LLM-Guided Graph Generation for Structure-Based Local Improvement Methods

Large neighborhood search normally selects a random subset of decision variables for iterative optimization. For efficiently solving different problems, researchers tend to design variable selection strategies by taking into account structural features from different domains. In this paper, we build an automatic pipeline that is problem-agnostic to all problems in the MiniZinc format. By prompting an LLM with our semantic guidelines, we guide the LLM to produce a graph generator that maps any instance of a problem type to a uniform weighted graph, where nodes represent decision variables and edges represent constraint relationships. These problem-agnostic graphs guide our structure-based local improvement framework (SLIM) in variable selection. Meanwhile, the weighted graph enables all problem instances to share the same generic graph representation, from which the same graph features can be extracted and used for configuration selection. We evaluated our pipeline on instances across 20 MiniZinc competition problems, finding that algorithm selection achieves a 39.5% average problem-weighted win rate against a one-shot Gurobi baseline, more than doubling the best single configuration (19.3%). Configuration and feature ablation boost the performance further to 44.0%, demonstrating that LLM-based semantic generation enables effective automated structure extraction and feature extraction for constraint optimization.

KNOWPLAN: Knowledge-Driven AI Agents for Smart Degree Pathway Planning

Planning a degree from official university sources requires solving two problems in order. The institution's curriculum must first be reconstructed from catalogs, departmental pages, JSON endpoints, and PDFs that share no schema, and only then can a student-specific path be optimized under prerequisite logic and overlapping requirement constraints. Coupling the two lets each failure mode hide the other, because a planner that drives its own crawling never learns facts its current plan does not need. We present KnowPlan, which enforces an extraction-first boundary and measures the interface between the stages rather than assuming it. CatalogBrowse explores with no access to any user profile. It scores legal actions by lower-confidence expected marginal gain over a finite set of atomic catalog obligations per unit of source access, parses deterministically through platform adapters with a span-constrained clause-to-AST model fallback, and terminates on a closure certificate over index, schema, provenance, and reference completeness instead of a reward threshold. Its output contract is three provenance-linked JSON documents. DegreeMap consumes only those documents. It compiles them into a typed requirement hypergraph and optimizes lexicographically with CP-SAT over hard feasibility, completion horizon, load and risk, personalized utility, and option value, so that each stage optimizes inside the previous stage's proven optimum and stays certifiable within the solver budget. Across a 100-university broad track and a six-school dense track, CatalogBrowse reaches 96.2% inventory recall and 88.7% masked-source recovery at 47% less source access than an exhaustive crawler, DegreeMap holds 100.0% hard feasibility while improving personalized utility by +0.066 over the strongest baseline, and the full pipeline certifies 99.5% of requests with a utility gap to the privileged gold graph of 0.015.