A mixed integer linear program and tabu search approach for the complementary edge covering problem

In this paper we study a complementary edge covering problem (CECP) as a variant of the total edge covering problem (TECP) which has application in the area of facility location. Unlike TECP, the partial cover of an edge through vertices is allowed in CECP such that in a feasible solution the entire edge will be covered. We propose a new mixed integer linear formulation for the problem. A number of size reduction rules are proposed which speed up getting optimal solution(s). Since the CECP is NP-Hard, a solution method based on tabu search is designed to search for optimal or near-optimal solutions. Computational experiments are carried out to evaluate effectiveness of the proposed mathematical formulation and the modified tabu search algorithm. Results justify that the proposed mathematical model can solves problems with up to 40 vertices and 456 edges optimally. Our computational efforts signify that the proposed tabu search is very effective and can find high quality solutions for larger problems in reasonable amount of time.