## 1 Introduction
Against this backdrop of specific and evolving regulatory challenges, including changing cost structures, environmental rules, and geopolitical pressures, existing research has extensively studied a wide range of operational decisions in liner shipping, particularly in areas such as multi-route scheduling, fleet deployment under cost variability, ship speed optimization, and port time windows. Numerous studies develop optimization models for ship routing and scheduling, addressing both industrial and tramp segments as well as liner shipping, and often tackle multi-ship, multi-route scenarios, variable ship speeds, and constraints arising from port schedules and ship heterogeneity [11; 12; 15; 16; 17]. These frequently employ mathematical programming techniques like mixed-integer linear programming (MILP), mixed-integer nonlinear programming (MINLP), and advanced heuristic methods to handle large-scale, realistic instances [12]. Given the inherent trade-offs in liner shipping operations between economic performance, service quality, energy consumption, and environmental regulations, multi-objective optimization frameworks have gained prominence for addressing these complex decisions [18]. These frameworks aim to identify effective operational strategies by considering divergent objectives like cost minimization, profit maximization, service coverage, and on-time delivery, with much research dedicated to finding robust solutions in these multifaceted decision environments [18; 19; 20]. Separately, the critical role of demand acceptance in revenue management is also well established, with numerous studies addressing its optimization, particularly for scenarios involving transit-time-sensitive demand [21]. These studies highlight effective strategies for maximizing revenue based on demand characteristics. While both multi-objective optimization and demand acceptance are _individually_ well explored, their _integration_ within comprehensive models for optimizing ship routing, fleet deployment, and service design, particularly for models that must also account for dynamic slot allocation alongside periodic demand structures or heterogeneous fleet operations, represents an area with ongoing research opportunities [22]. In tackling such comprehensive models, they must incorporate complexities like ship heterogeneity, multi-objective trade-offs, and general regulatory constraints [12; 17]. In addition, the latest U.S. measures underscore a more profound research gap: while operational decision making under general regulatory and cost constraints has been widely examined, most existing research on fleet deployment and ship routing does not fully account for the specific impacts of regulatory measures like Section 301 surcharges, which are based on a ship's country of build or ownership [23]. Most prior studies on ship routing and fleet deployment assume homogeneous fleets or do not explicitly model the bi-objective trade-offs, indicating a clear lack of integrated models that simultaneously optimize heterogeneous ship routing in the context of specific and impactful regulatory shocks such as the Section 301 surcharges. Even when general regulatory constraints are considered, analyses rarely examine the specific operational impacts of surcharges differentiated by ship build country on route selection, ship assignment with particular attention to China-built ships compared to others, and transport demand acceptance strategies within a unified bi-objective optimization framework. Such a framework should incorporate both operational heterogeneity and policy-driven risks. There is a clear need for new models to investigate the consequences of these policies, especially regarding global fleet renewal, cross-border cargo flows, and the resilience and adaptability of international shipping networks amid shifting regulatory landscapes. To address these gaps comprehensively, this study formulates a heterogeneous ship routing and demand acceptance (HSR-DA) problem under the influence of U.S. regulatory surcharges on China-built ships.