Abstract
The bi-objective shortest-path problem (BSP) has attracted much attention since its great theoretical significance and wide application. The solution of this problem is to seek for the Pareto-optimal set of paths between two nodes in a graph, in which the edges refer to two attributes. The traditional methods either are highly time-consuming or only find the approximate solutions. In this paper, based on the Physarum Polycephalum model, we propose an algorithm to solve the BSP. By aid of adaptability of the Physarum Polycephalum model, the proposed method can find the multi-shortest paths with a low time consuming. The Pareto-optimal set, obtained from the multi-shortest paths, is the solution of the BSP. To test the performance of the proposed method, we conduct the experiments on some simulative graphs selected from the recently related works. The results show that the proposed method is efficient.
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