Evolving Collective Behavior in Self-Organizing Particle Systems

TL;DR

The paper tackles the challenge of engineering collective behavior in self-organizing particle systems (SOPS) by evolving stochastic, memoryless local rules that map extended neighborhoods $N(p,v)$ to movement probabilities $A[N(p,v)]$. The authors introduce EvoSOPS, a genome-based evolutionary framework that evaluates candidate rules across multiple system sizes and trials using a defined fitness $F_b$ that aggregates multi-objective quality measures. Across aggregation, phototaxing, separation, and object coating, EvoSOPS discovers high-fitness, scalable rules that outperform theory-based baselines where available and reveals diverse, interpretable genome strategies, including simple, effective rules for sparse neighborhoods. This work demonstrates the viability of automated design for programmable matter and provides a foundation to bootstrap future theoretical analyses and explorations of new collective behaviors in SOPS.

Abstract

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.

Figures (8)

• Figure 1: (a) A SOPS exists on the triangular lattice $G_\Delta$, but (b) each particle $p$ can only view its extended neighborhood $N(p, v)$ to decide whether to move to an adjacent node $v$.
• Figure 2: The genome representation of an algorithm $\mathcal{A}$ is a list of integer-valued genes indexed by groups of extended neighborhoods. For example, the aggregation genome groups extended neighborhoods by the number of neighbors in their back (blue), middle (green), and front (yellow) regions. Loci vary by behavior. The alleles $i \in \{0, \ldots, 10\}$ correspond to movement probabilities $2^{-i} \in \mathcal{A}$.
• Figure 3: The (near-)optimal configurations used to normalize the quality measures for (a) aggregation, (b) phototaxing, (c) separation, and (d) object coating.
• Figure 4: Best fitness (orange dots), population fitness (mean $\pm$ std. dev., green), and population diversity (mean $\pm$ std. dev., gold) progressions for three EvoSOPS runs per collective behavior. Fitness values for the stochastic approach's aggregation Li2021-programmingactive, phototaxing Savoie2018-phototacticsupersmarticles, and separation Cannon2019-localstochastic algorithms are shown as dark blue dashed lines.
• Figure 5: Mean $\pm$ standard deviation of normalized quality measures $\sum_{i=1}^K w_i \cdot \frac{q_{b,i}(\sigma(n))}{q_{b,i}(\sigma_b^*(n))}$ of 100 SOPS executions of each of the top five fitness genomes per EvoSOPS run for each collective behavior $b$ over a range of SOPS sizes $n$.