# A Multi-Agent Optimization Approach for Multimodal Collaboration in Marine Terminals
## 1 Introduction  
The unprecedented growth of international maritime trade over the last three decades has resulted in significantly increased cargo volumes, heavily affecting marine terminal operations globally. Ports face daily issues such as congestion, air pollution, and delays that hinder their effectiveness and competitiveness. During peak hours, irregular truck arrivals and equipment shortages on the landslide as well as increased vessel traffic on the seaside exacerbate these problems and highlight operational inefficiencies. These problems can create a domino effect on other port activities, further reducing productivity [1]. Port operations inherently involve a multimodal aspect because they serve as critical hubs where different transportation modes, such as maritime, road, rail, converge to facilitate the movement of goods. Hence, the aforementioned issues can be addressed by enabling terminals' transition towards an advanced multimodal transport system thatleverages digital technologies and cooperation across stakeholders. Achieving coordination within multimodal systems requires streamlining administrative boundaries, fostering flexible and polycentric forms of management across modes, and increasing system resilience as emphasized by the Strategic Transport Research and Innovation Agenda [2]. Effective coordination is crucial because of the diverse and often conflicting goals of different stakeholders, varying private and public values, and differing preferences that must be harmonized to optimize the overall system performance. Coordination among stakeholders in a multimodal marine terminal can be achieved across strategic, tactical, and operational levels. At the strategic level, stakeholders, including shipping lines, terminal operators, and logistics companies, can engage in collaborative planning to align long-term goals and investments. At the tactical level, coordination can be enhanced through data sharing among stakeholders and collaborative decision support systems that facilitate day-to-day operational decisions concerning interrelated activities, such as berth allocation, truck scheduling, and cargo processing. Tactical planning assumes some degree of information system integration and many ports already use systems such as Port Community Systems (PCSs). Operational coordination further involves real-time decisions and the interplay of various actors, including not only terminal operators and carriers but also port authorities, tug services, pilots, truck companies, and shippers. This study focuses on the coordination of multimodal terminal operations at a tactical level, an area previously explored in works such as [3; 4]. However, these studies often rely on a fixed set of rules and centralize decision-making around a single actor. This overlooks the inherently distributed nature of coordination in multimodal terminals, where numerous independent stakeholders operate with distinct objectives, constraints, and procedures. Additionally, terminal planning is typically multi-objective, further complicating coordination and raising critical questions about how to ensure fairness and transparency in decision-making processes, issues that remain insufficiently addressed in the literature [5]. These observations highlight a clear gap, namely the lack of distributed modeling approaches that reflect the autonomy of different actors while enabling fair, multi-objective coordination in port terminal operations. To address this, the paper sets as its main objective developing a novel approach to model collaboration among terminal stakeholders in a distributed manner using a Multi-Agent System (MAS) framework. This approach aims to tackle the challenge of synchronizing vessel arrivals with truck scheduling in order to reduce delays and congestion in a coordinated manner.