Improving discrete model representations via symmetry considerations

In this paper, we focus on a useful modeling concept that is frequently ign ored while formulating discrete optimization problems. Very often, there ex ists a natural symmetry inherent in the problem itself that, if propagated to the model, can hopelessly mire a branch-and-bound solver by burdening it to explore and eliminate such alternative symmetric solutions. We discuss three applications where such a symmetry arises: a telecommunications netwo rk design problem, a noise pollution problem, and a machine procurement and operation problem. For each case, we identify the indistinguishable object s in the model that create the problem symmetry and show how imposing certa in decision hierarchies within the model significantly enhances its solvabi lity, while using a popular modern-day commercial branch-and-cut software ( CPLEX 6.5).