EVOLUTIONARY STRATEGY

Population-based optimization via mutation, selection, and adaptation

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Rastrigin
Evolutionary Strategies (ES) are derivative-free optimization algorithms inspired by natural selection. Each generation: (1) evaluate fitness of all individuals, (2) select the top μ parents (truncation selection), (3) recombine parents, and (4) mutate offspring by adding Gaussian noise with adaptive step size σ. The key innovation of (1+1)-ES and CMA-ES is adapting σ online — increase when successful, decrease otherwise. ES excel at non-convex, non-differentiable landscapes. OpenAI ES (2017) showed they match RL on many benchmarks using simple parallel noise perturbations. The colored dots show the population evolving toward the landscape's global minimum (bright region).