Distributed Task Allocation for Multi-Agent Systems: A Submodular Optimization Approach

TL;DR

To address dynamic task allocation in MAS under resource constraints, this work casts the problem as submodular maximization with a $q$-independent system and introduces the Distributed Greedy Bundles Algorithm (DGBA). DGBA operates in three phases—assignment, communication, and implementation update—yielding a conflict-free allocation in polynomial time with a time complexity of $\\mathcal{O}(N^2+NM)$ and space complexity $\\mathcal{O}(N^2+M)$. Theoretical guarantees include a baseline $1/2$-approximation, with a tighter bound of $\\frac{1}{1+\\kappa_e \\xi((1-\\frac{1}{q})N)}$ under elemental curvature and $q$-independence. The approach is validated via an active observation scenario in a micro-satellite constellation, where DGBA attains higher global utility and lower communication and running times than CBBA and DGA, demonstrating real-time, distributed scalability for NP-hard task allocation problems.

Abstract

This paper investigates dynamic task allocation for multi-agent systems (MASs) under resource constraints, with a focus on maximizing the global utility of agents while ensuring a conflict-free allocation of targets. We present a more adaptable submodular maximization framework for the MAS task allocation under resource constraints. Our proposed distributed greedy bundles algorithm (DGBA) is specifically designed to address communication limitations in MASs and provides rigorous approximation guarantees for submodular maximization under $q$-independent systems, with low computational complexity. Specifically, DGBA can generate a feasible task allocation policy within polynomial time complexity, significantly reducing space complexity compared to existing methods. To demonstrate practical viability of our approach, we apply DGBA to the scenario of active observation information acquisition within a micro-satellite constellation, transforming the NP-hard task allocation problem into a tractable submodular maximization problem under a $q$-independent system constraint. Our method not only provides a specific performance bound but also surpasses benchmark algorithms in metrics such as utility, cost, communication time, and running time.

Figures (4)

• Figure 1: Active Observation Information Acquisition: This scenario involves 5 mobile satellites assigned to observe 5 targets dispersed randomly within the environment. Due to the limited communication constraint, each satellite can only interact with neighboring satellites. Targets with different shades of gray represent varying levels of information value. At each time step, each satellite evaluates the objective function and marginal utility based on its current knowledge of the targets' states and selects the target that offers the maximum marginal utility for observation. The limited communication range can lead to multiple satellites selecting the same target during the task assignment phase (Fig. 1a). To achieve conflict-free task allocation, each satellite continuously updates the information within its task bundles. Additionally, their motion trajectories are incessantly replanned using the optimal control model (Fig. 1b).
• Figure 2: Application Simulation for Active Observation Information Acquisition: The proposed DGBA facilitates dynamic task allocation among 5 satellites, each conducting an independent observation task, and the parameters are set as $\phi_i = 0.3$ and $\lambda=0.8$. Targets with different shades of gray represent varying levels of information value. Given the limited communication range of each satellite ($\phi_i = 0.3$), a target is selected for observation, leveraging limited communication and local information. Each satellite actively approaches its assigned target, continuously updating its state and exchanging real-time information to dynamically optimize its trajectory.
• Figure 3: Performance comparison of CBBA, DGA, and DGBA in terms of global utility and communication time over iterative time steps, with parameters set to $\phi_i = 0.3$ and $\lambda = 0.8$. This figure presents a scenario where 6 satellites are tasked with observing 6 targets in real-time. To mitigate the stochastic nature of the simulations, the results are derived from the mean of ten Monte Carlo simulations, with each simulation averaging over 100 instances both preceding and succeeding each time step. The average global utility at each time step is illustrated in Fig. 3a, used to optimize the multi-agent allocation policy. Moreover, the communication time among satellites at each time step is quantified in Fig. 3b, depicting communication negotiation to achieve a conflict-free allocation.
• Figure 4: Performance comparison of CBBA, DGA, and DGBA in terms of total cost and running time for different numbers of satellites, with parameters set to $\phi_i = 0.3$ and $\lambda = 0.8$. The figure summarizes the statistical results from ten Monte Carlo simulations, each simulating real-time observations of random spatial targets by satellite constellations. The comparative analysis of total cost and running time for each algorithm is presented in Fig. 4a and Fig. 4b, taking into account the varying number of satellites involved.

Theorems & Definitions (26)

• Remark 1
• Remark 2
• Remark 3
• Remark 4
• Lemma 1
• Lemma 2
• Theorem 1
• Lemma 3
• Remark 5
• Theorem 2