With the green transformation of port equipment, tugboat scheduling faces new opportunities and challenges. On the one hand, the deployment of new energy tugboats helps reduce port operating costs and carbon emissions; on the other hand, research on new energy tugboats remains relatively scarce. To address this research gap, a mixed-integer linear programming model for heterogeneous tugboat scheduling under the context of multiple port areas is established based on the characteristics of hybrid tugboats, aiming to minimize port costs, tugboat operation costs, and carbon emission costs. To solve the model, a Multi-Verse Optimization algorithm embedded with heuristic rules is applied, and its effectiveness and accuracy are verified through comparison with the Gurobi solver. In large-scale instances, the proposed algorithm achieved objective values that were, on average, 4% and 3.25% better than those obtained by the GA and IGA, respectively. The research results show that configuring high-power tugboats can effectively reduce ship port costs and tugboat operation costs. However, when the number of high-power tugboats is too large, it may increase operation costs, and at this point, appropriately configuring lower-power tugboats can leverage their low operation cost advantage. An appropriate configuration of a certain number of hybrid tugboats can effectively reduce the total scheduling cost as well as the carbon emission cost of tugboat operations. Meanwhile, the proportion of carbon emission costs in the overall operational cost can be continuously reduced from 8% to approximately 1.51%.