Collaborative optimization of fuel bunkering and voyage speed for routes of alternative fuel bulk carrier

In response to increasingly stringent maritime emission regulations, vessels using alternative fuels—such as Liquefied Natural Gas（LNG） and methanol—are being gradually deployed. However, the number of ports offering bunkering for these new fuels remains significantly lower than those supplying conventional fuels, making route planning and operational management more challenging for alternatively fueled vessels. Shipping companies urgently need to rationally design routes and support the operation of alternative fuel bulk carriers within the context of scarce refueling infrastructure.To this end, this study develops a mixed-integer nonlinear programming（MINLP） model aiming to minimize total emissions, incorporating constraints such as total voyage duration and adjustable speed ranges. To address the nonlinear nature of the model, a heuristic algorithm based on variable neighborhood search is proposed to efficiently obtain nearoptimal solutions. Finally, through case studies under both single-voyage and continuous-voyage scenarios, the collaborative optimization of refueling strategies and speed adjustments is thoroughly analyzed, demonstrating the effectiveness of the proposed model and algorithm.