Analysis of Optimality of Large Language Models on Planning Problems

Classic AI planning problems have been revisited in the Large Language Model (LLM) era, with a focus of recent benchmarks on success rates rather than plan efficiency. We examine the degree to which frontier models reason optimally versus relying on simple, heuristic, and possibly inefficient strategies. We focus on the Blocksworld domain involving towers of labeled blocks which have to be moved from an initial to a goal configuration via a set of primitive actions. We also study a formally equivalent task, the generalized Path-Star ($P^*$) graph, in order to isolate true topological reasoning from semantic priors. We systematically manipulate problem depth (the height of block towers), width (the number of towers), and compositionality (the number of goal blocks). Reasoning-enhanced LLMs significantly outperform traditional satisficing planners (e.g., LAMA) in complex, multi-goal configurations. Although classical search algorithms hit a wall as the search space expands, LLMs track theoretical optimality limits with near-perfect precision, even when domain-specific semantic hints are stripped away. To explain these surprising findings, we consider (and find evidence to support) two hypotheses: an active Algorithmic Simulation executed via reasoning tokens and a Geometric Memory that allows models to represent the $P^*$ topology as a navigable global geometry, effectively bypassing exponential combinatorial complexity.