A two-stage method for doubly resource constrained elementary shortest path problems

Abstract

The resource constrained shortest path problem (RCSPP) has been extensively studied. However, its more general version, the doubly resource constrained (elementary) shortest path problem (DRCESPP), is usually not concerned and no exact solution algorithm has been found in the literature. In this work, an exact two-stage method is proposed for solving the DRCESPP. For leveraging resource lower limits, an estimation to the maximum resource consumption of all elementary source–destination paths is proposed in the first stage. This makes the network be reduced more significantly and the algorithm be terminated in the first stage. By introducing an effective search direction into the conventional Pulse algorithm, a LB-first Pulse algorithm is proposed in the second stage to find the exact solution from the reduced network output in the first stage. Extensive computational experiments on various test instances are conducted. The numerical results show that the maximum resource consumption estimation method and the improved Pulse algorithm are effective, and the proposed two-stage method outperforms the Pulse algorithm in solving complex instances.