A dynamic domain contraction algorithm for nonconvex piecewise linear network flow problems

We consider the Nonconvex Piecewise Linear Network Flow Problem (NPLNFP) wh ich is known to be XP-hard. Although exact methods such as branch and bound have been developed to solve the NPLNFP, their computational requirements increase exponentially with the size of the problem. Hence, an efficient he uristic approach is in need to solve large scale problems appearing in many practical applications including transportation, production-inventory mana gement, supply chain, facility expansion and location decision, and logisti cs. In this paper, we present a new approach for solving the general NPLNFP in a continuous formulation by adapting a dynamic domain contraction. A Dy namic Domain Contraction (DDC) algorithm is presented and preliminary compu tational results on a wide range of test problems are reported. The results show that the proposed algorithm generates solutions within 0 to 0.94 % of optimality in all instances that the exact solutions are available from a branch and bound method.