Reoptimization of minimum and maximum traveling salesman's tours (février 2006)

Giorgio Ausiello (1) , Bruno Escoffier (2) , Jérôme Monnot (2) , Vangelis Th. Paschos (2)

1 UNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome]
2 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

 In this paper, reoptimization versions of the traveling salesman problem (TSP) are addressed. Assume that an optimum solution of an instance is given and the goal is to determine if one can maintain a good solution when the instance is subject to minor modifications. We study the case where nodes are inserted in, or deleted from, the graph. When inserting a node, we show that the reoptimization problem for MinTSP is approximable within ratio 4/3 if the distance matrix is metric. We show that, dealing with metric MaxTSP, a simple heuristic is asymptotically optimum when a constant number of nodes are inserted. In the general case, we propose a 4/5-approximation algorithm for the reoptimization version of MaxTSP.

Giorgio Ausiello, Bruno Escoffier, Jérôme Monnot, Vangelis Th. Paschos. Reoptimization of minimum and maximum traveling salesman's tours (février 2006). 2006. ⟨hal-00023583⟩