Efficient separation routines for the symmetric travelling salesman problem I: General tools and comb separation

This is the first of a series of two papers dedicated to efficient separation heuristics for violated inequalities in the context of solving to optimality instances of the Traveling Salesman Problem via branch-and-cut. In this paper we give the basic ideas behind these heuristics and design heuristics for comb separation. The second paper will deal with more complex inequalities such as Clique Tree, Star or Path and Ladder inequalities and give computational results.