Visual-Enhanced Fireworks Algorithm via Multimodal Large Language Models

Large language models (LLMs) have recently demonstrated strong potential in heuristic algorithm design, yet existing approaches are confined to text-only interactions and fail to exploit visual structure in optimization trajectories. We propose \textbf{VE-FWA} (Visual-Enhanced Fireworks Algorithm), a multimodal framework that incorporates visual feedback into LLM-driven evolution of the Fireworks Algorithm (FWA), governed by a \emph{Critical Part} (CP) abstraction that unifies global optimizer evolution and local subroutine customization. We validate VE-FWA on two challenging domains: the Traveling Salesman Problem (combinatorial optimization) and VLSI placement (high-dimensional physical design). On the full TSPLIB29 benchmark, VE-FWA achieves a 0.0038\% average optimality gap, reaching the known optimum on 25 out of 29 instances, while multimodal feedback reduces the gap by $54\times$ compared to the text-only variant. On EDA placement, VE-FWA achieves the best wirelength on 6 out of 8 ISPD2005 benchmarks using only a single 12\,GB GPU, outperforming prior LLM-based approaches that require large-scale compute clusters.