Genetic Programming Mathematical Complexities: Principles, Applications, and Open Problems

Genetic Programming (GP) is a method within evolutionary computation that focuses on creating computer programs by mimicking the process of natural evolution. Unlike traditional programming, where code is written in fixed-length strings, GP represents programs as tree structures, allowing for more complex and flexible solutions. This approach enables the evolution of programs that can adapt and improve over time, making it a powerful tool for solving various computational problems. The complexity of Genetic Programming (GP) arises from its use of tree structures to represent computer programs, which differs from traditional methods that use fixed-length strings. This unique representation creates specific mathematical challenges, such as how to effectively evaluate and optimize these tree structures. As a result, researchers face important questions about how to improve GP techniques and understand the underlying mathematical principles that govern its behavior and performance. The current exposition explores the mathematical challenges and complexities associated with Genetic Programming (GP), which involves evolving computer programs in the form of tree structures. It also discusses the essential concepts that underlie GP, highlights its important applications in various fields, and identifies significant unresolved issues that researchers are currently facing. By addressing these aspects, the paper aims to provide a comprehensive overview of the state of research in GP.