Computational study of separation algorithms for clique inequalities

Clique inequalities appear in linear descriptions of many combinatorial optimisation problems. In general, they form an exponential family and, in addition, the associated separation problem is strongly NP-hard, being equivalent to a maximum weight clique problem. Therefore, most of the known (both exact and heuristic) separation procedures follow the decomposition scheme of a maximum clique algorithm. We introduce a new heuristic, aimed at constructing a collection of (violated) clique inequalities covering all the edges of the underlying graph. We present an extensive computational experience showing that this closely approximates the results of an exact separation oracle while being faster than standard heuristics.