The Shortest Path Problem on a Time-Dependent Network with Mixed Uncertainty of Randomness and Fuzziness

The uncertainty of travel times on a time-dependent network is conventionally considered as randomness or fuzziness. However, sometimes, randomness or fuzziness cannot describe the uncertainty of the travel times on the time-dependent network. In this paper, we introduce a random fuzzy time-dependent network (RFTDN), in which travel times of a time-dependent network are represented as mixed uncertainty of randomness and fuzziness. With these conditions, the resulting RFTDN is far more complex when compared with the known networks. The complexity stems from estimating the length of a path, which is a basic and core issue when analyzing a network. To address this problem, we propose an optimized method that is suitable to cope with the shortest path problem of the RFTDN. The proposed method is realized by means of random fuzzy simulation and a new repair-based genetic optimization. Random fuzzy simulation is used to estimate the random fuzzy functions that describe the length of arcs, whereas the repair-based genetic algorithm is presented for finding the shortest path on the network. Furthermore, the proposed repair-based genetic operators are demonstrated their effectiveness by analyzing running time. A numerical example is also provided to show the robustness of the proposed approach.