Improved ADMM-based approach for optimizing intercity express transportation networks: A novel dual decomposition strategy with partial retention of coupling constraints

The rapid expansion of express delivery volume necessitates the development of logistics centers and the optimization of parcel transportation routes between cities within an extensive express transportation network. This study addresses the intercity express transportation network optimization problem (IETNP), which integrates the hub location problem with the multi-commodity flow problem. An integer linear programming model is introduced to represent the IETNP. To leverage the decomposable structure of the IETNP model, an improved Alternating direction method of multipliers (ADMM)-based algorithm is developed for solving the IETNP. A novel dual decomposition strategy is proposed to mitigate the negative effects of numerous coupling constraints on achieving high-quality upper-bound solutions. This strategy, incorporating penalty-term-reduction and multiplier-replacement methods, diminishes the number of penalty terms and the search space, thus enhancing computational efficiency while maintaining solution quality. A Lagrangian relaxation (LR)-based algorithm is employed to generate lower-bound solutions that assess the quality of the upper-bound solutions. Auxiliary constraints are integrated into the dualized formulation to enhance these lower-bound solutions. The effectiveness and efficiency of the improved ADMM-based algorithm are validated using over 100 artificial instances with 10–500 nodes and a realistic instance involving 338 cities. Comparative analysis with an off-the-shelf solver and existing ADMM- and LR-based algorithms reveals that the improved ADMM-based algorithm reduced the upper-bound values by 11.44% on average and by up to 22.09%.