Large Language Models (LLMs), built upon Transformer-based architectures with massive pretraining on diverse data, 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, reveals intriguing parallels, especially in their shared optimization nature, black-box characteristics, and proficiency in handling complex problems. Meanwhile, EA can not only provide an optimization framework for LLM's further enhancement under black-box settings but also empower LLM with flexible global search and iterative mechanism in applications. On the other hand, LLM's abundant domain knowledge enables EA to perform smarter searches, while its text processing capability assist in deploying EA across various tasks. Based on their complementary advantages, this paper presents a comprehensive review and forward-looking roadmap, categorizing their mutual inspiration into LLM-enhanced evolutionary optimization and EA-enhanced LLM. Some integrated synergy methods are further introduced to exemplify the amalgamation of LLMs and EAs in various application scenarios, including neural architecture search, code generation, software engineering, and text generation. As the first comprehensive review specifically focused on the EA research in the era of LLMs, this paper provides a foundational stepping stone for understanding and harnessing the collaborative potential of LLMs and EAs. By presenting a comprehensive review, categorization, and critical analysis, we contribute to the ongoing discourse on the cross-disciplinary study of these two powerful paradigms. The identified challenges and future directions offer guidance to unlock the full potential of this innovative collaboration.
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