LLM-Guided Evolutionary Search for Constraint Model Reformulation to Improve Solver Efficiency

Improving Constraint Models with LLM Agents

The runtime of Constraint Programming (CP) solvers is highly sensitive to modeling choices, such as symmetry breaking, implied constraints, global constraints, constraint reformulation, and variable representation. Improving these constraint models has traditionally required human expertise, and existing automated reformulation systems are restricted to a predefined library of hand-crafted transformation rules. We introduce an agentic framework that instead reformulates a constraint model from an open-ended space and establishes correctness empirically rather than by construction: a Large Language Model (LLM) agent, given a model and three training instances, proposes alternative formulations, validates each by injecting its solution back into the original model, and diagnoses and repairs failures, returning the best variant it finds in a median of about fifteen minutes. The models are expressed in the CPMpy modeling library, and each proposed model is evaluated on three larger test instances. Across nine combinatorial optimization problems, the generated models outperform the originals on 21 of 27 test instances, and on some problems solve more than two orders of magnitude faster. A comparison against non-agentic baselines that reuse the same validation and selection tools indicates that the gains stem from the agent's iterative diagnosis and repair, not merely from sampling several candidates. These results demonstrate that autonomous agentic methods can support the improvement of constraint models.

From LLM Suggestions to Lean Proofs: Verified Redundant Constraints for MiniZinc

Partition to Evolve: Niching-enhanced Evolution with LLMs for Automated Algorithm Discovery

This work proposes a general LES framework that incorporates feature-assisted niche construction within abstract search spaces, enabling the seamless integration of niche-based search strategies from evolutionary computation and introduces PartEvo (Partition to Evolve), an LES method that combines niche collaborative search and advanced prompting strategies to improve algorithm discovery efficiency.

LLM Policy Induction for Heuristic Search Control: A Trace-Driven ALNS Framework

Nowadays, large-scale combinatorial optimization problems such as Job Shop Scheduling (JSP), Flexible Job Shop Scheduling (FJSP), and Flow Shop Scheduling (FSP) are widely encountered in manufacturing, logistics, and service systems. Despite substantial progress in metaheuristic frameworks, the design of effective search control policies, including neighborhood selection, move size, acceptance criteria, and diversification strategies, remains heavily reliant on handcrafted rules and domain expertise. In this paper, we propose a trace-driven LLM-controlled Adaptive Large Neighborhood Search (ALNS) framework for scheduling problems, in which large language models (LLMs) are employed exclusively during a policy induction phase to learn high-level search control strategies from historical optimization traces. Rather than evaluating candidate solutions or directly manipulating objective functions, the LLM infers symbolic control policies that map summarized search-state features to ALNS control actions. The induced policy is then integrated into a classical ALNS solver and executed without further LLM involvement. We evaluate the proposed approach on standard benchmark instances of JSP, FJSP, and FSP. Experimental results demonstrate that the proposed framework consistently outperforms classical ALNS baselines and several competitive metaheuristic methods in terms of solution quality and convergence speed.

MILP-Evo: Closed-Loop Fully Automatic Design of MILP Solvers

Machine learning methods have shown that data-driven policies can accelerate mixed-integer linear programming (MILP) solvers, but many such approaches remain difficult to inspect, adapt, and deploy because the learned policy is represented as an external predictor or other opaque model. By contrast, explicit solver logic is easier to understand and integrate, but is usually hand-designed rather than learned from solver feedback. We study whether the automatic design of MILP solver logic can instead be cast as LLM-guided closed-loop search over executable white-box components evaluated directly by end-to-end solver behavior. To this end, we propose a closed-loop program evolution framework for MILP solver auto-design, implemented through PySCIPOpt, and instantiate it on the joint design of a cut selector and a branching rule. Candidate programs are iteratively generated, loaded into SCIP, and evaluated by direct execution on MILP instances, with the resulting feedback guiding performance-based selection, targeted repair, diagnostic reflection, and diversity-aware population maintenance. The method outputs explicit solver components that can be inspected, modified, and deployed within standard solver workflows. Across four benchmark families, we find that LLM-guided program evolution can discover competitive domain-specialized policies in several settings.

Semantic Mutation via LLMs: A Hybrid Approach to Evolutionary Program Synthesis

This work proposes a hybrid framework that integrates Large Language Models into GP in two complementary roles: as a semantic mutation operator that proposes non-local program rewrites during evolution, and as a post-evolution repair that iteratively refines single failed programs after search terminates.