In collective systems, the available agents are a limited resource that must be allocated among tasks to maximize collective performance. Computing the optimal allocation of several agents to numerous tasks through a brute-force approach can be infeasible, especially when each task's performance scales differently with the increase of agents. For example, difficult tasks may require more agents to achieve similar performances compared to simpler tasks, but performance may saturate nonlinearly as the number of allocated agents increases. We propose a computationally efficient algorithm, based on marginal performance gains, for optimally allocating agents to tasks with concave scalability functions, including linear, saturating, and retrograde scaling, to achieve maximum collective performance. We test the algorithm by allocating a simulated robot swarm among collective decision-making tasks, where embodied agents sample their environment and exchange information to reach a consensus on spatially distributed environmental features. We vary task difficulties by different geometrical arrangements of environmental features in space (patchiness). In this scenario, decision performance in each task scales either as a saturating curve (following the Condorcet's Jury Theorem in an interference-free setup) or as a retrograde curve (when physical interference among robots restricts their movement). Using simple robot simulations, we show that our algorithm can be useful in allocating robots among tasks. Our approach aims to advance the deployment of future real-world multi-robot systems.

翻译：在集体系统中，可用智能体是一种有限资源，必须在任务间进行分配以最大化集体性能。通过暴力方法计算多个智能体在众多任务中的最优分配可能不可行，尤其当每个任务的性能随智能体数量增加而呈现不同缩放特性时。例如，与简单任务相比，困难任务可能需要更多智能体才能达到相似性能，但随着分配智能体数量的增加，性能可能以非线性方式饱和。我们提出一种基于边际性能增益的计算高效算法，用于将智能体最优分配到具有凹可扩展性函数（包括线性、饱和及逆向缩放）的任务中，以实现最大集体性能。我们通过将模拟机器人群体分配到集体决策任务中来测试该算法，其中具身智能体对环境进行采样并交换信息，以就空间分布的环境特征达成共识。我们通过环境特征在空间中的不同几何排列（斑块性）来改变任务难度。在此场景中，每个任务的决策性能要么呈现为饱和曲线（遵循无干扰设置中的孔多塞陪审团定理），要么呈现为逆向曲线（当机器人间的物理干扰限制其运动时）。通过简单的机器人仿真，我们证明该算法在机器人任务分配中具有实用价值。我们的方法旨在推动未来真实世界多机器人系统的部署。