Optimizing berth allocation problem with irregular layout using an improved genetic algorithm under uncertain conditions

This study addresses the berth allocation problem (BAP) in container terminals with irregular layouts under epistemic uncertainty conditions, proposing a mixed-integer linear programming (MILP) model to minimize operational costs via spatial-temporal optimal vessel assignments. To tackle the inherent non-determinism and ambiguity in vessel arrival, handling, departure times, and waiting and delay costs caused by adverse weather, scheduling errors, and equipment failures, a credibility-based fuzzy programming framework with triangular fuzzy numbers is introduced. This approach enables decision-makers to adjust confidence levels (α) for constraint satisfaction, offering flexibility in modeling qualitative uncertainties. An improved genetic algorithm (IGA) is developed, integrating adaptive mutation operators (swap, displacement, and reverse), dynamic mutation rates, various crossover operators, and penalty functions to enhance convergence and solution quality. Additionally, a reduced matrix solution representation is employed to streamline the search space, ensuring scalability for large-scale terminals. Computational experiments demonstrate that IGA outperforms basic genetic algorithms (GA) and simulated annealing (SA) in reducing vessel waiting and delay times, and consequently total operational costs, while maintaining feasibility under complex physical constraints such as berth adjacency, opposition, and blocking. The integration of fuzzy credibility theory with hybrid metaheuristics bridges a critical gap in handling terminals with irregular layouts under uncertainty, which deterministic models inadequately address. This work provides a practical tool for terminal operators to optimize berth utilization and resilience under uncertainty, advancing both theoretical and operational paradigms in maritime logistics.