Efficient human-database interaction is a core problem in software engineering. Text-to-SQL (Text2SQL) tackles this by mapping natural language questions to executable SQL queries, enabling automatic SQL synthesis and reliable interaction. Although large language models (LLMs) have advanced significantly, current approaches struggle with poor transferability to open-source LLMs, limited robustness against logic and function errors in complex queries, and inefficiencies in structured search. We introduce SQL-o1, a self-reward-driven heuristic search framework built on an agent-based architecture to enhance model reasoning capabilities. SQL-o1 leverages Monte Carlo Tree Search (MCTS) for structured, multi-step exploration and incorporates a dynamic pruning strategy to accelerate inference without sacrificing accuracy. On the Spider and BIRD benchmarks, SQL-o1 achieves a 10.8-point execution accuracy improvement on the complex BIRD dataset, surpassing even GPT-4-based models. It exhibits strong few-shot generalization and robust cross-model transferability across open-source LLMs. Our code is available at https://github.com/ShuaiLyu0110/SQL-o1.
LLMs' reliance on static knowledge and fragile tool invocation severely hinders the orchestration of complex, heterogeneous toolchains, particularly at large scales. Existing methods typically use rigid single-path execution, resulting in poor error recovery and exponentially growing search spaces. We introduce NaviAgent, a graph-navigated bilevel planning architecture for robust function calling, comprising a Multi-Path Decider and Graph-Encoded Navigator. As an LLM-powered agent, the Multi-Path Decider defines a four-dimensional decision space and continuously perceives environmental states, dynamically selecting the optimal action to fully cover all tool invocation scenarios. The Graph-Encoded Navigator constructs a Tool Dependency Heterogeneous Graph (TDHG), where node embeddings explicitly fuse API schema structure with historical invocation behavior. It also integrates a novel heuristic search strategy that guides the Decider toward efficient and highly successful toolchains, even for unseen tool combinations. Experiments show that NaviAgent consistently achieves the highest task success rate (TSR) across all foundation models and task complexities, outperforming the average baselines (ReAct, ToolLLM, {\alpha}-UMI) by 13.5%, 16.4%, and 19.0% on Qwen2.5-14B, Qwen2.5-32B, and Deepseek-V3, respectively. Its execution steps are typically within one step of the most efficient baseline, ensuring a strong balance between quality and efficiency. Notably, a fine-tuned Qwen2.5-14B model achieves a TSR of 49.5%, surpassing the much larger 32B model (44.9%) under our architecture. Incorporating the Graph-Encoded Navigator further boosts TSR by an average of 2.4 points, with gains up over 9 points on complex tasks for larger models (Deepseek-V3 and GPT-4o), highlighting its essential role in toolchain orchestration.
Extended Stability Runge-Kutta (ESRK) methods are crucial for solving large-scale computational problems in science and engineering, including weather forecasting, aerodynamic analysis, and complex biological modelling. However, balancing accuracy, stability, and computational efficiency remains challenging, particularly for high-order, low-storage schemes. This study introduces a hybrid Genetic Algorithm (GA) and Reinforcement Learning (RL) approach for automated heuristic discovery, optimising low-storage ESRK methods. Unlike traditional approaches that rely on manually designed heuristics or exhaustive numerical searches, our method leverages GA-driven mutations for search-space exploration and an RL-inspired state transition mechanism to refine heuristic selection dynamically. This enables systematic parameter reduction, preserving fourth-order accuracy while significantly improving computational efficiency.The proposed GA-RL heuristic optimisation framework is validated through rigorous testing on benchmark problems, including the 1D and 2D Brusselator systems and the steady-state Navier-Stokes equations. The best-performing heuristic achieves a 25\% reduction in IPOPT runtime compared to traditional ESRK optimisation processes while maintaining numerical stability and accuracy. These findings demonstrate the potential of adaptive heuristic discovery to improve resource efficiency in high-fidelity simulations and broaden the applicability of low-storage Runge-Kutta methods in real-world computational fluid dynamics, physics simulations, and other demanding fields. This work establishes a new paradigm in heuristic optimisation for numerical methods, opening pathways for further exploration using Deep RL and AutoML-based heuristic search
Large Language Models (LLMs) struggle with complex reasoning due to limited diversity and inefficient search. We propose Soft Reasoning, an embedding-based search framework that optimises the embedding of the first token to guide generation. It combines (1) embedding perturbation for controlled exploration and (2) Bayesian optimisation to refine embeddings via a verifier-guided objective, balancing exploration and exploitation. This approach improves reasoning accuracy and coherence while avoiding reliance on heuristic search. Experiments demonstrate superior correctness with minimal computation, making it a scalable, model-agnostic solution.
