Statistically Distinct Plans for Multi-Objective Task Assignment

TL;DR

This paper introduces an adaptive sampling algorithm for multi-objective stochastic planning, specifically for multi-robot pickup and delivery, to find statistically distinct, approximately optimal policies that balance multiple competing objectives.

Contribution

It presents a novel adaptive sampling method that efficiently finds a set of statistically distinguishable, near-optimal policies in complex multi-objective stochastic planning problems.

Findings

The method effectively finds diverse trade-off policies in simulations.

It outperforms baseline approaches in robustness and efficiency.

The approach is adaptable to various multi-objective planning problems.

Abstract

We study the problem of finding statistically distinct plans for stochastic planning and task assignment problems such as online multi-robot pickup and delivery (MRPD) when facing multiple competing objectives. In many real-world settings robot fleets do not only need to fulfil delivery requests, but also have to consider auxiliary objectives such as energy efficiency or avoiding human-centered work spaces. We pose MRPD as a multi-objective optimization problem where the goal is to find MRPD policies that yield different trade-offs between given objectives. There are two main challenges: 1) MRPD is computationally hard, which limits the number of trade-offs that can reasonably be computed, and 2) due to the random task arrivals, one needs to consider statistical variance of the objective values in addition to the average. We present an adaptive sampling algorithm that finds a set of policies which i) are approximately optimal, ii) approximate the set of all optimal solutions, and iii) are statistically distinguishable. We prove completeness and adapt a state-of-the-art MRPD solver to the multi-objective 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 multi-objective task assignment and planning problems under uncertainty.