IR2Solve: Structured Intermediate Representations for Cost-Efficient Optimization Autoformulation

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

Combinatorial problems appear in numerous industrial applications. A common approach is to formulate these problems as declarative constraint models that can subsequently be compiled to and solved by a range of back-end solvers. Recent work shows that Large Language Models (LLMs) can produce correct models from natural language, but even a correct model can be expensive to solve because performance remains sensitive to modelling choices. In this work, we investigate whether LLMs can automate performance-oriented model reformulation. Inspired by Automatic Heuristic Design (AHD), we use an evolutionary framework in which an LLM proposes candidate reformulations that are verified and benchmarked against the user-defined baseline model. We compare AHD-adapted search strategies that control which prior attempts, instructions, and measured feedback enter each prompt. Existing retention strategies prioritize recency or performance, but do not explicitly diversify the context. To cover this gap, we introduce Profile-Diverse Retention (PDR), which applies Maximal Marginal Relevance (MMR) to instance-level runtime vectors to retain behaviourally diverse attempts. We systematically evaluate the strategies on eight CSPLib problems using validation-based final model selection. The results show that: (i) iterative reformulation can produce substantial held-out speedups; (ii) strategies that keep the retained context diverse outperform those that retain only recent or the fastest attempts; and (iii) validation-based selection improves the held-out speedup of every strategy.

MetaInfer: A Knowledge Only LLM Inference Engine Generator SKILL Toolbox

As LLM technology advances, the space of model families, compute hardware, quantization schemes, parallelization strategies, and specialized optimization kernels continues to expand, sharply increasing the code complexity and maintenance cost of general-purpose inference frameworks. Conventional software engineering uses multiple layers of abstraction to support diverse application scenarios, but these abstractions also increase system complexity and may introduce additional performance overhead. This paper presents metainfer, an'LLM-as-Compiler'approach in which users specify only the runtime constraints of an inference program. An LLM-driven multi-agent collaboration system, coupled with a contract knowledge base, then automatically generates a compact customized inference framework that satisfies these constraints. We evaluate metainfer from three perspectives: the effect of source-code reference, the runtime behavior and performance profile of engines generated under the zero-reference constraint on CKB-covered targets, and knowledge-base evolution for new model and platform scenarios. The results show that metainfer organizes generation constraints, validation feedback, and knowledge consolidation into a continuous closed loop, enabling runnable customized inference solutions to be generated from explicit knowledge. The code is publicly available at https://github.com/MetaInfer/MetaInfer.

Optimization and Constraint Modeling using LLMs with a Retrieval Augmented Generation Process

Both optimization modeling and constraint modeling are non-trivial problems requiring deep domain expertise and proficiency in modeling formalism languages. Despite their importance across logistics, healthcare, and supply chain management, current large language models regularly produce structurally inconsistent or incomplete optimization formulations, particularly in combinatorial settings. This paper evaluates whether a Retrieval-Augmented Generation pipeline built on a curated synthetic dataset can meaningfully improve LLM optimization modeling performance. A total of 500 optimization problems were synthesized using seed descriptions from the Text2Zinc dataset and professional personas created using an LLM, specified in JSON and associated with validated Python solver scripts. These problems were encoded in a Chroma vector database. For each inference problem, semantically similar problems were retrieved and used as contextual guidance for a LangChain LLM agent. Three benchmark testbeds were used to evaluate the proposed pipeline under the Qwen 3 30B Instruct model. Accuracy rose from 40% to 72% on NL4OPT, 40% to 56% on MAMO Easy, and 32% to 56% on MAMO Complex. The use of semantically validated synthetic examples greatly improves both solution accuracy and structure. The combination of synthetic dataset generation with retrieval augmentation provides an effective alternative to fine-tuning, suggesting that domain-specific synthetic corpora paired with retrieval augmentation can serve as a practical pathway for deploying LLM-based optimization tools in real-world decision-support contexts without costly model retraining.

BRIDGE: Building Representations in Domain-Guided Program Synthesis

Uncertainty-Aware Test-Time Search for Optimization Problem Solving

Automatically solving optimization problems from natural language descriptions with both efficiency and reliability is highly desirable but remains challenging. Language model hallucinations and the limited availability of labeled datasets often result in misaligned formulations, code errors, and feasibility failures. We pro-pose UMCTS , an Uncertainty-aware Monte Carlo Tree Search framework that combines the language understanding capability of large language models with the reliability of well-established solvers. UMCTS structures the solution process into four stages: global instruction, assumptions, mathematical formulation, and solver code generation. It employs Monte Carlo Tree Search with semantic-equivalence pruning, prior-guided exploration, and solver-based feasibility checks. An LLM judge provides numerical reward signals, qualitative error information, and uncertainty estimates. These signals are backpropagated to guide the search and flag unreliable outputs. Across six public benchmarks, UMCTS achieves state-of-the-art solution accuracy and improves efficiency by reducing token usage.

OptGraph: Large Language Models Enhanced Evolutionary Optimization Via Graph Retrieval-Augmented Generation

Large language models (LLMs) have emerged as a powerful tool for automated evolutionary optimization, but existing methods remain limited in pattern reuse, error-aware refinement, and retrieval robustness across diverse tasks. To address these limitations, we propose OptGraph, the first optimization agentic workflow that introduces graph retrieval-augmented generation (GraphRAG). Specifically, OptGraph first constructs reusable experience as a typed graph, capturing the relationships among modeling patterns, problem formalization, implementation details, and error corrections. In the inference stage, OptGraph leverages graph neighborhood information to enrich retrieved knowledge, providing structured context to improve modeling, verification, and iterative refinement. Moreover, OptGraph supports adaptive knowledge updates, enabling the distillation of execution traces and verification feedback into reusable graph knowledge without ndertaking LLM parameter tuning. Extensive experiments on benchmark datasets show that our proposed OptGraph achieves an average exact accuracy 8.9% higher than the state-of-the-art prompt-based automated optimization frameworks. Our code has been made available at https://github.com/xianchaoxiu/OptGraph.