Approximate algorithms for the discrete network design problem

The discrete network design problem is one of finding a set of feasible actions (projects) from among a collection of possible actions, that when implemented, optimizes some objective function(s). This is a combinatorial optimization problem that is very expensive to solve exactly. This paper proposes two algorithms for obtaining approximate solutions to the discrete network design problem with much less computational effeort. The computational savings are achieved by approximating the original problem with a new formulation which is easier to solve. The first algorithm proposed solves this approximate problem exactly, while the second is even more efficient, but provides only a near-optimal solution to the approximate problem. Experience with test problems indicates that these approximations can reduce the computational effort by a factor of 3–5, with little loss in solution accuracy.