A Multi-Ant Colony System for Vehicle Routing Problem with Time-Dependent Travel Times

In this paper, a dynamic road network problem is described where dynamic travel times are considered. We present a method of getting the road time function based on analyzing strategy for solving time dependent vehicle routing problem (TDVRP). Obtain the model based on time-dependent travel speeds which satisfies the "first in first out" property. An experimental evaluation of the proposed model is performed using modify multi-ant colony system. Tow-stage optimizations are considered. The results show that the algorithm is feasible and valid for TDVRP.