Multi-criteria shortest path for rough graph

Abstract

Shortest path problem in real life applications has to deal with multiple criteria. This article intends to solve a proposed multi-criteria shortest path problem of a weighted connected directed network whose associated edge weights are represented as rough variables in order to tackle the imprecision. We have exhibited two different approaches to determine the optimum path(s) of the proposed problem. The first approach is the proposed modified rough Dijkstra’s labelling algorithm. The second approach considers the rough chance constrained programming technique to formulate the proposed multi-criteria shortest path problem which is eventually solved by two different methods: the goal attainment method and the nondominated sorting genetic algorithm II. These methodologies are numerically illustrated for a multi-criteria weighted connected directed network. Moreover, the simulated results on similar networks of large order and size are analyzed to show the efficiency of the algorithms.