Minimum And Maximum Category Constraints In The Orienteering Problem With Time Windows

We introduce a new variation of the Orienteering Problem (OP), the Minimum-Maximum Category Constraints Orienteering Problem with Time Windows. In the Orienteering Problem we seek to determine a path from node S to node T in a weighted graph where each node has a score. The total weight of the path must not exceed a predetermined budget and the goal is to maximize the total score. In this variation, each Activity is associated with a category and the final solution is required to contain at least a minimum and at most a maximum of specific categories. This variation better captures the problem of tourists visiting cities. For example, the tourists can decide to visit exactly one restaurant at a specific time window and at least one park. We present a Replace Local Search and an Iterated Local Search which utilizes Stochastic Gradient Descent to identify the tightness of the constraints. We perform exhaustive experimental evaluation of our results against state of the art implementations for the unconstrained problem and examine how it performs against increasingly more restricting settings.