can have a cost approaching 5/3 that of the optimal tour. We then describe a branch-and-cut algorithm for computing the best compatible tour, and present extensive computational results for TSPLIB instances. It turns out that, in practice, the tour is usually of very good quality. Moreover, the computational effort for computing the compatible tour is considerably smaller than that of solving the full problem with the best available software, i.e., Concorde.
AB - We consider the following natural heuristic for the Symmetric Traveling Salesman Problem: solve the subtour relaxation, yielding a solution x*, and then find the best tour x-bar that is 'compatible' with x*, where compatible means that every subtour elimination constraint that is satisfied at equality at x* is also satisfied at equality at x-bar. We prove that finding the best compatible tour is NP-hard and show that the tour can have a cost approaching 5/3 that of the optimal tour. We then describe a branch-and-cut algorithm for computing the best compatible tour, and present extensive computational results for TSPLIB instances. It turns out that, in practice, the tour is usually of very good quality. Moreover, the computational effort for computing the compatible tour is considerably smaller than that of solving the full problem with the best available software, i.e., Concorde.
KW - traveling salesman problem
KW - heuristics
KW - branch-and-cut
U2 - 10.1007/s12532-010-0021-5
DO - 10.1007/s12532-010-0021-5
M3 - Journal article
VL - 3
SP - 59
EP - 78
JO - Mathematical Programming Computation
JF - Mathematical Programming Computation
SN - 1867-2957
IS - 1
ER -