A novel movable-element simultaneously transmitting and reflecting surface (ME-STARS)-assisted near-field wideband communication framework is proposed. In particular, the position of each STARS element can be adjusted to combat the significant wideband beam squint issue in the near field instead of using costly true-time delay components. Four practical ME-STARS element movement modes are proposed, namely region-based (RB), horizontal-based (HB), vertical-based (VB), and diagonal-based (DB) modes. Based on this, a near-field wideband multi-user downlink communication scenario is considered, where a sum rate maximization problem is formulated by jointly optimizing the base station (BS) precoding, ME-STARS beamforming, and element positions. To solve this intractable problem, a two-layer algorithm is developed. For the inner layer, the block coordinate descent optimization framework is utilized to solve the BS precoding and ME-STARS beamforming in an iterative manner. For the outer layer, the particle swarm optimization-based heuristic search method is employed to determine the desired element positions. Numerical results show that:1) the ME-STARSs can effectively address the beam squint for near-field wideband communications compared to conventional STARSs with fixed element positions; 2) the RB mode achieves the most efficient beam squint effect mitigation, while the DB mode achieves the best trade-off between performance gain and hardware overhead; and 3) an increase in the number of ME-STARS elements or BS subcarriers substantially improves the system performance.
Chain-of-thought (CoT) distillation allows a large language model (LLM) to guide a small language model (SLM) in reasoning tasks. Existing methods train the SLM to learn the long rationale in one iteration, resulting in two issues: 1) Long rationales lead to a large token-level batch size during training, making gradients of core reasoning tokens (i.e., the token will directly affect the correctness of subsequent reasoning) over-smoothed as they contribute a tiny fraction of the rationale. As a result, the SLM converges to sharp minima where it fails to grasp the reasoning logic. 2) The response is slow, as the SLM must generate a long rationale before reaching the answer. Therefore, we propose chunk-wise training (CWT), which uses a heuristic search to divide the rationale into internal semantically coherent chunks and focuses SLM on learning from only one chunk per iteration. In this way, CWT naturally isolates non-reasoning chunks that do not involve the core reasoning token (e.g., summary and transitional chunks) from the SLM learning for reasoning chunks, making the fraction of the core reasoning token increase in the corresponding iteration. Based on CWT, skip-thinking training (STT) is proposed. STT makes the SLM automatically skip non-reasoning medium chunks to reach the answer, improving reasoning speed while maintaining accuracy. We validate our approach on a variety of SLMs and multiple reasoning tasks.
The deployment of pre-trained perception models in novel environments often leads to performance degradation due to distributional shifts. Although recent artificial intelligence approaches for metacognition use logical rules to characterize and filter model errors, improving precision often comes at the cost of reduced recall. This paper addresses the hypothesis that leveraging multiple pre-trained models can mitigate this recall reduction. We formulate the challenge of identifying and managing conflicting predictions from various models as a consistency-based abduction problem. The input predictions and the learned error detection rules derived from each model are encoded in a logic program. We then seek an abductive explanation--a subset of model predictions--that maximizes prediction coverage while ensuring the rate of logical inconsistencies (derived from domain constraints) remains below a specified threshold. We propose two algorithms for this knowledge representation task: an exact method based on Integer Programming (IP) and an efficient Heuristic Search (HS). Through extensive experiments on a simulated aerial imagery dataset featuring controlled, complex distributional shifts, we demonstrate that our abduction-based framework outperforms individual models and standard ensemble baselines, achieving, for instance, average relative improvements of approximately 13.6% in F1-score and 16.6% in accuracy across 15 diverse test datasets when compared to the best individual model. Our results validate the use of consistency-based abduction as an effective mechanism to robustly integrate knowledge from multiple imperfect reasoners in challenging, novel scenarios.
