A new exact method and matheuristics for bi-objective 0/1 ILPs: Application to FTTx-network design

Heuristics and metaheuristics are inevitable ingredients of most of the general purpose MIP solvers today, because of their contribution to the significant boost of the performance of exact methods. In the field of bi/multi-objective optimization, the interaction between the exact and metaheuristic communities is still fairly low. This article is one of the first steps towards reducing this gap and bringing the attention of both communities to still unexplored possibilities for performance improvements of exact and heuristic multi-objective optimization algorithms. We focus on bi-objective optimization problems whose feasible solutions can be described as 0/1 integer linear programs and propose a new exact method called adaptive search in objective space (ASOS). ASOS combines features of the -constraint method with the binary search in the objective space. In addition, two matheuristics, boundary induced neighborhood search (BINS) and directional local branching are proposed. Their main idea is to combine the features and explore the neighborhoods of solutions that are relatively close in the objective space. Finally, a two-phase ILP-based heuristic framework relying on BINS and directional local branching is proposed. Our new methods are computationally evaluated on two problems of particular relevance for the design of FTTx-networks. Comparison with other known exact methods (relying on the exploration of the objective space) is conducted on a set of realistic benchmark instances representing telecommunication access networks from Germany.