2. Urban Mobility in Multi-Modal Networks Using Multi-Objective Algorithms

The multi-modal transportation problem is a type of shortest path problem (SPP). Its goal is to find the best path between two points in a network with more than one means of transportation. This network can be modeled using a weighted directed colored graph. Hence, an optimization method can be applied to find a better path between two nodes. There are some digital applications, like the well-known Google Maps, that present solution to this problem. Most of them choose the best path according to one objective function: the minimum travel time. However, this optimization process can consider multiple objective functions if different user’s interests are treated in the model such as the cheapest or the most comfortable path. In this work, we implemented and compared two different approaches of algorithms with multiple objectives. One of them is an exact method based on Dijkstra’s algorithm added by sum weight method, and the other one is a heuristic approach based on the non-dominated sorting genetic algorithm (NSGA-II). The computational results of the two methods were compared. The comparison shows that the heuristic method is promising due to the low execution time—around 20 s—and the quality of the results. This quality was measured by the closeness of the points found by the two methods in the objective domain. The runtime and the quality of the results can indicate that this modeling is suitable to a real-time problem, for instance, the multi-modal transportation problem.