Local interactions drive emergent collective behavior, which pervades biological and social complex systems. But uncovering the interactions that produce a desired behavior remains a core challenge. In this paper, we present EvoSOPS, an evolutionary framework that searches landscapes of stochastic distributed algorithms for those that achieve a mathematically specified target behavior. These algorithms govern self-organizing particle systems (SOPS) comprising individuals with no persistent memory and strictly local sensing and movement. For aggregation, phototaxing, and separation behaviors, EvoSOPS discovers algorithms that achieve 4.2-15.3% higher fitness than those from the existing "stochastic approach to SOPS" based on mathematical theory from statistical physics. EvoSOPS is also flexibly applied to new behaviors such as object coating where the stochastic approach would require bespoke, extensive analysis. Finally, we distill insights from the diverse, best-fitness genomes produced for aggregation across repeated EvoSOPS runs to demonstrate how EvoSOPS can bootstrap future theoretical investigations into SOPS algorithms for new behaviors.
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