A genetic algorithm improvement by tour constraint violation penalty discount for maritime cargo delivery





maritime cargo delivery, tour length, genetic algorithm, tour constraint violation penalty, penalty discount


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.

Author Biographies

Vadim Romanuke, Vinnytsia Institute of Trade and Economics of State University of Trade and Economics, Vinnytsia

Doctor of Technical Sciences, a professor at the Department of Economic Cybernetics and Information Systems of the Vinnytsia Institute of Trade and Economics of State University of Trade and Economics, Vinnytsia, Ukraine.

Andriy Romanov, Odessa National Maritime University, Odessa

Ph.D. student at the Department of Technical Cybernetics and Information Technology named after prof. R.V. Merkt of Odessa National Maritime University, Odessa, Ukraine.

Mykola Malaksiano, Odessa National Maritime University, Odessa

Associate Professor, Doctor of Technical Sciences, the head of the Department of Technical Cybernetics and Information Technology named after prof. R.V. Merkt of Odessa National Maritime University, Odessa, Ukraine.


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Methods of optimization, optimum control and theory of games