Researchers built LACE, a framework that uses language models to create and combine rules for finding strong plans without checking every possible arrangement. Across 36 established optimization benchmarks, it scored higher than earlier language-model methods.
Combinatorial optimization means choosing a strong arrangement from many options while meeting constraints, such as assigning jobs to machines or scheduling tugboats. A heuristic is a practical search rule that looks for good answers without testing every possible arrangement.
Four language-model agents work in sequence to define what information goes in, what counts as a valid answer and which tools check feasibility and score a result. LACE then tests, repairs and selects specialist heuristics, keeping a set that performs well on different cases rather than relying on one general-purpose rule.
Across the 36 problems in CO-Bench, LACE averaged 0.945, compared with 0.870 for the strongest earlier language-model method and 0.571 for direct prompting without a framework. The study reused CO-Bench's input parser and scoring tool, with 10 seconds allowed for each test instance.
On CO-Bench, these are normalized objective scores, not percentages of problems solved: 1 means a result matches the optimal or best-known solution, while an error or infeasible answer scores 0. Each problem's score averages its test instances; the overall score averages all 36 problems.
The team also tested four new container-terminal problems, covering berth assignments and tugboat routing. LACE generated each problem's input and solution formats, plus rules for checking feasibility and scoring a solution, from the task description. On test instances, its generated algorithms scored 0.97–0.99 using those rules; five other language-model methods produced no feasible algorithm. Each instance had a 60-second limit. These were benchmark tests, not live port operations.
The authors make the paper's code, data and figure-reproduction scripts available under the MIT license. For brand-new problems, no external reference verifies whether generated feasibility and scoring rules match the intended constraints and objective; the authors say human review remains necessary.
Image credit: PortCalls Asia, North Port, Manila, via Unsplash. Used under the Unsplash License; illustrative photo, not an image of the LACE study.