Valid Inequalities and Separation for the Symmetric Sequential Ordering Problem

The sequential ordering problem (SOP) is the generalisation of the asymmetric TSP in which the tour must obey given precedence relations between pairs of nodes. Many solution approaches have been devised for the SOP, but the version with symmetric costs, which we call the SSOP, has received very little attention. To fill this gap, we present a new 0-1 linear programming formulation for the SSOP, and derive several new families of strong valid inequalities for it, along with efficient separation routines. Some encouraging computational results are also presented. One remarkable result is that, in the case of the SSOP, there exists an efficient separation routine for the so-called simple source-destination inequalities. No such separation routine is known for the SOP, or indeed for the symmetric or asymmetric TSP.