  Large language models (LLMs) have not only revolutionized natural language
processing but also extended their prowess to various domains, marking a
significant stride towards artificial general intelligence. The interplay
between LLMs and evolutionary algorithms (EAs), despite differing in objectives
and methodologies, share a common pursuit of applicability in complex problems.
Meanwhile, EA can provide an optimization framework for LLM's further
enhancement under black-box settings, empowering LLM with flexible global
search capacities. On the other hand, the abundant domain knowledge inherent in
LLMs could enable EA to conduct more intelligent searches. Furthermore, the
text processing and generative capabilities of LLMs would aid in deploying EAs
across a wide range of tasks. Based on these complementary advantages, this
paper provides a thorough review and a forward-looking roadmap, categorizing
the reciprocal inspiration into two main avenues: LLM-enhanced EA and
EA-enhanced LLM. Some integrated synergy methods are further introduced to
exemplify the complementarity between LLMs and EAs in diverse scenarios,
including code generation, software engineering, neural architecture search,
and various generation tasks. As the first comprehensive review focused on the
EA research in the era of LLMs, this paper provides a foundational stepping
stone for understanding the collaborative potential of LLMs and EAs. The
identified challenges and future directions offer guidance for researchers and
practitioners to unlock the full potential of this innovative collaboration in
propelling advancements in optimization and artificial intelligence. We have
created a GitHub repository to index the relevant papers:
https://github.com/wuxingyu-ai/LLM4EC.
