MMP-A*: Multimodal Perception Enhanced Incremental Heuristic Search on Path Planning

Autonomous path planning requires a synergy between global reasoning and geometric precision, especially in complex or cluttered environments. While classical A* is valued for its optimality, it incurs prohibitive computational and memory costs in large-scale scenarios. Recent attempts to mitigate these limitations by using Large Language Models for waypoint guidance remain insufficient, as they rely only on text-based reasoning without spatial grounding. As a result, such models often produce incorrect waypoints in topologically complex environments with dead ends, and lack the perceptual capacity to interpret ambiguous physical boundaries. These inconsistencies lead to costly corrective expansions and undermine the intended computational efficiency. We introduce MMP-A*, a multimodal framework that integrates the spatial grounding capabilities of vision-language models with a novel adaptive decay mechanism. By anchoring high-level reasoning in physical geometry, the framework produces coherent waypoint guidance that addresses the limitations of text-only planners. The adaptive decay mechanism dynamically regulates the influence of uncertain waypoints within the heuristic, ensuring geometric validity while substantially reducing memory overhead. To evaluate robustness, we test the framework in challenging environments characterized by severe clutter and topological complexity. Experimental results show that MMP-A* achieves near-optimal trajectories with significantly reduced operational costs, demonstrating its potential as a perception-grounded and computationally efficient paradigm for autonomous navigation.

Pareto-Grid-Guided Large Language Models for Fast and High-Quality Heuristics Design in Multi-Objective Combinatorial Optimization

Multi-objective combinatorial optimization problems (MOCOP) frequently arise in practical applications that require the simultaneous optimization of conflicting objectives. Although traditional evolutionary algorithms can be effective, they typically depend on domain knowledge and repeated parameter tuning, limiting flexibility when applied to unseen MOCOP instances. Recently, integration of Large Language Models (LLMs) into evolutionary computation has opened new avenues for automatic heuristic generation, using their advanced language understanding and code synthesis capabilities. Nevertheless, most existing approaches predominantly focus on single-objective tasks, often neglecting key considerations such as runtime efficiency and heuristic diversity in multi-objective settings. To bridge this gap, we introduce Multi-heuristics for MOCOP via Pareto-Grid-guided Evolution of LLMs (MPaGE), a novel enhancement of the Simple Evolutionary Multiobjective Optimization (SEMO) framework that leverages LLMs and Pareto Front Grid (PFG) technique. By partitioning the objective space into grids and retaining top-performing candidates to guide heuristic generation, MPaGE utilizes LLMs to prioritize heuristics with semantically distinct logical structures during variation, thus promoting diversity and mitigating redundancy within the population. Through extensive evaluations, MPaGE demonstrates superior performance over existing LLM-based frameworks, and achieves competitive results to traditional Multi-objective evolutionary algorithms (MOEAs), with significantly faster runtime. Our code is available at: https://github.com/langkhachhoha/MPaGE.