Gotta (efficiently) catch them all: Pokémon GO meets Orienteering Problems

In this paper a new routing problem referred to as the Generalized Clustered Orienteering Problem (GCOP) is studied. The problem is motivated by the mobile phone game Pokémon GO, an augmented reality game for mobile devices holding a record-breaking reception: within the first month of its release, more than 100 million users have installed the game on their device. The game’s immense popularity has spawned several side businesses, including taxi-tours visiting locations where the game can be played, as well as companies offering to play the game for users during times when they cannot. The GCOP applies – but is not limited to – these business cases. Additional applications arise naturally in typical operative transportation problems which necessitate the availability of tours that are both time-effective and profitable. The studied problem combines aspects from several well-known routing problems, including the Traveling Salesman Problem (TSP), the Generalized TSP, and the Orienteering Problem. In order to solve the GCOP to optimality, a polynomial-sized Mixed-Integer Linear Programming (MIP) formulation and an exponential-sized MIP formulation are presented. Based on these formulations, branch-and-bound (B&B) and branch-and-cut (B&C) algorithms are developed. The framework is further enhanced with valid inequalities, a lifting procedure for strengthening inequalities, as well as initialization and primal heuristics. The computational performance of the proposed approaches is assessed in an extensive computational study, using real-world instances that combine crowd-sourced data associated with the Pokémon GO game with street maps of three European cities, as well as instances derived from the TSPLIB testbed.