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In 2018, the International Maritime Organization adopted a plan to reduce greenhouse gas emissions from ships. As a result, ocean carriers and cruise lines are exploring alternative fuels, such as ammonia, which offers zero CO₂emissions. Understanding ammonia-based fuel’s impact on range, speed, and fuel logistics can help companies assess its benefits and limitations. To address this, a mixed-integer non-linear programming model is developed to determine the optimal ships’ routes with the objective of minimizing the total travel time while considering factors such as ship speeds, refueling time, and the non-linear fuel consumption rates. A unique aspect of this study is the consideration of a group of ships with different origins and destinations. To solve the non-linear and NP-hard model, a hybrid genetic algorithm–particle swarm optimization algorithm is developed. The proposed model and meta-heuristics are demonstrated using an actual network consisting of ports around the world. Numerical results from a full factorial design with three factors (number of ships, number of origins, and number of destinations) comparing the travel time differences between using ammonia and conventional fuel indicate that NH₃-fueled ships generally experience longer travel times than jet-propulsion fuel 8-fueled ships because of NH₃’s lower energy density and more frequent refueling requirements. On average, the increase in total travel time is less than 20%. This study serves as a foundation for decision-makers who must also consider additional factors such as economic feasibility, infrastructure costs, environmental impact, and regulatory requirements when assessing ammonia’s viability as an alternative fuel for fleet-wide adoption.