Large Language Model-Guided Optimization

An increasing number of NLP applications interact with large language models (LLMs) through black-box APIs, making prompt engineering critical for controlling model behavior. Recent Automatic Prompt Optimization (APO) methods iteratively refine prompts using model-generated critiques (often called textual gradients), but they predominantly optimize from failures and underutilize information contained in correct predictions, leading to instability and semantic drift. We propose TRAS (Textual Regularization with Aggregated Signals), a feedback-centric framework that is plug-and-play with existing APO search backbones. It retains the standard textual gradient signal from prior work for error correction and introduces a complementary textual regularizer derived from successful predictions to preserve beneficial prompt components. Because both signals are stochastic and can be noisy, we further introduce Monte Carlo Signal Aggregation (MCSA), which samples multiple gradients or regularizers and aggregates them into a single actionable directive, emphasizing consistent, actionable advice while filtering out outliers. Motivated by rapid model churn, we also formalize Automatic Prompt Migration (APM), the practical problem of adapting an expert prompt across model versions or API providers without losing critical instructions. Across standard APO and APM scenarios, our approach consistently outperforms strong baselines, yielding higher accuracy, faster convergence, and lower query cost, while substantially reducing the degradation observed under naive prompt migration.

LLM-based prompt optimization, which uses LLM-provided ``textual gradients'' (feedback) to refine prompts, has emerged as an effective method for automatic prompt engineering. However, its scalability and stability are unclear when using more data in training. We systematically investigate the potential and challenges of scaling training data in textual gradient descent. We show that naively scaling training examples is infeasible due to both explicit context-length limits and an implicit context wall, where long-context degradation yields diminishing returns. Inspired by prior wisdom in stochastic gradient descent, we propose Textual Stochastic Gradient Descent with Momentum (TSGD-M), which reweights updates through momentum sampling, using bootstrapped minibatch validation accuracy as importance weights over historical prompts. To stabilize TSGD and enable effective scaling within a limited context window, TSGD-M carries prior prompts information by \textit{dynamically} exploring the past top performing prompts without expanding input context length. TSGD-M integrates seamlessly into existing prompt optimization frameworks, including TextGrad, DSPy-COPRO, and AdalFlow, and achieves consistent gains across 6 benchmarks.

Search-based software engineering (SBSE), which integrates metaheuristic search techniques with software engineering, has been an active area of research for about 25 years. It has been applied to solve numerous problems across the entire software engineering lifecycle and has demonstrated its versatility in multiple domains. With recent advances in Artificial Intelligence (AI), particularly the emergence of foundation models (FMs) such as large language models (LLMs), the evolution of SBSE alongside these models remains undetermined. In this window of opportunity, we present a research roadmap that articulates the current landscape of SBSE in relation to FMs, identifies open challenges, and outlines potential research directions to advance SBSE through its synergy with FMs. Specifically, we analyze three core aspects: utilizing FMs to enhance SBSE, applying SBSE to advance FMs, and exploring the integration of SBSE and FMs. Furthermore, we present a forward-thinking perspective that envisions the future of SBSE in the era of FMs, highlighting promising research opportunities to address challenges in emerging domains.

Current large language models (LLMs) are constrained by human-derived training data and limited by a single level of abstraction that impedes definitive truth judgments. This paper introduces a novel framework in which AI models autonomously generate and validate new knowledge through direct interaction with their environment. Central to this approach is an unbounded, ungamable numeric reward - such as annexed disk space or follower count - that guides learning without requiring human benchmarks. AI agents iteratively generate strategies and executable code to maximize this metric, with successful outcomes forming the basis for self-retraining and incremental generalisation. To mitigate model collapse and the warm start problem, the framework emphasizes empirical validation over textual similarity and supports fine-tuning via GRPO. The system architecture employs modular agents for environment analysis, strategy generation, and code synthesis, enabling scalable experimentation. This work outlines a pathway toward self-improving AI systems capable of advancing beyond human-imposed constraints toward autonomous general intelligence.

While guided decoding, especially value-guided methods, has emerged as a cost-effective alternative for controlling language model outputs without re-training models, its effectiveness is limited by the accuracy of the value function. We identify that this inaccuracy stems from a core distributional gap: existing methods train static value functions on trajectories sampled exclusively from the base policy, which inherently confines their training to a narrow and suboptimal view of the potential output space. We propose Iterative Value Refinement, a evolutionary framework designed to narrow this gap. It employs Value Exploration to provide a more comprehensive and robust training signal, complemented by Iterative Self-Refinement, which uses the improved value function from one iteration to guide the generation of higher-quality data for the next. Extensive experiments on text summarization, multi-turn dialogue, and instruction following demonstrate the effectiveness of our framework in aligning language models. Our approach not only achieves alignment but also significantly reduces computational costs by leveraging principled value function optimization for efficient and effective control.

