  Due to a substantial growth in the world waterborne trade volumes and drastic
changes in the global climate accounted for CO2 emissions, the shipping
companies need to escalate their operational and energy efficiency. Therefore,
a multi-objective mixed-integer non-linear programming (MINLP) model is
proposed in this study to simultaneously determine the optimal service
schedule, number of vessels in a fleet serving each route, vessel speed between
two ports of call, and flow of cargo considering transshipment operations for
each pair of origin-destination. This MINLP model presents a trade-off between
economic and environmental aspects considering total shipping time and overall
shipping cost as the two conflicting objectives. The shipping cost comprises of
CO2 emission, fuel consumption and several operational costs where fuel
consumption is determined using speed and load. Two efficient evolutionary
algorithms: Nondominated Sorting Genetic Algorithm II (NSGA-II) and Online
Clustering-based Evolutionary Algorithm (OCEA) are applied to attain the
near-optimal solution of the proposed problem. Furthermore, six problem
instances of different sizes are solved using these algorithms to validate the
proposed model.
