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.
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.
Kostis Michailidis, Dimos Tsouros, D. Nguyen et al.· 0 citations
This work proposes an LLM-guided cutting-plane management framework that removes dependence on domain-specific training data and substantially reduces reliance on expert-crafted configurations.
This paper finds that solutions produced at the early search stage of MILP solvers are often structurally close to the solutions found after full-budget search, and proposes a new solver-informed paradigm that shifts the learning target from variable assignment to early-to-final consistency.
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OptiDSL is proposed, a framework that shifts the focus from rigid MILP formulations to domain-specific language (DSL) representations, and enables seamless integration with a diverse library of specialized solvers, ranging from traditional heuristics to modern learning-based methods.
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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.
T. M. Nguyen· Annual Conference on Genetic...· 0 citations
This work introduces an agentic framework that reformulates a constraint model from an open-ended space and establishes correctness empirically rather than by construction, and demonstrates that autonomous agentic methods can support the improvement of constraint models.