SpecAHD: Localize to Specialize for Automated Heuristic Design in Large-Scale Routing Problems

LLM-Driven Joint Evolution of Coupled Heuristics Components for Routing Optimization

Heuristic design for combinatorial optimization remains heavily reliant on expert knowledge, while existing large language model (LLM)-enhanced evolutionary methods typically evolve isolated algorithmic components, even when one determines the search state on which another operates. This paper proposes LLM-driven Heuristic Components Joint Generation (LLM-HCJG), a population-based framework that jointly generates and co-evolves interdependent heuristic components under a shared design blueprint. Applied to guided local search (GLS), LLM-HCJG couples solution initialization with penalty construction and embeds the generated pair into an enhanced online search mechanism. The resulting form is further transferred from the traveling salesman problem (TSP) to the capacitated vehicle routing problem (CVRP). Theoretical analysis establishes the non-separable state-transition effects between the two components and the advantage in generation consistency. Across synthetic instances and 41 public TSPLIB/CVRPLIB benchmarks, LLM-HCJG attains consistently low optimality gaps, including best or tied-best results on 28 of 29 TSPLIB instances and all 12 CVRPLIB instances. Ablation and structural analyses further indicate that these gains are associated with cross-component compatibility and alignment rather than isolated-component recombination. These results support effective cross-instance transfer within the evaluated routing settings under limited-sample, modest-cost training.

An LLM-Driven Beam Search Framework for Automated Heuristic Design for Capacitated Vehicle Routing Problem

Large language model (LLM) based automated heuristic design (AHD) frameworks, such as EoH, FunSearch, and ReEvo, have shown promising performance on a variety of combinatorial optimization problems. However, most existing LLM-based AHD frameworks mainly focus on designing heuristics with the same functional role, although jointly designing functionally complementary heuristics often leads to better solution quality. To address this limitation, this study proposes LLM-BS, an LLM-driven beam search framework for AHD for the capacitated vehicle routing problem (CVRP). LLM-BS simultaneously designs a construction heuristic and a guided local search heuristic, and iteratively refines their combination through expansion and pruning to maintain effective coordination between the two heuristics. Extensive experiments on CVRPLIB benchmark instances show that LLM-BS achieves small gaps relative to the best-known solutions identified by heuristics while outperforming representative LLM-based AHD frameworks in terms of solution quality.

Accelerating LLM-Based Algorithm Evolution for the 3D Container Loading Problem

This work proposes a pipeline that introduces a novel regularization architecture balancing performance and complexity, and mitigate the side effects of automated tuning through two novel components: a symbolic pruning mutator and a complexity-aware mutation gate that explicitly filters out mutations leading to excessive code growth.

AlgoWorlds: Benchmarking Tool Use for Global Optimization in Algorithmic Worlds

Tool-use benchmarks generally evaluate whether an agent completes a workflow using appropriate tools and valid arguments. However, feasibility alone is insufficient in real-world decision settings such as route planning and fleet dispatch. Individual choices interact through shared constraints and costs, so a feasible solution may still be substantially suboptimal. This raises a harder question: can an agent turn information gathered through tools into a globally optimal decision? We introduce AlgoWorlds, a benchmark that transforms formally specified combinatorial optimization problems into partially observed decision environments with verifiable global optima. Each environment contains a hidden instance observed only through task-specific information tools, after which the agent commits to one structured decision evaluated for feasibility and optimality. AlgoWorlds contains 240 environments covering ten combinatorial optimization families and four workload levels. Family-specific deterministic programs generate the instances, exact algorithms certify their optima and determine workload levels, and two structurally different tool interfaces present each underlying instance. We evaluate seven leading LLMs, including Claude Opus 4.8 and GPT-5.6 Sol. Achieving global optimality remains highly challenging: although leading models produce feasible decisions in most cases, the best-performing model reaches exact optimality in only 38.61% of cases. Even when agents collect sufficient information to reconstruct the hidden instance, most failures end in feasible but suboptimal decisions. The challenge therefore extends beyond information acquisition to information integration, global constraint reasoning, and decision verification. The project homepage is available at https://xzx34.github.io/AlgoWorlds/, and the code is available at https://github.com/xzx34/AlgoWorlds.

Coding agents for automated metaheuristic design

The results suggest that recent progress in language models and tool use may already be sufficient to support practical automated metaheuristic design, and that recent progress in language models and tool use may already be sufficient to support practical automated metaheuristic design.

Random-Key Optimization for 2D Irregular Packing with Reusable Area Evaluation