Mathematical reasoning and optimization are fundamental to artificial intelligence and computational problem-solving. Recent advancements in Large Language Models (LLMs) have significantly improved AI-driven mathematical reasoning, theorem proving, and optimization techniques. This survey explores the evolution of mathematical problem-solving in AI, from early statistical learning approaches to modern deep learning and transformer-based methodologies. We review the capabilities of pretrained language models and LLMs in performing arithmetic operations, complex reasoning, theorem proving, and structured symbolic computation. A key focus is on how LLMs integrate with optimization and control frameworks, including mixed-integer programming, linear quadratic control, and multi-agent optimization strategies. We examine how LLMs assist in problem formulation, constraint generation, and heuristic search, bridging theoretical reasoning with practical applications. We also discuss enhancement techniques such as Chain-of-Thought reasoning, instruction tuning, and tool-augmented methods that improve LLM's problem-solving performance. Despite their progress, LLMs face challenges in numerical precision, logical consistency, and proof verification. Emerging trends such as hybrid neural-symbolic reasoning, structured prompt engineering, and multi-step self-correction aim to overcome these limitations. Future research should focus on interpretability, integration with domain-specific solvers, and improving the robustness of AI-driven decision-making. This survey offers a comprehensive review of the current landscape and future directions of mathematical reasoning and optimization with LLMs, with applications across engineering, finance, and scientific research.
In this study, we present a block-based heuristic search algorithm to address the nuclear waste container packing problem in the context of real-world nuclear power plants. Additionally, we provide a dataset comprising 1600 problem instances for future researchers to use. Experimental results on this dataset demonstrate that the proposed algorithm effectively enhances the disposal pool's space utilization while minimizing the radiation dose within the pool. The code and data employed in this study are publicly available to facilitate reproducibility and further investigation.
The problem of finding a minimum vertex cover (MVC) in a graph is a well-known NP-hard problem with significant practical applications in optimization and scheduling. Its complexity, combined with the increasing scale of problems, underscores the need for efficient and effective algorithms. However, existing heuristic algorithms for MVC often rely on simplistic initialization strategies and overlook the impact of edge attributes and neighborhood information on vertex selection. In this paper, we introduce GCNIVC, a novel heuristic search algorithm designed to address the limitations of existing methods for solving MVC problems in large-scale graphs. Our approach features two main innovations. First, it utilizes a Graph Convolutional Network (GCN) to capture the global structure of graphs, which enables the generation of high-quality initial solutions that enhance the efficiency of the subsequent search process. Second, GCNIVC introduces a new heuristic that employs three containers and the concept of double-covered edges (dc-edges), improving search efficiency and providing greater flexibility for adding and removing operations based on edge attributes. Through extensive experiments on benchmark datasets, we demonstrate that GCNIVC outperforms state-of-the-art MVC algorithms in terms of both accuracy and efficiency. Our results highlight the effectiveness of GCNIVC's GCN-assisted initialization and its edge-informed search strategy. This study not only advances the understanding of MVC problem-solving but also contributes a new tool for addressing large-scale graph optimization challenges.
Recent advances in Large Language Models have led to remarkable achievements across a variety of Natural Language Processing tasks, making prompt engineering increasingly central to guiding model outputs. While manual methods can be effective, they typically rely on intuition and do not automatically refine prompts over time. In contrast, automatic prompt optimization employing heuristic-based search algorithms can systematically explore and improve prompts with minimal human oversight. This survey proposes a comprehensive taxonomy of these methods, categorizing them by where optimization occurs, what is optimized, what criteria drive the optimization, which operators generate new prompts, and which iterative search algorithms are applied. We further highlight specialized datasets and tools that support and accelerate automated prompt refinement. We conclude by discussing key open challenges pointing toward future opportunities for more robust and versatile LLM applications.
Knowledge Base Question Answering (KBQA) aims to answer natural language questions with a large-scale structured knowledge base (KB). Despite advancements with large language models (LLMs), KBQA still faces challenges in weak KB awareness, imbalance between effectiveness and efficiency, and high reliance on annotated data. To address these challenges, we propose KBQA-o1, a novel agentic KBQA method with Monte Carlo Tree Search (MCTS). It introduces a ReAct-based agent process for stepwise logical form generation with KB environment exploration. Moreover, it employs MCTS, a heuristic search method driven by policy and reward models, to balance agentic exploration's performance and search space. With heuristic exploration, KBQA-o1 generates high-quality annotations for further improvement by incremental fine-tuning. Experimental results show that KBQA-o1 outperforms previous low-resource KBQA methods with limited annotated data, boosting Llama-3.1-8B model's GrailQA F1 performance to 78.5% compared to 48.5% of the previous sota method with GPT-3.5-turbo. Our code is publicly available.
