A branch-and-price algorithm for switch-box routing

Routing in VLSI design concerns the wiring of a chip after the logical modules have been placed. A subproblem occurring in VLSI design is switch-box routing. Switch-box routing can be formulated as the problem of packing Steiner trees in a grid graph. The only previous exact solution method for switch-box routing uses a branch-and-cut approach. The aim of this work was to solve the switch-box routing problem to optimality by using a branch-and-price algorithm based on an IP model where variables represent Steiner trees and where the pricing problem becomes the problem of finding a Steiner tree in a graph. In the primal algorithm, the focal points are branching strategy, pricing strategy, perturbation of the lienar program, and computation of lower bounds to terminate column generation early. The final implementation yielded optimal solutions in the knock-knee model to seven classic switch-box instances, of which three had not been solved to optimality prior to this work.