A Joint Optimization Method for Berth Allocation and Energy Scheduling Based on Non-dominated Sorting Dung Beetle Optimizer

The integrated berth allocation and energy scheduling optimization in port microgrids is a system where logistics and energy are closely coupled. In order to balance the efficiency of port logistics transportation and the economic viability of the energy system while ensuring the stable and reliable operation of the port energy system, a multi-objective joint optimization model is established. The model considers both berth allocation of ships and the operating cost of the microgrid. To address the limitations of single-objective solution algorithms, the use of non-dominated sorting dung beetle optimizer (NSDBO) is investigated to solve the multi-objective problem. The non-dominated sorting strategy is introduced into the algorithm to enhance its accuracy and convergence speed. To maintain the diversity and uniform distribution of the population, a congestion distance calculation is introduced to measure the density of solutions at each layer after non-dominated sorting and to reorder the population, obtaining a well-distributed Pareto optimal solutions. This addressed the issues inherent in dung beetle optimization algorithm, such as local optima, poor global search capability, and low convergence precision. While ensuring the uniformity and the population diversity, the computational complexity is reduced. The performance of the improved multi-objective dung beetle optimization algorithm (NSDBO) is tested and compared with the non-dominated sorting genetic algorithm Ⅱ (NSGA-Ⅱ), the decomposition-based multi-objective evolutionary algorithm (MOEA/D), the improved multi-objective particle swarm optimization (IMOPSO), and the crowding distance multi-objective particle swarm optimization (DCMOPSO). The results show that the NSDBO algorithm provides better distribution, convergence, and uniformity. Taking a port in Tianjin as an example, the multi-objective joint optimization model is solved, and several alternative solutions are compared. The results indicate that the proposed berth allocation model distributes ships more evenly across the berths. Compared with the independent optimization of berth allocation and energy scheduling, the waiting time for ships increases by 4 hours, but the total operational costs are decreased by 121 283 Yuan. Compared with the single-objective joint optimization, the total operational costs increased by only 40 225 Yuan, while the waiting time for ships is decreased by 28 hours. This demonstrates that the reasonable joint optimization of berth allocation and energy scheduling can effectively balance the waiting time of ships and the operational costs without significantly increasing the waiting time of ships. The results verify the effectiveness and accuracy of the proposed model and algorithm strategy for berth allocation and energy scheduling problem, highlighting the economic advantages of the optimization model and its outstanding ability to optimize the transportation efficiency of the logistics system.