Publications of Giovanni Rinaldi

This page shows all publications that appeared in the IASI annual research reports. Authors currently affiliated with the Institute are always listed with the full name.

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IASI Research Report n. 247  (Previous    Next)


Padberg M., Giovanni Rinaldi

A branch-and-cut algorithm for the resolution of large-scale symmetric traveling Salesman problems.

ABSTRACT
We describe an algorithm for solving large-scale instances of the Symmetric Traveling Salesman Problem (STSP) to optimality. The core of the algorithm is a "polyhedral" cutting-plane procedure that exploits a subset of the system of linear inequalities defining the convex hull of the incidence vectors of the hamiltonian cycles of a complete graph. The cuts are generated by several identification procedures that we have described in a companion paper. Whenever the cutting-plane procedure does not terminate with an optimal solution the algorithm uses a tree-search strategy that, differently from branch-and-bound, keeps on producing cuts after branching. The algorithm has been implemented in FORTRAN. We used two different linear programming (LP) packages as the LP solver. We describe the implementation of the algorithm and the interface with one of the LP solvers in sufficient detail to permit the replication of our experiments. We report computational results with up to 42 STSPs with sizes ranging from 48 to 2,392 nodes. Most of the medium-sized test problems are taken from the literature, all others are large-scale real-world problems. All of the instances we consider in our study were solved to optimality by the algorithm in "reasonable" computation times.
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