Recent work has demonstrated the potential of large language models (LLMs) for program optimization, a key challenge in programming languages. We propose a blackbox adaptation method called Retrieval Augmented Search (RAS) that performs beam search over candidate optimizations; at each step, it retrieves in-context examples from a given training dataset of slow-fast program pairs to guide the LLM. Critically, we find that performing contextual retrieval based on an LLM-generated natural language description significantly outperforms retrieval based on the source code. We also propose AEGIS, a method for improving interpretability by decomposing training examples into ''atomic edits'' that are significantly more incremental in nature. We show that RAS performs up to 2.06$\times$ better than prior state-of-the-art blackbox adaptation strategies on optimizing C++ programs, and that AEGIS performs up to 1.37$\times$ better while making significantly smaller edits. We also show that using RAS improves the mean runtime percentile of Python programs by 10.27 compared to baselines.

Optimization problems are pervasive in sectors from manufacturing and distribution to healthcare. However, most such problems are still solved heuristically by hand rather than optimally by state-of-the-art solvers because the expertise required to formulate and solve these problems limits the widespread adoption of optimization tools and techniques. We introduce a Large Language Model (LLM)-based system designed to formulate and solve (mixed integer) linear programming problems from their natural language descriptions. Our system can develop mathematical models, write and debug solver code, evaluate the generated solutions, and improve efficiency and correctness of its model and code based on these evaluations. OptiMUS is designed as a productivity tool for optimization practitioners who understand the problem domain and can describe it precisely, but seek to accelerate the modeling and implementation workflow. OptiMUS-0.3 utilizes a modular structure to process problems, allowing it to handle problems with long descriptions and complex data without long prompts. Experiments demonstrate that OptiMUS-0.3 outperforms direct-prompting baselines by over 43% on easy and 18% on hard instances. It remains competitive with fine-tuned specialist models on benchmark problems, and outperforms them on real-world case studies (28.6% vs. 0%) where fine-tuned models fail to generalize. Ablation studies show that modular architecture with error correction is central to these gains. A key finding is that system architecture is a stronger driver of performance than model capability. Structured decomposition with targeted error correction enables weaker models to match stronger models under naive prompting, and remains competitive with fine-tuned specialist models without retraining costs.

Molecular optimization, the process of designing molecules with desirable properties, represents a critical challenge in drug discovery. The recent advancements in large language models (LLMs) have opened new opportunities for their integration with traditional molecular optimization algorithms to improve performance. In this work, we propose Molecular Language Model powered Evolutionary Algorithm (Mol-E), an evolutionary algorithm that relies on the generative capabilities of LLMs trained on molecules and molecular properties. Scientific Contribution. Mol-E obtains the highest aggregate Top-10 AUC among the comparable full-23-task results considered here, scoring 17.500 in the task-agnostic regime, in which the oracle is treated strictly as a black box, and 20.551 in the task-informed regime, in which the optimizer receives a fixed semantic description of the objective. Mol-E also improves over the evaluated baselines on multi-property optimization with docking against DRD2, MK2, and AChE.

Self-evolving agents powered by Large Language Models (LLMs) have emerged as a promising direction across diverse domains, including code optimization and scientific discovery, yet their core failure modes remain underexplored. Through a comprehensive empirical study, we identify that the model's reasoning becomes anchored to the local context of current hypotheses, overemphasizing low-level details while neglecting the broader search landscape. As a result, such agents become prone to context pollution and mode collapse, repeatedly revisiting flawed hypotheses and converging on suboptimal solutions. To address this challenge, we propose Progress-Aware Consistent Evolution (PACEvolve), a systematic framework for governing agent memory and search dynamics. PACEvolve overcomes these limitations through three key techniques: (1) Hierarchical Context Management (HCM), which structures historical trajectories while dynamically pruning branches to preserve a high-signal memory state; (2) Momentum-Based Backtracking (MBB), which monitors optimization progress to escape local minima; and (3) a self-adaptive Collaborative Evolution policy (CE) that balances intra-trajectory refinement with inter-trajectory knowledge transfer. By decoupling high-level idea generation from low-level code evaluation, PACEvolve maintains a global view of search momentum and achieves state-of-the-art results across complex evolutionary benchmarks.

