Using Ant Colony Optimization for Fractional Orienteering Problem with Mandatory Nodes

We study the fractional orienteering problem with mandatory nodes, which aims to design the optimal tourist trip that maximizes the ratio of time spent at places of interest to time spent traveling. Some places of interest are mandatory, while others are optional. Therefore, the problem involves both selecting the optimal set of places to visit and determining the best route between them. We demonstrate how this problem can be efficiently solved using a modified ant colony optimization algorithm. This approach has potential applications in various mobile apps that assist tourists in planning personalized itineraries.