Trading optimality for computational feasibility in a sample gathering problem

Abstract

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.

Numerical Evaluation of Sample Gathering Solutions for Mobile Robots

“…This section includes two approaches for overcoming this issue. Section 4.1 reformulates the MILP problem (4) as in [34] and obtains a QP formulation. Section 4.2 proposes an IH algorithm, inspired by allocation ideas from [35].…”

“…To the best of our knowledge, none of the mentioned works contains a directly applicable formulation that yields a solution for our specific problem. This work builds on solutions reported in [33][34][35]. In [33] we constructed a MILP problem that solves the minimum time sample gathering problem.…”

“…Besides the MILP formulations, one of the main goals of this research are to provide computationally efficient sub-optimal solutions for the targeted problems. The MILP solution was relaxed to a QP formulation in [34]. Here we also construct an iterative sub-optimal solution inspired by [35] as a QP alternative.…”

“…The problem reduces to a specific case of optimal assignment or task allocation [15,17,18]. The paper combines results from our previous research reported in [34,36,37]. We first build an optimal solution involving a MILP formulation.…”