Abstract:High-level synthesis (HLS) design space exploration (DSE) is an optimization process in electronic design automation (EDA) that systematically explores high-level design configurations to achieve Pareto-optimal hardware implementations balancing performance, area, and power (PPA). To optimize this process, HLS prediction tasks often employ message-passing neural networks (MPNNs), leveraging complex architectures to achieve high accuracy. These predictors serve as evaluators in the DSE process, effectively bypassing the time-consuming estimations traditionally required by HLS tools. However, existing models often prioritize structural complexity and minimization of training loss, overlooking task-specific characteristics. Additionally, while evolutionary algorithms are widely used in DSE, they typically require extensive domain-specific knowledge to design effective crossover and mutation operators. To address these limitations, we propose CoGNNs-LLMEA, a framework that integrates a graph neural network with task-adaptive message passing and a large language model-enhanced evolutionary algorithm. As a predictive model, CoGNNs directly leverages intermediate representations generated from source code after compiler front-end processing, enabling prediction of quality of results (QoR) without invoking HLS tools. Due to its strong adaptability to tasks, CoGNNs can be tuned to predict post-HLS and post-implementation outcomes, effectively bridging the gap between high-level abstractions and physical implementation characteristics. CoGNNs achieves state-of-the-art prediction accuracy in post-HLS QoR prediction, reducing mean prediction errors by 2.8$\times$ for latency and 3.4$\times$ for resource utilization compared to baseline models.