| dc.description.abstract | Traditionally, the minimum cost transshipment problems were simplified as linear cost problems in order to reduce problem complexity. In practice, the unit cost for transporting freight usually decreases as the amount of freight increases. Hence, in actual operations the transportation cost function can usually be formulated as a concave cost function. Recently, some advanced neighborhood search algorithms have been used to solve concave cost network problems. However, they were easily encountered degeneracy problems or confined to local regions, resulting in decreased solution efficiency. Recently, there has been research adopting the genetic algorithm (GA) and the ant colony system algorithm (ACS) for solving concave cost network problems, and obtaining better solutions than some neighborhood search algorithms. The particle swarm optimization algorithm (PSO), a global search algorithm, has led to good results in many applications. In some applications, PSO was even more effective than GA. Since there has not yet been any research applying PSO to minimum concave cost network flow problems, we employ PSO, coupled with the techniques of GA and TA, to develop two global search algorithms for efficiently solving minimum concave cost network flow problems.
The algorithms are designed as follows: First, two heuristics for generating the initial solutions are proposed: one is the random initial solution algorithm and the other is the concave cost initial solution algorithm. Then, two methods for generating feasible solutions are proposed: In the arc-based method, we employed the roulette wheel method in GA to design several ways for selecting and adding arcs into the spanning tree obtained from the previous iteration. In the path-based method, we developed several methods to select supply/demand node pair paths to form a new feasible solution. The flow augmentation algorithm is then used to adjust the non-spanning trees to become feasible spanning trees for both methods. In addition, for the path-based method we developed a strategy for updating the path set by incorporating the new paths from better feasible spanning trees. Followed by the two steps, we developed a new rule for updating the particle velocities, incorporating the inertia weight method and the spanning tree’s characteristics. We also employed the TA technique for updating the feasible solutions. To enhance the depth search we employed a neighborhood search technique. Finally, to evaluate our algorithms we designed a network generator to generate a sufficient number of problem instances. The C++ computer language was used to code all the necessary programs and the tests was performed on personal computers. To evaluate our algorithms, we also tested the recently designed TA, GDA, GA and ACS that solve minimum concave cost network flow problems. | en_US |