Statistically Distinct Plans for Multiobjective Task Assignment

We study the problem of finding statistically distinct plans for stochastic task assignment problems such as online multirobot pickup and delivery (MRPD) when facing multiple competing objectives. In many real-world settings, robot fleets do not only need to fulfill delivery requests but also have to consider auxiliary objectives such as energy efficiency or avoiding human-centered work spaces. We pose MRPD as a multiobjective optimization problem where the goal is to find MRPD policies that yield different tradeoffs between given objectives. There are two main challenges: 1) MRPD is computationally hard, which limits the number of tradeoffs that can reasonably be computed and 2) due to the random task arrivals, one needs to consider the statistical variance of the objective values in addition to the average. We present an adaptive sampling algorithm that finds a set of policies that 1) are approximately optimal, 2) approximate the set of all optimal solutions, and 3) are statistically distinguishable. We prove completeness and adapt a state-of-the-art MRPD solver to the multiobjective setting for three example objectives. In a series of simulation experiments, we demonstrate the advantages of the proposed method compared to baseline approaches and show its robustness in a sensitivity analysis. The approach is general and could be adapted to other multiobjective task assignments and planning problems under uncertainty.