Min-max regret approach to the optimal path finding problem in stochastic time-dependent networks

A theoretical study was conducted on finding optimal paths in transportation networks where link travel times were stochastic and time-dependent (STD). The methodology of robust optimization was applied as measures for comparing time-varying, random path travel times for a priori optimization. In accordance with the situation in real world, a stochastic consistent condition was provided for the STD networks and under this condition, a mathematical proof was given that the STD robust optimal path problem can be simplified into a minimum problem in a specific time-dependent network. Then a modified label setting algorithm was designed and tested to find travelers´ robust optimal path in a sampled STD network with computation complexity of O(n²∗ e). The computational results confirmed the validity of the Min-Max regret approach and proved that the proposed algorithm can solve for the optimal path in STD networks with a polynomial-time computation complexity. Besides, some other advantages of the Min-Max regret approach are also discussed.