A Solution Approach to the Nonconvex Piecewise Linear Network Flow Problems

In this work, we concentrate on the Nonconvex Piecewise Linear Network Flow Problems (NPLNFP) with discontinuous piecewise linear cost functions. Based on the piecewise linearity and discontinuity of the cost functions, we equivalently transform the NPLNFP into a range of linear Minimum Cost Network Flow Problem (MCNFP) in subdomains, and propose an approach based on a network simplex method (NSM) and a Dynamic Domain Contraction (DDC) technique. Experiment results show that the proposed approach has higher optimization efficiency compared with the other relevant algorithms.