greedy local-search heuristic

This work addresses the limitation in combinatorial optimization where local search neighborhoods typically require manual construction. It proposes, for the first time, a method that automatically generates functional neighborhoods by exploiting symmetries present in constraint specifications. By integrating constraint programming, symmetry analysis, and local search techniques, the approach enables automated neighborhood construction within the IDP system, substantially reducing the need for human intervention. Empirical evaluation across six classical optimization problems demonstrates the effectiveness of the generated neighborhoods, confirming both the feasibility of the method and its capacity to enhance the automation and generality of local search algorithms.

Dynamic heuristics—functions updated in real time based on search history—pose a fundamental challenge to optimality guarantees in heuristic search. Traditional analyses assume static heuristics, rendering existing theoretical foundations inapplicable. Method: This work formally defines dynamic heuristics and introduces a generalized search framework that integrates dynamism into the foundational design of A*-style algorithms. Through formal semantic modeling and rigorous analysis of dynamic heuristic functions, we establish sufficient conditions for admissibility and optimality. Contribution/Results: We prove that our algorithm variants retain admissibility and guarantee optimal solutions under any valid dynamic heuristic. Our framework transcends the static-heuristic assumption, unifying and explaining classical planning heuristics—including FF and LM-cut—under a common theoretical umbrella. This provides the first rigorous, provable foundation for dynamic heuristic search, advancing it from empirical practice to a sound, analyzable algorithmic paradigm.

This work addresses the limitations of existing automated heuristic design approaches, which predominantly rely on bottom-up code search and struggle to extract reusable, transferable high-level knowledge. The authors propose a top-down, knowledge-first search paradigm that treats knowledge as the primary object of search, using code merely for instantiation and validation. By formulating explainable hypotheses, the method enables knowledge reuse across problems and solution trajectories. It establishes, for the first time, a bidirectional bridge between knowledge and code, introduces a statistical learning perspective to characterize the distortion–compression trade-off, and integrates large language models with population-based and tree search mechanisms into a unified, knowledge-driven iterative optimization framework. Experiments demonstrate that this approach significantly outperforms code-centric methods in heuristic discovery efficiency, transferability, and generalization across combinatorial optimization and extended tasks.

This paper addresses three NP-hard combinatorial optimization problems: the α-neighborhood p-median problem, tree-shaped hub location, and node-capacitated graph partitioning. To tackle them uniformly, we propose a generic Random-Key Optimization (RKO) framework. RKO employs a modular random-key encoding scheme coupled with problem-specific decoding mechanisms, integrates multiple parallel metaheuristics—including simulated annealing, iterative local search, and GRASP—and coordinates search via an elite solution pool. Its novel plug-and-play architecture enables rapid cross-domain adaptation. Implemented efficiently in C++, RKO consistently delivers high-quality solutions across all three problem classes, significantly enhancing both robustness and generalization capability. The framework establishes a scalable, unified paradigm for solving diverse NP-hard combinatorial optimization problems.

This study investigates the efficiency of neighborhood exploration strategies in multi-objective local search, with a focus on the performance gap between systematic traversal and random sampling. Through empirical analysis across diverse multi-objective optimization problems and supporting probabilistic modeling, the work provides the first theoretical and experimental evidence that random sampling consistently outperforms systematic exploration—including both best-improvement and first-improvement strategies. This advantage stems from the observation that high-quality neighboring solutions are sparsely and approximately uniformly distributed in the solution space, enabling random sampling to discover non-dominated solutions more efficiently at lower computational cost. These findings establish a new paradigm for designing multi-objective local search algorithms.

This work addresses the limitations of existing large language model (LLM)-driven automated heuristic design (AHD) methods, which struggle with structurally diverse local repair regions in large-scale path planning, leading to performance trade-offs across heterogeneous subtasks. To overcome this, the authors propose SpecAHD, a novel framework that introduces, for the first time, an intra-instance heuristic specialization mechanism. In SpecAHD, a high-level search identifies bounded repair regions, while a low-level optimizer jointly refines a set of executable heuristics via a monotone submodular objective, enabling greedy selection with a provable $(1 - 1/e)$ approximation guarantee. Integrating LLMs, bilevel optimization, and local restructuring, SpecAHD reduces objective costs by up to 57.7% over the strongest AHD baseline across four routing problems and multiple LLM backbones, and surpasses instance-specific optimization approaches on most public benchmarks.

This work addresses the limitations of existing large language model (LLM)-driven heuristic design methods in combinatorial optimization, which often rely on manual trial-and-error or domain-specific knowledge and lack a systematic mechanism for improvement. To overcome this, the authors propose a structured framework that formalizes heuristic discovery as a language-guided program optimization process, comprising three modular phases: forward evaluation, backward feedback, and program update. This design enables an iterative and composable optimization workflow, unifying and generalizing prior approaches while allowing flexible enhancements through modularity. Empirical evaluation across four real-world combinatorial optimization tasks demonstrates that the proposed method significantly outperforms baseline techniques, achieving up to a 0.17 improvement in the QYI metric on unseen test instances.

This work proposes an adaptive hyper-heuristic approach based on stochastic gradient policy to overcome the limitation of traditional selection hyper-heuristics, which require manual tuning of the learning period parameter τ and thus lack adaptability during optimization. The proposed method automatically adjusts τ and dynamically determines the optimal neighborhood size without user intervention. Integrated within a randomized local search (RLS) framework and enhanced with an adaptive learning mechanism, the algorithm achieves the theoretically optimal runtime—up to lower-order terms—on the LeadingOnes benchmark problem. This advancement significantly improves both the efficiency and generality of hyper-heuristic algorithms.

This work addresses the limitations of traditional stochastic local search in multi-objective combinatorial optimization, where fixed neighborhood structures often lead to premature convergence and insufficient exploration. To overcome this, the authors propose Variable-Step Stochastic Local Search (VS-RLS), a novel approach that dynamically adjusts step size and neighborhood range throughout the search process. Initially employing large steps to enhance global exploration, VS-RLS progressively reduces step size to enable fine-grained exploitation in later stages, thereby effectively balancing exploration and exploitation. As the first method to incorporate a dynamic variable-step mechanism into local search for multi-objective combinatorial optimization, VS-RLS significantly improves the ability to escape local optima and enhances solution set diversity. Experimental results demonstrate its superior performance over state-of-the-art local search and multi-objective evolutionary algorithms across multiple benchmark problems, highlighting its robustness and generalization capability.

Existing automated heuristic design methods struggle to effectively accumulate and reuse search experience and rely on fixed evolutionary operators, lacking dynamic adaptability. This work proposes RefineEvo, a novel framework that introduces a planner-driven dynamic operator scheduling mechanism and a reflector-constructed bidirectional experience pool encompassing both positive and negative experiences. This enables state-aware, trajectory-driven adaptive heuristic evolution. By integrating large language models, evolutionary algorithms, and experience distillation techniques, RefineEvo significantly outperforms strong baselines across multiple classical combinatorial optimization benchmarks, achieving superior solution quality while substantially improving token efficiency. The framework advances heuristic design toward an experience-driven paradigm.