An improved particle swarm optimization algorithm for berth allocation and time-variant quay crane scheduling problem during an emergency - Ran, Lingyu; Liu, Boning; Zhang, Guiqing; Cheng, Yongxi (Expert systems with applications, 2025)
This study investigated the combined continuous berth allocation and time-variant quay crane-scheduling problem in container ports during emergencies (BACASP_TVE), which is a new extension of the classical berth allocation and quay crane assignment and scheduling problem (BACASP). We proposed a bi-objective mixed-integer linear programming formulation for the problem, to minimize the maximum makespan of all ships and total energy consumption. In particular, the energy consumption caused by movement of quay-cranes are first considered in our model. Owing to the complexity of the model, we designed an extended non-dominated sorting genetic algorithm (ENSGA-II), and an improved particle swarm optimization algorithm (IPSO) integrated with a two-dimensional bin-packing strategy and a feasibility re-check strategy (IPSO-BP), to obtain near-optimal solutions. The formulation of the time–space constraints for allocating berth to ships as a two-dimensional bin-packing problem is also first proposed in our paper. A Taguchi experiment was performed to set the parameter combination of the ENSGA-II and IPSO-BP. A total number of 191 randomly generated instances are tested for the validation and robustness of the approaches (ENSGA-II, IPSO-BP, and Gurobi) and the mathematical model proposed. The experimental results confirm the effectiveness of IPSO-BP, which outperforms ENSGA-II and Gurobi in both solution quality and computation time. For an instance with 100 ships, the model is solved for five different combinations of the two objectives, and discussions on the results for the five scenarios and guidance for the port operators are given. The conclusions drawn from this study can be regarded as an operational guide for container operators for making trade-off decisions between the makespan of all ships and energy consumption, when encountered with emergencies.