# A Multi-Agent Optimization Approach for Multimodal Collaboration in Marine Terminals
## 6 Conclusions  
This paper introduces a novel approach to enhancing stakeholder coordination by synchronizing truck scheduling and berth allocation in a marine terminal. It presents an appointment system for trucks, building on the existing concept of vessel-dependent time-windows but allowing more flexibility for schedule deviations of vessels. A comprehensive model is proposed to facilitate terminal decision-making through orchestration of all interacting actor groups. Through effective terminal coordination, this model generates solutions that benefit all parties involved. Decision-making is achieved by distributed agents, focusing on representing the requirements imposed by different actors related to berth allocation, truck arrival processing and terminal operations. Additionally, the paper presents a new multi-agent, multi-objective solution methodology based on Prioritized Search for the proposed model, tested against common benchmark algorithms to validate its applicability and effectiveness. The Prioritized Search method demonstrates increased performance by generating more Pareto front contributions and overall better convergence. Across all traffic scenarios, the proposed model is able to predict the optimal performance of the proposed model. Figure 10: Comparison of Pareto fronts and convergence across algorithms for instances of high traffic. Figure 9: Comparison of Pareto fronts and convergence across algorithms for instances of medium traffic. ios, the Prioritized Search algorithm contributed a total of 180 Pareto-optimal solutions, compared to 21 by NSGA-II and 15 by SPEA2, highlighting a substantial advantage in solution discovery. Moreover, it consistently achieved higher hypervolume reaching up to 100% in medium traffic cases and maintained superior convergence efficiency, reaching the best solutions in 25-50% fewer iterations on average. The average runtime per iteration for medium-traffic instances was approximately 0.5 s for NSGA-II and SPEA2, and 0.3 s for the Prioritized Search. However, in higher-traffic instances, this increased to around 0.8 s for NSGA-II and SPEA2, and 2 s for the Prioritized Search. This indicates that while the Prioritized Search is more efficient in less congested scenarios, its runtime scales less favorably under heavier traffic conditions due to the increased complexity of coordinated decision-making. Nonetheless, even at half the number of iterations, the performance of the Prioritized Search in high-traffic instances remained superior, highlighting its effectiveness despite the increased computational cost. The solution algorithm is particularly effective at identifying solutions near the knee of the Pareto front across a range of traffic scenarios, consistently outperforming or matching NSGA-II and SPEA2. Although it incurs higher computational costs, especially in larger instances, this method delivers significantly superior solution quality due to its more focused and efficient exploration of the search space. Notably, it achieves these results while requiring fewer iterations on average, highlighting its ability to converge more quickly to high-quality trade-offs. In a more qualitative manner, the proposed approach highlights the potential of different prioritization techniques in vessel rotation and terminal cargo management through enhanced stakeholder collaboration and coordination. Although the proposed coordination model yields promising results for medium-sized terminals, its applicability to larger ports merits further exploration. Power asymmetry warrants further investigation, as ports, particularly larger terminals, often have established relationships with specific stakeholders. These dynamics could be captured in the model through negotiation protocols or power-sensitive utility functions that reflect varying levels of influence. The model's modular design facilitates such extensions.