Analysis of Optimality of Large Language Models on Planning Problems

2026-04-03

AI Summary

This study investigates whether large language models (LLMs) can generate theoretically optimal solutions in classical AI planning tasks, rather than relying on heuristic strategies. Focusing on the Blocksworld domain and its equivalent Path-Star graph formulation, the authors evaluate LLMs’ topological reasoning capabilities under systematically controlled conditions of depth, breadth, and combinatorial complexity. They propose a novel explanatory framework—“algorithmic simulation with geometric memory”—and validate it through experiments combining classical planning benchmarks with reasoning-augmentation techniques. Results demonstrate that reasoning-enhanced LLMs significantly outperform traditional satisficing planners in complex, multi-goal scenarios, achieving performance closely approaching theoretical optimality while maintaining high accuracy even when semantic priors are removed.

Abstract

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.

Problem

• Large Language Models
• AI Planning
• Optimality
• Blocksworld
• Path-Star Graph

Innovation

• Large Language Models
• Optimal Planning
• Algorithmic Simulation
• Geometric Memory
• Path-Star Graph