A Proposal of a Genetic Algorithm for Fixed-charge Transportation Problem and Related Numerical Experiments

Abstract

Fixed-charge transportation problem (FCTP) is one of the generalizations of transportation problems (TPs), which are fundamental problems of logistics. Since it is shown that FCTP is NP-hard, it is thought that there exists no hope in finding a polynomial time algorithm through which an optimal solution is always obtained. In this paper, we propose a genetic algorithm for solving FCTP. By reducing the number of destinations to which products are transported by one supplier, the fixed charge can be saved. Therefore, in our proposed method the priority levels on delivery route are generated based on the property of the instance. A subinstance is selected randomly, and the transportation plan is partially reconstructed by obeying the selected priority level. By reconstructing of the transportation plan, a local search on the parent is realized. To introduce plural priority levels is effective for generating the various children. In our proposed mutation, the good characteristics of the parents can be inherited by the children. Moreover, our mutation displays great ability as the local search. Therefore, in our method, a crossover operation is not used, and children are generated only by our mutation. In the respect of execution time, there exists the advantage of not applying the crossover operation. The effectiveness is shown by numerical experiments where our method is compared with existing methods.