  Building upon the strength of modern large language models (LLMs), generative
error correction (GEC) has emerged as a promising paradigm that can elevate the
performance of modern automatic speech recognition (ASR) systems. One
representative approach is to leverage in-context learning to prompt LLMs so
that a better hypothesis can be generated by the LLMs based on a
carefully-designed prompt and an $N$-best list of hypotheses produced by ASR
systems. However, it is yet unknown whether the existing prompts are the most
effective ones for the task of post-ASR error correction. In this context, this
paper first explores alternative prompts to identify an initial set of
effective prompts, and then proposes to employ an evolutionary prompt
optimization algorithm to refine the initial prompts. Evaluations results on
the CHiME-4 subset of the Task $1$ of the SLT $2024$ GenSEC challenge show the
effectiveness and potential of the proposed algorithms.
