Well-Tuned ILS for Extended Team Orienteering Problem with Time Windows

The Team Orienteering Problem with Time Windows (TOPTW) is the extension of the Team Orienteering Problem (TOP) by incorporating the time window constraints. Given a set of nodes including their scores, service times and time windows, the goal is to maximize the total of scores collected by a fixed number of routes considering a predefined time window during which the service has to start. In this paper, we propose a mathematical model for the TOPTW that incorporates more real-world constraints, such as different total travel time \ budgets, different start and end nodes for routes. This extension is motivated by a real-world application, namely the Tourist Trip Design Problem (TTDP). We then propose an Iterated Local Search (ILS) algorithm to solve both TOPTW and TTDP. While there have been multiple research works on ILS for TOP and variants, the challenge remains in determining appropriate parameter values to solve them. Here we apply Design of Experiments (DOE), namely factorial experiment design, to first screen and rank all the parameters thereby allowing us to focus on the parameter search space of the important parameters. We demonstrate that well-tuned ILS leads to improvements in terms of the quality of the solutions. More precisely, it is able to improve 31 best known solution values on benchmark TOPTW instances. Our proposed algorithm is also effective for solving real-world problem instances of the TTDP within a few seconds on a regular desktop machine.