Collaborative Optimization of Continuous Berth Allocation and Shore Power Scheduling via a Q-Learning-Based Selection Hyper-Heuristic

This study addresses the joint scheduling of continuous berth allocation and shore power connection under uncertainty in ships' power demand. A mixed-integer programming model is formulated to minimize the total cost. The model considers non-overlapping spatiotemporal berth occupation, shore power coverage, ship-shore interface compatibility, and shore power capacity constraints. An uncertainty budget is introduced to reformulate the capacity constraint into a linear robust counterpart. A Q-learning-based selection hyper-heuristic algorithm (QLSHH) is proposed. A hybrid encoding scheme represents berthing positions and shore power decisions. Q-learning dynamically selects low-level heuristic operators, and eight complementary operators are integrated with a structured decoding mechanism. For small-scale instances, the average deviation of QLSHH from the exact solutions of Gurobi ranges from 0.1% to 5.0%. For medium and large-scale instances, QLSHH reduces the total cost by 4.12%-11.65% compared with a genetic algorithm (GA). It outperforms an adaptive large neighborhood search algorithm (ALNS) by 3.75%-25.33%. The average shore power utilization rate remains between 90% and 95.41%. As the uncertainty budget increases, the shore power utilization rate decreases and the total cost increases. A higher shore power capacity limit improves the utilization rate and reduces the total cost. However, the marginal benefit diminishes when the capacity exceeds approximately 4 500 kW. Therefore, the capacity should be configured according to practical electricity demand under a given uncertainty budget.