Optimizing multi-criteria k-shortest paths in graph by a natural routing genotype-based genetic algorithm

Abstract

k-shortest path problem (KSP) is a more general form of the classical shortest path problem in graph. Its task is no longer to find the shortest path between two vertices, but to find the shortest k paths. So far, the reported KSP-algorithms only considers finding shortest k paths with regard to a single criterion, while far more application scenarios of the KSP require to determine k paths by taking more criteria into account. This article formulates the KSP as a multi-objective optimization problem. In consideration of the problem's property and genetic algorithm's great success in multi-objective optimization, the genetic algorithm is utilized as the optimization tool. The genotype is directly represented as the form of natural routing. In order to make the related genetic operators risk-free, the conception of gene-bank is introduced. And the crossover and mutation are both implemented based on the introduced gene-bank. The proposed genetic algorithm is tested on an undirected graph of 9-vertex/65-edge. The testing result shows that, our proposed algorithm is valid and outperforms some other swarm intelligence-based algorithms in terms of the obtained paths' quality.