Shortest path problems

Consider a city with a large number of roads interconnecting all its core areas, and you need to drive from an area P to an area Q. As the network of road is dense, you can have multiple options to reach area Q; nonetheless, you would desire to take the shortest route. However, the shortest route can have higher traffic; hence, you may now desire to take a new route, which minimizes travel time with a trade-off with distance. Adding further constraints, not all the routes allow bi-directional traffic. In other words, the shortest route needs to satisfy multiple constraints, and then, suggest the best possible route. Analogously, in a graph, each node corresponds to a city, and the edges correspond to the interconnecting roads. The weights of the edges can either be compared to distance or to travel time (based on traffic). These graphs can also be directed or un-directed based on whether a lane allows traffic in a single direction or both. Hence, it is not trivial...