Submodular Optimization for Coupled Task Allocation and Intermittent Deployment Problems

TL;DR

This paper introduces a greedy algorithm with provable bounds for optimizing coupled submodular problems, exemplified by multi-robot environmental monitoring, achieving near-optimal solutions efficiently.

Contribution

It presents a novel formulation and solution method for coupled submodular maximization problems with matroid constraints, including theoretical guarantees and practical performance analysis.

Findings

The proposed greedy algorithm achieves high-quality solutions with sub-optimality guarantees.

Monte Carlo simulations demonstrate near-optimal solutions in practical scenarios.

The method effectively handles coupled problems in robotics and environmental monitoring.

Abstract

In this paper, we demonstrate a formulation for optimizing coupled submodular maximization problems with provable sub-optimality bounds. In robotics applications, it is quite common that optimization problems are coupled with one another and therefore cannot be solved independently. Specifically, we consider two problems coupled if the outcome of the first problem affects the solution of a second problem that operates over a longer time scale. For example, in our motivating problem of environmental monitoring, we posit that multi-robot task allocation will potentially impact environmental dynamics and thus influence the quality of future monitoring, here modeled as a multi-robot intermittent deployment problem. The general theoretical approach for solving this type of coupled problem is demonstrated through this motivating example. Specifically, we propose a method for solving coupled problems modeled by submodular set functions with matroid constraints. A greedy algorithm for solving this class of problem is presented, along with sub-optimality guarantees. Finally, practical optimality ratios are shown through Monte Carlo simulations to demonstrate that the proposed algorithm can generate near-optimal solutions with high efficiency.