A global optimization algorithm for reliable network design

In this paper, we consider the problem of designing reliable networks that satisfy supply/demand, flow balance, and capacity constraints, while simultaneously allocating certain resources to mitigate the arc failure probabilities in such a manner as to minimize the total cost of network design and resource allocation. The resulting model formulation is a nonconvex mixed-integer 0-1 program, for which a tight linear programming relaxation is derived using RLT-based variable substitution strategies and a polyhedral outer-approximation technique. This LP relaxation is subsequently embedded within a specialized branch-and-bound procedure, and the proposed approach is proven to converge to a global optimum. Various alternative partitioning strategies that could potentially be employed in the context of this branch-and-bound framework, while preserving the theoretical convergence property, are also explored. Computational results are reported for a hypothetical scenario based on different parameter inputs and alternative branching strategies. Related optimization models that conform to the same class of problems are also briefly presented.