SA-DREAM: Utility-Aligned World Modeling for Automatic Algorithm Design

Automated algorithm design increasingly uses large language models to propose solver modifications, but identifying which candidates deserve costly real evaluation remains a key bottleneck. We introduce SA-DREAM, a closed-loop framework that predicts the consequences of structured algorithm interventions before allocating evaluation budget. Each proposal is represented as a typed parent–edit–child transition, grounded with retrieved execution evidence, and scored by its predicted improvement over the current incumbent. Executed outcomes then update the search state and inform subsequent decisions. We evaluate SA-DREAM on five combinatorial optimization families and four scales, covering 20 problem–scale settings. Under a controlled typed-intervention protocol, SA-DREAM achieves an average rank of 1.15, compared with 2.20 for the strongest alternative, against native automated algorithm-design systems, it achieves 1.05, compared with 2.00 for the next best method. SA-DREAM also attains the highest problem-balanced best-so-far quality at every tested real-evaluation budget. Ablations confirm the importance of consequence prediction, retrieval grounding, incumbent alignment, and closed-loop adaptation. Moreover, permuting consequence–action correspondence reduces selected utility from 0.325 to 0.244, demonstrating that the gains depend on action-specific consequence information.