Energy-Efficient Container Stacking in Terminals: A Multi-Objective Optimization Framework

Efficient container stacking in terminal yards plays a critical role in improving the sustainability and productivity of port operations, as it directly affects unproductive movements, energy consumption, and cargo flows between vessels and the hinterland. This study addresses a multi-objective container stacking problem that jointly considers operational productivity and energy efficiency of yard equipment. A scattered stacking policy can reduce container reshuffles and improve service levels, but may increase energy consumption due to longer travel distances of yard cranes and trucks. Conversely, consolidating containers within smaller yard areas can reduce energy consumption but may result in higher reshuffle rates. To capture this trade-off, two evolutionary multi-objective optimization algorithms, the Pareto Archived Evolutionary Strategy (PAES) and the Non-dominated Sorting Genetic Algorithm II (NSGA-II), are adapted to the container stacking problem through a problem-specific solution representation and tailored initialization procedures, enabling the generation of diverse sets of non-dominated solutions. Extensive computational experiments on 450 instances derived from realistic terminal layouts and operational data are conducted to compare the performance of the two algorithms. The results show that NSGA-II consistently provides higher-quality Pareto front approximations, outperforming PAES by up to 115% on average. In addition, a case study based on 30 real-world instances from the Vigo Container Terminal in Spain demonstrates that the proposed approach can reduce unproductive container movements by approximately 74% while improving energy efficiency by up to 26%, highlighting its potential to support more sustainable container terminal operations.