The set team orienteering problem

Abstract

We introduce the Set Team Orienteering Problem (STOP), a generalised variant of the Set Orienteering Problem (SOP), in which customer locations are split into multiple clusters (or groups). Each cluster is associated with a profit that can be gained only if at least one customer from the cluster is visited. There is a fleet of homogeneous vehicles at a depot, and each vehicle has a limited travel time. The goal of the STOP is to find a set of feasible vehicle routes to collect the maximum profit. We first formulate the problem as a Mixed Integer Linear Programming (MILP) to mathematically describe it. A branch-and-price (B&P) algorithm is then developed to solve the problem to optimality. To deal with large instances, we propose a Large Neighbourhood Search (LNS), which relies on problem-tailored solution representation, removal, and insertion operators. Multiple experiments on newly generated instances confirm the performance of our approaches. Remarkably, when tested on the SOP using benchmarks available in the literature, our B&P method achieves optimality in 61.9% of these instances. This is the first time such a large number of SOP instances are solved to optimality. Our LNS outperforms existing algorithms proposed to solve the SOP in terms of solution quality. Out of 612 considered instances, it improves 40 best-known solutions.