We consider a problem of minimizing the maritime cargo delivery route length to reduce the delivery cost. In our model, the cost is equivalent to the sum of tour lengths of feeders used for the delivery to cover the route. Formulated as a multiple tr...

The problem of minimizing the cost of maritime cargo delivery is considered. The cost is equivalent to the sum of the tour lengths of feeders used for the delivery. The problem is formulated as a multiple traveling salesman problem. In order to find its solution as the shortest route of the tours of feeders, a genetic algorithm is used where we present two inequalities constraining the tour length of every feeder to lie between the shortest and longest lengths. Apart from the constant tour constraint violation penalty in the genetic algorithm, we suggest a changeable penalty as an exponential function of the algorithm iteration, where we maintain the possibility of the penalty rate to be either increasing or decreasing, whose steepness is controlled by a positive parameter. Our tests show that the changeable penalty algorithm may return shorter routes, although the constant penalty algorithms cannot be neglected. As the longest possible tour of the feeder is shortened, the changeable penalty becomes more useful owing to a penalty discount required either at the beginning or at the end of the algorithm run to improve the selectivity of the best feeder tours. In optimizing maritime cargo delivery, we propose to run the genetic algorithm by the low and constant penalties along with the increasing and decreasing penalties. The solution is the minimal value of the four route lengths. In addition, we recommend that four algorithm versions be initialized by four different pseudorandom number generator states. The expected gain is a few percent, by which the route length is shortened, but it substantially reduces expenses for maritime cargo delivery.

Background. Maritime cargo delivery accumulates over 80% of international transport operations, providing a cost-effective method for global trade, particularly vital for developing countries. However, maritime transportation is heavily dependent on fossil fuels, which results in significant emissions of carbon dioxide (CO2) and creates environmental problems for water resources. To address these issues, this study proposes a solution to optimize maritime delivery route planning projects, and reduce fuel consumption and CO2 emissions. Objective. The objective is to develop an algorithm for planning delivery routes at optimal vessel speed, consisting of a genetic algorithm and a speed optimization step, to reduce fuel consumption and CO2 emissions during maritime transportation. In addition, the results will be validated and the efficiency of the developed algorithm will be compared with a standard genetic algorithm without a speed optimization step. Methods. This article proposes an implementation of an additional step of vessel speed optimization into the algorithm for calculating delivery routes, which can significantly reduce fuel consumption and CO2 emissions without increasing the complexity of the algorithm itself. The route is computed by solving the vehicle routing problem. Results. The study demonstrates that the application of the speed optimization step in the algorithm for planning delivery routes significantly reduces the volumes of fuel consumption and CO2 emissions. Comparison of the experimental results showed that the genetic algorithm with a speed optimization step outperforms the standard genetic algorithm in terms of the volumes of fuel used and CO2 emissions. Detailed analysis of various combinations of fleet composition emphasizes the need to balance the capacity of vessels to achieve maximum efficiency of cargo delivery. While adding more feeders initially reduces overall fuel consumption, overloading the fleet with underutilized vessels can lead to inefficiencies and increased operational costs. The study also considers alternative approaches such as increasing capacity and reallocating vessels among routes, highlighting their impact on fuel consumption and CO2 emissions. Conclusions. The study proposes an improved algorithm for constructing maritime cargo delivery routes using a genetic algorithm with a speed optimization step. Such an algorithm ensures effective management of maritime delivery route planning projects, while significantly reducing fuel consumption and CO2 emissions into the environment. Also, optimal control of the fleet composition ensures the reduction of CO2 emissions due to the efficient use of each vessel.