Effective traffic signal control (TSC) requires policies that respond to changing traffic demand and network conditions while meeting different control objectives. However, adapting existing strategies often involves repeated manual design and adjustment, making it difficult to systematically explore better control rules for a target network. Large language models (LLMs) can automate this process, but directly using them to select signal phases leaves decision rules embedded in black-box models and incurs recurring inference costs and latency. This paper formulates TSC as a modular program design problem and proposes EvoSignal, an LLM-guided evolutionary framework using traffic knowledge and performance feedback. The modular representation separates traffic feature extraction, local phase prioritization, and optional network-based priority adjustment. Starting from several established strategies, EvoSignal improves programs through feedback on congestion and signal operation, retaining strategies with different performance trade-offs. The resulting programs operate without online LLM inference. Simulation experiments across five scenarios on two real-world road networks show that the selected default EvoSignal program reduces waiting time by 16.8--49.2\% relative to the lowest waiting time achieved by the 20 conventional, reinforcement learning-based, and LLM-based baselines in each scenario. A program prioritizing travel time and queue length outperforms all 20 baselines on all three metrics in the search scenario and remains among the top three on each metric when transferred unchanged to the other four scenarios. These findings support automated design of inspectable control programs that transfer across the evaluated road networks and traffic demands.Code is available at https://github.com/georgewanglz2019/EvoSignal.

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