Symbolic regression (SR) is one of the most powerful machine learning techniques that produces transparent models, searching the space of mathematical expressions for a model that represents the relationship between the predictors and the dependent variable without the need of taking assumptions about the model structure. Currently, the most prevalent learning algorithms for SR are based on genetic programming (GP), an evolutionary algorithm inspired from the well-known principles of natural selection. This book is an in-depth guide to GP for SR, discussing its advanced techniques, as well as examples of applications in science and engineering.

The basic idea of GP is to evolve a population of solution candidates in an iterative, generational manner, by repeated application of selection, crossover, mutation, and replacement, thus allowing the model structure, coefficients, and input variables to be searched simultaneously. Given that explainability and interpretability are key elements for integrating humans into the loop of learning in AI, increasing the capacity for data scientists to understand internal algorithmic processes and their resultant models has beneficial implications for the learning process as a whole.

This book represents a practical guide for industry professionals and students across a range of disciplines, particularly data science, engineering, and applied mathematics. Focused on state-of-the-art SR methods and providing ready-to-use recipes, this book is especially appealing to those working with empirical or semi-analytical models in science and engineering.

Symbolic regression (SR) is one of the most powerful machine learning techniques that produces transparent models, searching the space of mathematical expressions for a model that represents the relationship between the predictors and the dependent variable without the need of taking assumptions about the model structure. Currently, the most prevalent learning algorithms for SR are based on genetic programming (GP), an evolutionary algorithm inspired from the well-known principles of natural selection. This book is an in-depth guide to GP for SR, discussing its advanced techniques, as well as examples of applications in science and engineering.

The basic idea of GP is to evolve a population of solution candidates in an iterative, generational manner, by repeated application of selection, crossover, mutation, and replacement, thus allowing the model structure, coefficients, and input variables to be searched simultaneously. Given that explainability and interpretability are key elements for integrating humans into the loop of learning in AI, increasing the capacity for data scientists to understand internal algorithmic processes and their resultant models has beneficial implications for the learning process as a whole.

This book represents a practical guide for industry professionals and students across a range of disciplines, particularly data science, engineering, and applied mathematics. Focused on state-of-the-art SR methods and providing ready-to-use recipes, this book is especially appealing to those working with empirical or semi-analytical models in science and engineering.

This multi-volume LNCS set, LNCS 15148-15151, constitutes the refereed proceedings of the 18th International Conference on Parallel Problem Solving from Nature, PPSN 2024, held in Hagenberg, Austria, in September 2024.

The 101 full papers presented in these proceedings were carefully reviewed and selected from 294 submissions. The papers presented in these four volumes are organized in the following topical sections:

Part I: Combinatorial Optimization; Genetic Programming; Fitness Landscape Modeling and Analysis.

Part II: Benchmarking and Performance Measures; Automated Algorithm Selection and Configuration; Numerical Optimization; Bayesian- and Surrogate-Assisted Optimization.

Part III: Theoretical Aspects of Nature-Inspired Optimization; (Evolutionary) Machine Learning and Neuroevolution; Evolvable Hardware and Evolutionary Robotics.

Part IV: Multi-Objective Optimization; Real-World Applications.

This multi-volume LNCS set, LNCS 15148-15151, constitutes the refereed proceedings of the 18th International Conference on Parallel Problem Solving from Nature, PPSN 2024, held in Hagenberg, Austria, in September 2024.

The 101 full papers presented in these proceedings were carefully reviewed and selected from 294 submissions. The papers presented in these four volumes are organized in the following topical sections:

Part I: Combinatorial Optimization; Genetic Programming; Fitness Landscape Modeling and Analysis.

Part II: Benchmarking and Performance Measures; Automated Algorithm Selection and Configuration; Numerical Optimization; Bayesian- and Surrogate-Assisted Optimization.

Part III: Theoretical Aspects of Nature-Inspired Optimization; (Evolutionary) Machine Learning and Neuroevolution; Evolvable Hardware and Evolutionary Robotics.

Part IV: Multi-Objective Optimization; Real-World Applications.

