BeNav: Behavior-Space Navigation for Automatic Heuristic Design

Large language models (LLMs) have recently enabled automatic heuristic design by generating and evolving optimization algorithms. However, existing methods mainly search directly in the algorithm space, leaving the direction of exploration largely implicit. This often leads to inefficient search and premature stagnation. In this work, we propose BeNav: a behavior-space navigation approach for automatic heuristic design. We represent each algorithm in an interpretable behavior space characterized by search style, information usage, uncertainty, and adaptivity. The behavior space is then used to explicitly navigate algorithm exploration: behavioral composition guides the generation of algorithms toward intermediate behaviors between two parent behaviors, while behavioral diversion drives the search toward under-explored behavioral regions. These mechanisms are integrated with local exploitation of the current best-performing algorithm to balance exploitation and exploration. Extensive experiments demonstrate that BeNav enables more effective search and consistently outperforms state-of-the-art LLM-driven automatic heuristic design methods.