A Constraint Programming Approach for the Team Orienteering Problem with Time Windows

The team orienteering problem with time windows (TOPTW) is a NP-hard combinatorial optimization problem. It has many real-world applications, for example, routing technicians and disaster relief routing. In the TOPTW, a set of locations is given. For each, the profit, service time and time window are known. A fleet of homogenous vehicles are available for visiting locations and collecting their associated profits. Each vehicle is constrained by a maximum tour duration. The problem is to plan a set of vehicle routes that begin and end at a depot, visit each location no more than once by incorporating time window constraints. The objective is to maximize the profit collected. In this study we discuss how to use constraint programming (CP) to formulate and solve TOPTW by applying interval variables, global constraints and domain filtering algorithms. We propose a CP model and two branching strategies for the TOPTW. The approach finds 119 of the best-known solutions for 304 TOPTW benchmark instances from the literature. Moreover, the proposed method finds one new best-known solution for TOPTW benchmark instances and proves the optimality of the best-known solutions for two additional instances