An enhanced sinh cosh optimizer for berth allocation and quay crane assignment considering shared crane

Container terminals are critical hubs in global supply chains, and optimizing their operational efficiency is essential for reducing costs and improving throughput. The Berth Allocation and Quay Crane Assignment Problem considering both the number and specific assignment of quay crane (BACASP) is central to port operations. This paper first formulates a mixed integer linear programming model (MILP) for BACASP with a time-invariant quay crane (QC) assignment. Given the NP-hard nature of the problem, especially for large-scale instances, an enhanced sinh cosh optimizer (ESCHO) is developed by integrating an adaptive reverse learning strategy based on a clustering factor. Furthermore, our research extends the QC assignment to time-variant setting where a shared-crane strategy is introduced for the scenario when there are dense traffic flows and the QC resources are constrained. We simultaneously consider the costs of crane movement and formulate a multi-objective partially time-variant BACASP. To address this complex problem, the non-dominated sorting framework is integrated with ESCHO and propose the NSESCHO. Extensive numerical experiments demonstrate the effectiveness of ESCHO and indicate that the NSESCHO can obtain high-quality Pareto solutions that reduce the waiting time of vessels while maintaining reasonable QC movement costs.