The design of reinforced concrete (RC) highway barriers is a safety-critical engineering task that requires strict compliance with regulatory provisions such as the AASHTO LRFD Bridge Design Specifications. Current engineering practice relies largely on manual, iterative, and experience-driven procedures to satisfy complex material, geometric, and mechanical constraints. Although standalone large language models (LLMs) show strong capabilities in knowledge representation and text generation, their direct use in structural engineering design is limited by hallucination, numerical reasoning errors, and insufficient integration with physics-based analysis. To address these limitations, this study proposes a "generation-validation-modification" closed-loop framework for automated RC barrier design based on the multi-agent orchestration capability of AutoGen. The framework integrates specialized agents for parameter generation, mechanics-based calculation, target-interval evaluation, deviation diagnosis, and rule-based design modification. The multi-agent framework (MAF) was evaluated on three barrier testing levels (TL-3, TL-4, and TL-5) using sixty RC barrier designs with different geometric configurations. Three DeepSeek models with different parameter scales, DS-8B, DS-32B, and DS-671B, were investigated. All designs were evaluated according to Section 13 of the AASHTO LRFD Bridge Design Specifications, 10th Edition (2024). Results show that MAF-DS-8B achieves a target-interval compliance rate of 98.3%, while the best-performing standalone LLM, DS-32B, achieves 11.7%. These results demonstrate that multi-agent architectures can improve the reliability, interpretability, and accessibility of AI-assisted engineering design for practical applications.

Quantitative strategy optimization remains largely manual, requiring domain experts to identify weak signals, tune risk-control rules, and repeatedly validate iterative revisions. Large language models can accelerate this process, but directly relying on them to rewrite trading strategies often introduces hallucinated edits, strategy drift, and backtest overfitting. We propose EVOQUANT, a self-Evolving Verifier-guided framework for strategy Optimization in Quantitative trading. Our method utilizes LLMs to deeply diagnose performance bottlenecks, generates semantically controlled candidate edits, selects the best strategy through a multi-stage verification pipeline, and distills optimization experience into reusable knowledge for continual self-improvement. We evaluate our method using seven representative strategies: four from the A-share market and three from the Crypto market. Experimental results show that our method significantly improves the Sharpe ratio across all tested strategies: the average test Sharpe increases from -0.298 to 0.538, and the best-performing strategy achieves a 199% relative improvement. Ablation studies and stress tests under stricter conditions further validate the effectiveness and robustness of the framework. Overall, this work transforms quantitative strategy optimization from costly manual trial and error into an automated and verifiable iterative paradigm, offering a new path for applying large language models to financial strategy research.

Combinatorial scheduling poses a significant challenge for language models, requiring them to identify feasible solutions within exponentially large search spaces while satisfying complex constraints. This challenge is especially pronounced in resource-constrained settings, where larger language models are impractical and selection is limited to smaller models which often fail to preserve feasibility when scheduling directly from natural language. To address these limitations, we introduce SDDL, a neuro-symbolic framework that translates natural-language scheduling problems into compact, solver-aligned representations of tasks, resources, constraints, and objectives, while delegating low-level modeling and search to a deterministic compiler and external solver. On a 300-instance, multi-family subset of scheduling problems, SDDL improves independently verified feasibility for every resource-constrained model tested. The two strongest SDDL configurations reach 55.3% and 28.3%, up from direct-generation baselines of 23.7% and 1.3% and solver-code baselines of 21.7% and 7.0%, with a 0.0% median optimality gap among feasible schedules. By expressing problem structure rather than generating solutions or solver code, SDDL enables smaller models to approach the strongest evaluated direct- and solver-code configurations, including substantially larger frontier models.

Can an agent learn a numerical search strategy through executable practice and then transfer that strategy as text? We study low-budget black-box optimization, where unaided language models remain well below strong classical optimizers. During development, an agent repeatedly writes and evaluates optimizer programs. It then distills the resulting program and practice record once into a 197-word primary Harness A, which is frozen before evaluation. Harness A reduces Gemini Flash regret by 48% in an independent $N=30$ study ($p<.001$), enters the GP-BO performance range on the practice family, and lowers mean regret on all three held-out BBOB landscapes. The same text improves every tested Gemini executor and transfers to Claude Sonnet, reducing regret by 43% and 49% ($p\leq.005$). An independent end-to-end replication produces Harness B, a different program and text at the same performance tier. The same framework also attains the lowest regret on a sealed YouTube reward-tuning production benchmark. Executable practice is thus a viable way to discover a search policy, and language a portable medium for deploying it.

Quadratic Unconstrained Binary Optimization (QUBO) is a central formulation for combinatorial optimization and has gained increasing attention due to its compatibility with quantum, hybrid quantum-classical, and quantum-inspired solvers. However, translating natural-language problem descriptions into correct QUBO formulations remains difficult, requiring the identification of binary variables, constraints, objective functions, penalty terms, and suitable penalty weights. This process is time-consuming and often demands substantial domain expertise. To address this challenge, we propose an end-to-end multi-agent framework that automatically generates QUBO formulations from natural-language problem descriptions, supported by structured or unstructured test cases. To evaluate its performance, We also introduce QUBOBench, a benchmark containing 100 combinatorial optimization problems across 12 application domains, curated from peer-reviewed literature, competitions, and canonical NP-hard problems. Experimental results show that our framework achieves 68% accuracy on QUBOBench, outperforming a direct single-call baseline by 22%. Further analysis identifies iterative self-repair as the most important component contributing to improved performance. The data and code are open-sourced at https://quitttcat.github.io/QuantumQUBOAgent.