The ability of Large Language Models (LLMs) to generate high-quality text and code has fuelled their rise in popularity. In this paper, we aim to demonstrate the potential of LLMs within the realm of optimization algorithms by integrating them into STNWeb. This is a web-based tool for the generation of Search Trajectory Networks (STNs), which are visualizations of optimization algorithm behavior. Although visualizations produced by STNWeb can be very informative for algorithm designers, they often require a certain level of prior knowledge to be interpreted. In an attempt to bridge this knowledge gap, we have incorporated LLMs, specifically GPT-4, into STNWeb to produce extensive written reports, complemented by automatically generated plots, thereby enhancing the user experience and reducing the barriers to the adoption of this tool by the research community. Moreover, our approach can be expanded to other tools from the optimization community, showcasing the versatility and potential of LLMs in this field.