Learn to Relax with Large Language Models: Solving Nonlinear Combinatorial Optimization Problems via Bidirectional Coevolution

Nonlinear Combinatorial Optimization Problems (NCOPs) present a formidable computational hurdle in practice, as their nonconvex nature gives rise to multi-modal solution spaces that defy efficient optimization. Traditional constraint relaxation approaches rely heavily on expert-driven, iterative design processes that lack systematic automation and scalable adaptability. While recent Large Language Model (LLM)-based optimization methods show promise for autonomous problem-solving, they predominantly function as passive constraint validators rather than proactive strategy architects, failing to handle the sophisticated constraint interactions inherent to NCOPs.To address these limitations, we introduce the first end-to-end \textbf{Auto}mated \textbf{C}onstraint \textbf{O}ptimization (AutoCO) method, which revolutionizes NCOPs resolution through learning to relax with LLMs.Specifically, we leverage structured LLM reasoning to generate constraint relaxation strategies, which are dynamically evolving with algorithmic principles and executable code through a unified triple-representation scheme. We further establish a novel bidirectional (global-local) coevolution mechanism that synergistically integrates Evolutionary Algorithms for intensive local refinement with Monte Carlo Tree Search for systematic global strategy space exploration, ensuring optimal balance between intensification and diversification in fragmented solution spaces. Finally, comprehensive experiments on three challenging NCOP benchmarks validate AutoCO's consistent effectiveness and superior performance over the baselines.

Towards Autonomous UAV Visual Object Search in City Space: Benchmark and Agentic Methodology

Aerial Visual Object Search (AVOS) tasks in urban environments require Unmanned Aerial Vehicles (UAVs) to autonomously search for and identify target objects using visual and textual cues without external guidance. Existing approaches struggle in complex urban environments due to redundant semantic processing, similar object distinction, and the exploration-exploitation dilemma. To bridge this gap and support the AVOS task, we introduce CityAVOS, the first benchmark dataset for autonomous search of common urban objects. This dataset comprises 2,420 tasks across six object categories with varying difficulty levels, enabling comprehensive evaluation of UAV agents' search capabilities. To solve the AVOS tasks, we also propose PRPSearcher (Perception-Reasoning-Planning Searcher), a novel agentic method powered by multi-modal large language models (MLLMs) that mimics human three-tier cognition. Specifically, PRPSearcher constructs three specialized maps: an object-centric dynamic semantic map enhancing spatial perception, a 3D cognitive map based on semantic attraction values for target reasoning, and a 3D uncertainty map for balanced exploration-exploitation search. Also, our approach incorporates a denoising mechanism to mitigate interference from similar objects and utilizes an Inspiration Promote Thought (IPT) prompting mechanism for adaptive action planning. Experimental results on CityAVOS demonstrate that PRPSearcher surpasses existing baselines in both success rate and search efficiency (on average: +37.69% SR, +28.96% SPL, -30.69% MSS, and -46.40% NE). While promising, the performance gap compared to humans highlights the need for better semantic reasoning and spatial exploration capabilities in AVOS tasks. This work establishes a foundation for future advances in embodied target search. Dataset and source code are available at https://anonymous.4open.science/r/CityAVOS-3DF8.