Memory-Guided Tree Search with Cross-Branch Knowledge Transfer for LLM Solver Synthesis

TL;DR

MEMOIR introduces a memory-guided tree search framework for LLM-based solver synthesis, significantly improving solution validity and consistency across various combinatorial optimization problems.

Contribution

It proposes a novel two-level memory hierarchy and reflection mechanism enabling cross-branch knowledge transfer in LLM solver synthesis.

Findings

Achieves 96.7% solution validity, a 9.2 point improvement over the strongest baseline.

Improves average normalized scores by 7.3 points at matched execution budgets.

Demonstrates more consistent run-to-run validity than baseline methods.

Abstract

Combinatorial optimization (CO) underlies decision-making from logistics to chip design, where infeasible solutions are operationally unusable and small quality gains translate into substantial economic value. Recent work uses large language models (LLMs) to automate solver synthesis: generating executable solver programs from natural-language specifications. However, existing tree-search and evolutionary agents refine candidate trajectories in parallel without explicit knowledge transfer, reintroducing the same constraint violations and converging on similar algorithm families. We introduce MEMOIR, a memory-guided tree-search framework with a two-level memory hierarchy: branch-local memory preserves execution-grounded refinement details within a branch as it iterates on a single algorithmic design, while global memory stores compressed algorithmic and failure-mode summaries across branches. A reflection step at branch termination distills these summaries, enabling cross-branch transfer without polluting future contexts with low-level debugging traces. Across seven CO problems spanning scheduling, routing, packing, and geometric design, MEMOIR achieves 96.7% solution validity (a 9.2 point gap over the strongest baseline) and improves the average normalized score by 7.3 points at matched per-method execution budget. Over three independent runs on four problems, MEMOIR's run-to-run validity standard deviation is more than an order of magnitude below that of every baseline we evaluated in this setting, suggesting that memory-guided exploration yields consistent improvements rather than reflecting sampling variance.