Adaptive NSGA-III for a tactical bi-objective optimization of integrated berth and quay crane assignment in transshipment operations

In this paper, we address the integrated Berth Allocation Problem (BAP) and Quay Crane Assignment Problem (QCAP) with ship-to-ship (STS) transshipment integral operations, namely BACAP-STS, a complex optimization challenge in container terminal operations. We formulate the BACAP-STS as a bi-objective mathematical model that simultaneously minimizes (1) total ship dwell time and delay penalties, and (2) the total number of quay cranes (QC) assigned. To solve this NP-hard problem, we develop an adapted version of the Non-Dominated Sorting Genetic Algorithm III (NSGA-III), comprising a problem-specific repair mechanism for constraint handling, tailored chromosome encoding for mixed continuous and binary variables, and adapted operators. The algorithm’s performance is evaluated using real-world data from the Port of Le Havre, and we implemented baseline versions of Simulated Annealing (SA) and Tabu Search (TS) following established protocols for a fair comparison under identical experimental conditions. Results demonstrate that our adapted NSGA-III outperforms the benchmark methods in terms of feasibility rate, error metrics (Mean Squared Error (MSE), Root Mean Squared Error (RMSE)), and Pareto front quality (Hypervolume (HV)). Solution quality is further evaluated using the Generational Distance (GD) metric to quantify the proximity of the obtained Pareto fronts to the reference front. Finally, the proposed approach provides port operators with a practical decision-support tool for balancing service efficiency with resource utilization in transshipment operations.