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.
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