We present a Spatially Embedded Evolutionary Algorithm where robot individuals exist in a physically simulated 2D environment, must navigate to encounter potential mates, and compete for survival under various spatially-aware selection pressures. Using HyperNEAT evolved neural controllers for ARIEL gecko-inspired quadrupeds in MuJoCo, we investigate how spatial structure fundamentally alters evolutionary dynamics. Our experiments show a modest 4.9% difference in peak fitness between proximity-based and random pairing possibly within stochastic variation while combining spatial parent selection with stochastic death selection produces unstable population dynamics. We discover a continuous phase transition in energy-based selection experiments, with critical zone count separating extinction-dominated and explosion-dominated regimes. Our density-dependent death selection mechanism achieves 97% completion rates but causes fitness decline, revealing a fundamental dilemma where decoupled mechanisms produce bistable dynamics, positively coupled mechanisms create counter-selection pressures, and only deterministic fitness-based selection maintains stability. These findings provide important constraints for future spatial EA design.

翻译：我们提出了一种空间嵌入式进化算法，其中机器人个体存在于物理模拟的二维环境中，必须导航以遇到潜在配偶，并在各种空间感知选择压力下竞争生存。使用HyperNEAT进化的神经控制器控制MuJoCo中基于ARIEL壁虎启发的四足机器人，我们研究了空间结构如何从根本上改变进化动力学。我们的实验表明，基于邻近的配对与随机配对之间的峰值适应度差异仅为4.9%，这可能落在随机变异范围内，而将空间亲本选择与随机死亡选择相结合则会产生不稳定的种群动力学。我们在基于能量的选择实验中发现了一个连续的相变，临界区域数量将灭绝主导和爆炸主导的机制区分开来。我们的密度依赖死亡选择机制实现了97%的完成率，但导致了适应度下降，揭示了一个基本困境：解耦机制产生双稳态动力学，正耦合机制产生反向选择压力，只有确定性基于适应度的选择才能维持稳定性。这些发现为未来空间进化算法的设计提供了重要约束条件。