Hardware distortion in large intelligent surfaces (LISs) may limit their performance when scaling up such systems. It is of great importance to model the non-ideal effects in their transceivers to study the hardware distortions that can affect their performance. Therefore, we have focused on modeling and studying the effects of nonlinear RX-chains in LISs. We first derive expressions for SNDR of a LIS with a memory-less polynomial-based model at its RX-chains. Then we propose a simplified double-parameter exponential model for the distortion power and show that compared to the polynomial based model, the exponential model can improve the analytical tractability for SNDR optimization problems. In particular, we consider a panel selection optimization problems in a panel-based LIS scenario and show that the proposed model enables us to derive two closed-form sub-optimal solutions for panel selection, and can be a favorable alternative to high-order polynomial models in terms of computation complexity, especially for theoretical works on hardware distortion in MIMO and LIS systems. Numerical results show that the sub-optimal closed-form solutions have a near-optimal performance in terms of SNDR compared to the global optimum found by high-complexity heuristic search methods.
While safety-aligned large language models (LLMs) are increasingly used as the cornerstone for powerful systems such as multi-agent frameworks to solve complex real-world problems, they still suffer from potential adversarial queries, such as jailbreak attacks, which attempt to induce harmful content. Researching attack methods allows us to better understand the limitations of LLM and make trade-offs between helpfulness and safety. However, existing jailbreak attacks are primarily based on opaque optimization techniques (e.g. token-level gradient descent) and heuristic search methods like LLM refinement, which fall short in terms of transparency, transferability, and computational cost. In light of these limitations, we draw inspiration from the evolution and infection processes of biological viruses and propose LLM-Virus, a jailbreak attack method based on evolutionary algorithm, termed evolutionary jailbreak. LLM-Virus treats jailbreak attacks as both an evolutionary and transfer learning problem, utilizing LLMs as heuristic evolutionary operators to ensure high attack efficiency, transferability, and low time cost. Our experimental results on multiple safety benchmarks show that LLM-Virus achieves competitive or even superior performance compared to existing attack methods.
Parallelization and External Memory (PEM) techniques have significantly enhanced the capabilities of search algorithms when solving large-scale problems. Previous research on PEM has primarily centered on unidirectional algorithms, with only one publication on bidirectional PEM that focuses on the meet-in-the-middle (MM) algorithm. Building upon this foundation, this paper presents a framework that integrates both uni- and bi-directional best-first search algorithms into this framework. We then develop a PEM variant of the state-of-the-art bidirectional heuristic search (BiHS) algorithm BAE* (PEM-BAE*). As previous work on BiHS did not focus on scaling problem sizes, this work enables us to evaluate bidirectional algorithms on hard problems. Empirical evaluation shows that PEM-BAE* outperforms the PEM variants of A* and the MM algorithm, as well as a parallel variant of IDA*. These findings mark a significant milestone, revealing that bidirectional search algorithms clearly outperform unidirectional search algorithms across several domains, even when equipped with state-of-the-art heuristics.
Automatic Heuristic Design (AHD) is an active research area due to its utility in solving complex search and NP-hard combinatorial optimization problems in the real world. The recent advancements in Large Language Models (LLMs) introduce new possibilities by coupling LLMs with evolutionary computation to automatically generate heuristics, known as LLM-based Evolutionary Program Search (LLM-EPS). While previous LLM-EPS studies obtained great performance on various tasks, there is still a gap in understanding the properties of heuristic search spaces and achieving a balance between exploration and exploitation, which is a critical factor in large heuristic search spaces. In this study, we address this gap by proposing two diversity measurement metrics and perform an analysis on previous LLM-EPS approaches, including FunSearch, EoH, and ReEvo. Results on black-box AHD problems reveal that while EoH demonstrates higher diversity than FunSearch and ReEvo, its objective score is unstable. Conversely, ReEvo's reflection mechanism yields good objective scores but fails to optimize diversity effectively. With this finding in mind, we introduce HSEvo, an adaptive LLM-EPS framework that maintains a balance between diversity and convergence with a harmony search algorithm. Through experimentation, we find that HSEvo achieved high diversity indices and good objective scores while remaining cost-effective. These results underscore the importance of balancing exploration and exploitation and understanding heuristic search spaces in designing frameworks in LLM-EPS.
