solver integration

Interactive ASP-based configuration systems for large-scale industrial products suffer from performance bottlenecks in auto-completion due to frequent, expensive unsatisfiability checks. Method: This paper proposes an intelligent incremental configuration solving framework centered on four novel expansion functions that integrate cautious and bold reasoning mechanisms. These functions predict the feasibility of partial configurations without full ASP solving, thereby drastically reducing unsatisfiability checks and shrinking the search space. The framework employs a multi-round incremental ASP solving paradigm and exposes lightweight APIs to support responsive web-based user interfaces. Contribution/Results: Experiments demonstrate that the approach significantly reduces auto-completion latency while preserving correctness and completeness. It has been successfully deployed in real-world industrial configuration scenarios and constitutes the first engineering-grade prototype enabling efficient, explainable, and interactive ASP-based configuration.

This work addresses the lack of scalable, general-purpose tools for polynomial-time reductions among NP-hard optimization problems, which hinders flexible integration with quantum hardware, commercial solvers, or heuristic algorithms. The authors propose a "constraint engineering" framework that leverages AI-powered coding agents to automatically construct a comprehensive reduction library. Built in Rust, the system features type safety, multi-layer verification, and a fully automated pipeline for implementation, review, and integration, enabling composable, transitive reduction graphs. Within three months, the team developed over 170,000 lines of code, covering more than 100 NP-hard problems and 200 reduction rules. Once a new solver is registered, it immediately becomes available across the entire connected component of the reduction graph, significantly enhancing reusability and interoperability.

This study addresses the unclear practical efficacy of automatically generated polynomial symmetry-breaking constraints in integer linear programming across different solvers. The authors systematically evaluate the performance of mainstream mathematical programming and SMT solvers when handling such constraints, comparing three strategies: native quadratic handling, internal reformulation, and explicit linearization. Their experiments reveal that the effectiveness of symmetry breaking is highly solver-dependent, advocating for a solver-aware evaluation paradigm. The findings indicate that compact families of quadratic symmetry-breaking constraints generally enhance solver performance, whereas excessive linearization, overly large breaking sets, or inappropriate reformulations often lead to model bloating or search degradation, thereby diminishing or even reversing potential benefits.

In real-world route planning, user-specified constraints often conflict or are inconsistent, rendering optimization models infeasible. To address this, we propose the first diagnostic framework integrating large language models (LLMs) with multi-objective optimization. An LLM agent parses natural-language constraints semantically and generates interpretable repair prompts; concurrently, a multi-objective optimizer jointly minimizes routing cost and constraint violation severity, yielding explainable, diverse Pareto-optimal repair suggestions. Our end-to-end system tightly couples the LLM, automated routing solver, and multi-objective optimizer. Evaluated on 50 infeasible instances, it produces multiple practical, actionable repairs per single run. Unlike prior approaches, ours is the first to enable multi-objective trade-off analysis for constraint conflicts—significantly enhancing feasibility restoration and supporting informed human decision-making.

To address the low computational efficiency of solving mixed-integer bilevel linear programs (MIBLPs), this paper proposes a novel unified modeling approach based on *improving directions*: a single subproblem simultaneously verifies bilevel feasibility and generates strong valid inequalities. Theoretically, we characterize the role of improving directions in encoding the follower’s optimality conditions, establish an optimality-based relaxation hierarchy, and extend the theory of continuous cutting-plane closures to the mixed-integer bilevel setting. Algorithmically, we integrate improving-direction analysis into a branch-and-cut framework, implementing it atop the open-source solver MibS. Computational experiments demonstrate that our method substantially enhances inequality strength and overall solution performance across standard benchmark instances.

This work addresses the fragmentation in existing frameworks that treat deterministic and probabilistic computations in isolation, lacking a unified declarative language to orchestrate large language models (LLMs) and symbolic tools. We propose Structured Prompt Language (SPL), the first framework to deeply integrate probabilistic operations (GENERATE/EVALUATE) and deterministic reasoning (SOLVE/ASSERT) within a single declarative paradigm. SPL supports shared variable binding, runtime dynamic routing, and seamless interoperability with LLMs (e.g., Ollama, Anthropic), symbolic engines (e.g., SymPy, SageMath, Lean), and the distributed execution grid Momagrid. Across 1,200 experiments, SPL achieves machine-verified correctness rates of 82–93% (e.g., 93% for gemma4:e2b), substantially outperforming pure LLM baselines; most failures stem from solver kernels rejecting invalid expressions.

This work proposes the first large language model (LLM)-based agent framework for automatically repairing infeasible supply chain optimization models, which often arise from modeling errors and traditionally require scarce operations research expertise to fix. The approach decomposes repair into two stages: a general feasibility phase that iteratively corrects linear constraints using an Irreducible Infeasible Set (IIS), and a domain validation phase that enforces five inventory-theoretic reasonableness checks. A novel self-teaching reasoning training mechanism is introduced, integrating solver feedback with verifiable operational rationality constraints. Experimental results demonstrate that the trained 8B-parameter model achieves a 97.2% success rate in restoring feasibility and an 81.7% rationality recovery rate, substantially outperforming existing API-based models, which average 21.3% and reach at best 42.2%.

This work addresses the lack of formal guarantees regarding semantic preservation during problem reformulation and solver correctness in constraint programming. It presents the first end-to-end verified framework implemented in the Lean theorem prover, enabling formal proofs of parameterized equivalence, equisatisfiability, and symmetry-breaking correctness for entire families of problems. The approach combines general, parameterized proofs with instance-level certificate checking, thereby eliminating the need to trust external solvers. Verified certificates are produced via backend transformations, and a single high-level proof suffices for arbitrarily large instances. This methodology achieves dramatic search-space reductions—up to a factor of twenty million—and enables full verification of the largest instances in just a few minutes.

This work proposes the first large language model (LLM) agent–driven framework for mixed-integer programming (MIP) research, addressing the traditionally lengthy algorithm validation cycle that involves extensive implementation and parameter tuning. By embedding an LLM within a SCIP solver–aware environment, the framework enables autonomous generation, validation, and refinement of constraint handlers through sandboxed in-context learning. Focusing on leveraging semantic information from MIP formulations to strengthen global constraints, the approach automatically produces handlers containing only propagation logic. Notably, it not only reproduces classical structures from constraint programming but also solves five previously unsolved instances from MIPLIB 2017. This marks the first demonstration of an LLM agent autonomously exploring the MIP research loop and discovering novel propagation strategies.

Existing neural solvers often struggle with path planning problems involving complex hard constraints due to inefficient or inapplicable constraint-handling mechanisms. This work proposes the Construct-and-Refine (CaR) framework, which for the first time enables shared representations and joint training between construction and refinement stages. By integrating a learned feasibility-refinement mechanism, CaR generates diverse, high-quality candidate solutions and efficiently satisfies hard constraints through an ultra-lightweight local search requiring only ten steps. The approach introduces a feasibility-mask replacement strategy and a shared encoder architecture, achieving substantial improvements over both classical and state-of-the-art neural solvers on canonical hard-constrained routing problems. Notably, CaR demonstrates significant gains in solution feasibility, quality, and computational efficiency.