Automated Design of Graph Search Strategies for Algorithmic Optimization

Large language models (LLMs) have shown great promise for algorithm design and open-ended optimization tasks; however, navigating vast solution spaces over long search horizons remains a persistent bottleneck. Existing approaches rely on tree-based algorithms such as I-MCTS or SELA, and recently graph-based methods like MLEvolve, but remain heavily dependent on human-engineered search heuristics and rigid topologies. Our work introduces the Automated Design of Graph Search Strategies (ADGSS), a novel paradigm that replaces manual search strategy design with automated discovery in code space. We instantiate this framework with Meta Agent Graph Search (MAGS), an evolutionary algorithm driven by an LLM Meta Agent that automatically discovers task-adaptive graph search strategies (GSS). Instead of relying on manually specified search heuristics and topologies, the discovered GSS directly define node selection policies, dynamic graph topologies, and cross-branch information sharing mechanisms. Evaluated on challenging mathematical optimization tasks from the AlphaEvolve benchmark, MAGS-discovered strategies achieve comparable or superior performance to hand-designed strategies including I-MCTS, MLEvolve and OpenEvolve.