Trading optimality for computational feasibility in a sample gathering problem

The work focuses on a sample gathering problem where a team of mobile robots has to collect and deposit into a storage facility all samples spread throughout the robotic environment. Recent results propose an optimal and off-line solution for this problem, based on a mixed integer linear programming optimization. However, this optimization may fail when there are many robots and/or samples. To overcome this problem, the current paper first formulates a quadratic programming relaxation that, at a price of obtaining sub-optimal robotic plans, is computationally feasible even when the optimal solution fails. Secondly, the paper comparatively analyzes the two possible formulations, in order to draw rules for choosing the appropriate optimization to be employed in a specific case.