A Penalized Sequential Convex Programming Approach for Continuous Network Design Problems

The continuous network design problem (CNDP) has been recognized as one of the most challenging issues in the field of transportation. Existing approaches to solving the CNDP are primarily heuristic without convergence guarantee or suitable for handling small networks because of the inherent nonconvexity arising from its bilevel hierarchical structure. An efficient and convergent approach for solving the CNDP on large networks has been fervently sought. In this paper, we present a novel convergent approach centered around exploiting the inherent convexity-related structure within the CNDP. We first demonstrate that the CNDP can be equivalently formulated as a difference of convex (DC) program with all involved functions being either convex functions or DC functions. Then, by exploiting the DC structure, we give a convex programming approximation for the CNDP and subsequently propose a penalized sequential convex programming approach. Finally, we show that the proposed method can yield an approximately stationary point under commonly used conditions. A numerical study is conducted on some real networks from a reputable network repository for transportation research. The numerical results demonstrate that the proposed method achieves better solutions with faster computational speed, particularly on larger networks, as compared with two heuristic approaches and two convergent approaches.