Code World Models for Parameter Control in Evolutionary Algorithms

Can an LLM learn how an optimizer behaves – and use that knowledge to control it? We extend Code World Models (CWMs), LLM-synthesized Python programs that predict environment dynamics, from deterministic games to stochastic combinatorial optimization. Given suboptimal trajectories of $(1+1)$-${\text{RLS}}_k$, the LLM synthesizes a simulator of the optimizer’s dynamics; greedy planning over this simulator then selects the mutation strength $k$ at each step. On \lo{} and \onemax{}, CWM-greedy performs within 6% of the theoretically optimal policy – without ever seeing optimal-policy trajectories. On \jump{${}_k$}, where a deceptive valley causes all adaptive baselines to fail (0% success rate), CWM-greedy achieves 100% success rate – without any collection policy using oracle knowledge of the gap parameter. On the NK-Landscape, where no closed-form model exists, CWM-greedy outperforms all baselines across fifteen independently generated instances ($36.94$ vs.\ $36.32$; $p<0.001$) when the prompt includes empirical transition statistics. The CWM also outperforms DQN in sample efficiency (200 offline trajectories vs.\ 500 online episodes), success rate (100% vs.\ 58%), and generalization ($k=3$: 78% vs.\ 0%). Robustness experiments confirm stable synthesis across 5 independent runs.