2015 Volume 9 Issue 3 Pages 103-109
Many network systems have been applied extensively in the real world, for example, a route guiding system and an optimal path of a network connection to Internet services. Many papers have dealt with networks with two specific nodes. Each edge has criteria, for example distances, costs, and the time required. The optimal path problem aims to obtain the particular path that has a minimum value of criteria. In this paper, we consider the optimal path problem for a three-objective network. In a multi-objective network, edges have two or more criteria. Few cases exist where multi-criteria are optimized at the same time. Thus, it is worth obtaining Pareto solutions as optimal paths in multi-objective networks. An extended Dijkstra's algorithm was proposed to obtain Pareto solutions of two- and threeobjective networks. Even if we use this existing algorithm, obtaining optimal paths is difficult in large networks that have many nodes. Therefore, more efficient algorithms than the extended Dijkstra's algorithm were proposed. However, these algorithms cannot obtain all Pareto solutions. Thus, an efficient and exact algorithm that can obtain all Pareto solutions is required. We describe an essential and effective idea in reducing search space. Using this idea, our algorithms can set bounds to search within less space than the extended Dijkstra's algorithm and obtain all Pareto solutions. For evaluating the algorithms, we conducted numerical experiments. As a result, we show our algorithms are more efficient than the extended Dijkstra's algorithm.
