An ILS Algorithm for the Team Orienteering Problem with Variable Profit

The Orienteering Problem (OP) is a routing problem that has numerous applications in various fields such as logistics and tourism. The objective is to determine a subset of nodes to visit so that the total collected score is maximized and a given time budget is not exceeded. The extensive application of OP has led to many different variants, including the Team Orienteering Problem (TOP) and the Orienteering Problem with Time Windows (OPTW). In this paper, the TOP with Variable Profits (TOPVP) is studied. The main characteristic of the TOPVP is that the amount of score collected from a particular node depends on the duration of stay on that node. We first propose a mathematical model for the TOPVP. We use the AIMMS Outer Approximation (AOA) algorithm to solve modified benchmark instances. We then propose a simple algorithm based on Iterated Local Search in order to solve some modified benchmark instances. Finally, we conclude that ILS is able to produce results which are comparable to those solved by the AOA algorithm.