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In this work, we investigate the application of a multi-objective genetic algorithm to the problem of task allocation in a self-organizing, decentralized, threshold-based swarm. We use a multi-objective genetic algorithm to evolve response thresholds for a simulated swarm engaged in dynamic task allocation problems: two-dimensional and three-dimensional collective tracking. We show that evolved thresholds not only outperform uniformly distributed thresholds and dynamic thresholds but achieve nearly optimal performance on a variety of tracking problem instances (target paths). More importantly, we demonstrate that thresholds evolved for some problem instances generalize to all other problem instances, eliminating the need to evolve new thresholds for each problem instance to be solved. We analyze the properties that allow these paths to serve as universal training instances and show that they are quite natural. After a priori evolution, the response thresholds in our system are static. The problem instances solved by the swarms are highly dynamic, with schedules of task demands that change over time with significant differences in rate and magnitude of change. That the swarm is able to achieve nearly optimal results refutes the common assumption that a swarm must be dynamic to perform well in a dynamic environment. 

In this work, we use a multiobjective genetic algorithm to evolve agent response thresholds for a decentralized swarm and demonstrate that swarms with evolved thresholds outperform swarms with thresholds set using other methods. In addition, we provide evidence that the effectiveness of evolved thresholds is due in part to the evolutionary process being able to find, not just good distributions of thresholds for a given task across all agents, but also good combinations of thresholds over all tasks for individual agents. Finally, we show that thresholds evolved for some problem instances can effectively generalize to other problem instances with very different task demands. 

Decentralized computational swarms have been used to simulate the workings of insect colonies or hives, often utilizing a response threshold model which underlies agent interaction with dynamic environmental stimuli. Here, we propose a logistics resupply problem in which agents must select from multiple incoming scheduled tasks that generate competing resource demands for workers. This work diverges from previous attempts toward analyzing swarm behaviors by examining relative amounts of stress placed on a multi-agent system in conjunction with two mechanisms of response: variable threshold distribution, or duration level. Further, we demonstrate changes to the general swarm performance’s dependence on paired desynchronization type and schedule design, as the result of varied swarm conditions. 

We argue that heterogeneous threshold ranges allow agents in a decentralized swarm to effectively adapt thresholds in response to dynamic task demands while avoiding the pitfalls of positive feedback sinks. Dynamic response thresholds allow agents to dynamically evolve specializations which can improve the responsiveness and stability of a swarm. Dynamic thresholds that adapt in response to previous experience, however, are vulnerable to getting stuck in sink states due to the positive feedback nature of such systems. We show that heterogeneous threshold ranges result in comparable task allocation and improved stability as compared to homogeneous threshold ranges, and that simple static random thresholds should be considered in situations where agent resources are plentiful. 

In self-organizing multi-agent systems, inter-agent variation is known to improve swarm performance significantly. Response duration, the amount of time that an agent spends on a task, has been proposed as a form of inter-agent variation that may be beneficial. In the biological literature, variability in agent response duration in natural swarms for desynchronizing agent actions has been discussed for some time. This form of variation, however, is not well understood in artificial swarms. In this work, we explore inter-agent variation in response duration as a desynchronization technique. We find that variation in response duration does desynchronize agent behaviors and does improve swarm performance on a two-dimensional tracking problem in which the swarm must push a tracker, staying as close as possible to a moving target. By preventing agents from reacting identically to task stimuli and keeping some agents on task longer, response duration helps smooth the swarm’s path and allows it to better track the target into path features such as corners.