Generalized local branching heuristics and the capacitated ring tree problem

In this paper we present a heuristic framework that is based on mathematical programming to solve network design problems. Our techniques combine local branching with locally exact refinements. In an iterative strategy an existing solution is refined by solving restricted mixed integer programs (MIPs) to optimality. These are obtained from the master problem MIP by limiting the number of variable flips for sets of variables of a partition of the binary variables. We introduce generalized local branching cuts which enforce the latter. Using these concepts we develop an efficient algorithm for the capacitated ring tree problem (CRTP), a recent network design model for reliable capacitated networks that combines cycle and tree structures. Our implementation operates on top of an efficient branch and cut algorithm for the CRTP. The sets of refinement variables are deduced from single and multi-ball CRTP-tailored network node clusters. We provide computational results using a set of literature instances. We show that the approach is capable of improving existing best results for the CRTP.