We study a path planning problem where the possible move actions are represented as a finite set of motion primitives aligned with the grid representation of the environment. That is, each primitive corresponds to a short kinodynamically-feasible motion of an agent and is represented as a sequence of the swept cells of a grid. Typically heuristic search, i.e. A*, is conducted over the lattice induced by these primitives (lattice-based planning) to find a path. However due to the large branching factor such search may be inefficient in practice. To this end we suggest a novel technique rooted in the idea of searching over the grid cells (as in vanilla A*) simultaneously fitting the possible sequences of the motion primitives into these cells. The resultant algorithm, MeshA*, provably preserves the guarantees on completeness and optimality, on the one hand, and is shown to notably outperform conventional lattice-based planning (x1.5 decrease in the runtime), on the other hand. Moreover, we suggest an additional pruning technique that additionally decreases the search space of MeshA*. The resultant planner is combined with the regular A* to retain completeness and is shown to further increase the search performance at the cost of negligible decrease of the solution quality.
Game solving is the process of finding the theoretical outcome for a game, assuming that all player choices are optimal. This paper focuses on a technique that can reduce the heuristic search space significantly for 7x7 Killall-Go. In Go and Killall-Go, live patterns are stones that are protected from opponent capture. Mutual life, also referred to as seki, is when both players' stones achieve life by sharing liberties with their opponent. Whichever player attempts to capture the opponent first will leave their own stones vulnerable. Therefore, it is critical to recognize seki patterns to avoid putting oneself in jeopardy. Recognizing seki can reduce the search depth significantly. In this paper, we enumerate all seki patterns up to a predetermined area size, then store these patterns into a seki table. This allows us to recognize seki during search, which significantly improves solving efficiency for the game of Killall-Go. Experiments show that a day-long, unsolvable position can be solved in 482 seconds with the addition of a seki table. For general positions, a 10% to 20% improvement in wall clock time and node count is observed.
Metaheuristic search methods have proven to be essential tools for tackling complex optimization challenges, but their full potential is often constrained by conventional algorithmic frameworks. In this paper, we introduce a novel approach called Deep Heuristic Search (DHS), which models metaheuristic search as a memory-driven process. DHS employs multiple search layers and memory-based exploration-exploitation mechanisms to navigate large, dynamic search spaces. By utilizing model-free memory representations, DHS enhances the ability to traverse temporal trajectories without relying on probabilistic transition models. The proposed method demonstrates significant improvements in search efficiency and performance across a range of heuristic optimization problems.
The Segment Anything Model 2 (SAM 2) has emerged as a powerful foundation model for object segmentation in both images and videos, paving the way for various downstream video applications. The crucial design of SAM 2 for video segmentation is its memory module, which prompts object-aware memories from previous frames for current frame prediction. However, its greedy-selection memory design suffers from the "error accumulation" problem, where an errored or missed mask will cascade and influence the segmentation of the subsequent frames, which limits the performance of SAM 2 toward complex long-term videos. To this end, we introduce SAM2Long, an improved training-free video object segmentation strategy, which considers the segmentation uncertainty within each frame and chooses the video-level optimal results from multiple segmentation pathways in a constrained tree search manner. In practice, we maintain a fixed number of segmentation pathways throughout the video. For each frame, multiple masks are proposed based on the existing pathways, creating various candidate branches. We then select the same fixed number of branches with higher cumulative scores as the new pathways for the next frame. After processing the final frame, the pathway with the highest cumulative score is chosen as the final segmentation result. Benefiting from its heuristic search design, SAM2Long is robust toward occlusions and object reappearances, and can effectively segment and track objects for complex long-term videos. Notably, SAM2Long achieves an average improvement of 3.0 points across all 24 head-to-head comparisons, with gains of up to 5.3 points in J&F on long-term video object segmentation benchmarks such as SA-V and LVOS. The code is released at https://github.com/Mark12Ding/SAM2Long.