This multi-volume LNCS set, LNCS 15148-15151, constitutes the refereed proceedings of the 18th International Conference on Parallel Problem Solving from Nature, PPSN 2024, held in Hagenberg, Austria, in September 2024.

The 101 full papers presented in these proceedings were carefully reviewed and selected from 294 submissions. The papers presented in these four volumes are organized in the following topical sections:

Part I: Combinatorial Optimization; Genetic Programming; Fitness Landscape Modeling and Analysis.

Part II: Benchmarking and Performance Measures; Automated Algorithm Selection and Configuration; Numerical Optimization; Bayesian- and Surrogate-Assisted Optimization.

Part III: Theoretical Aspects of Nature-Inspired Optimization; (Evolutionary) Machine Learning and Neuroevolution; Evolvable Hardware and Evolutionary Robotics.

Part IV: Multi-Objective Optimization; Real-World Applications.

This multi-volume LNCS set, LNCS 15148-15151, constitutes the refereed proceedings of the 18th International Conference on Parallel Problem Solving from Nature, PPSN 2024, held in Hagenberg, Austria, in September 2024.

The 101 full papers presented in these proceedings were carefully reviewed and selected from 294 submissions. The papers presented in these four volumes are organized in the following topical sections:

Part I: Combinatorial Optimization; Genetic Programming; Fitness Landscape Modeling and Analysis.

Part II: Benchmarking and Performance Measures; Automated Algorithm Selection and Configuration; Numerical Optimization; Bayesian- and Surrogate-Assisted Optimization.

Part III: Theoretical Aspects of Nature-Inspired Optimization; (Evolutionary) Machine Learning and Neuroevolution; Evolvable Hardware and Evolutionary Robotics.

Part IV: Multi-Objective Optimization; Real-World Applications.

This book brings together some of the most impactful researchers in the field of genetic programming (GP), each one working on unique and interesting intersections of theoretical development and practical applications of this evolutionary-based machine learning paradigm. Topics of particular interest for this year´s book include powerful modeling techniques through GP-based symbolic regression, novel selection mechanisms that help guide the evolutionary process, modular approaches to GP, and applications in cybersecurity, biomedicine, and program synthesis, as well as papers by practitioner of GP that focus on usability and real-world results. In summary, readers will get a glimpse of the current state-of-the-art in GP research.

Symbolic regression (SR) is one of the most powerful machine learning techniques that produces transparent models, searching the space of mathematical expressions for a model that represents the relationship between the predictors and the dependent variable without the need of taking assumptions about the model structure. Currently, the most prevalent learning algorithms for SR are based on genetic programming (GP), an evolutionary algorithm inspired from the well-known principles of natural selection. This book is an in-depth guide to GP for SR, discussing its advanced techniques, as well as examples of applications in science and engineering.

The basic idea of GP is to evolve a population of solution candidates in an iterative, generational manner, by repeated application of selection, crossover, mutation, and replacement, thus allowing the model structure, coefficients, and input variables to be searched simultaneously. Given that explainability and interpretability are key elements for integrating humans into the loop of learning in AI, increasing the capacity for data scientists to understand internal algorithmic processes and their resultant models has beneficial implications for the learning process as a whole.

This book represents a practical guide for industry professionals and students across a range of disciplines, particularly data science, engineering, and applied mathematics. Focused on state-of-the-art SR methods and providing ready-to-use recipes, this book is especially appealing to those working with empirical or semi-analytical models in science and engineering.

Symbolic regression (SR) is one of the most powerful machine learning techniques that produces transparent models, searching the space of mathematical expressions for a model that represents the relationship between the predictors and the dependent variable without the need of taking assumptions about the model structure. Currently, the most prevalent learning algorithms for SR are based on genetic programming (GP), an evolutionary algorithm inspired from the well-known principles of natural selection. This book is an in-depth guide to GP for SR, discussing its advanced techniques, as well as examples of applications in science and engineering.

The basic idea of GP is to evolve a population of solution candidates in an iterative, generational manner, by repeated application of selection, crossover, mutation, and replacement, thus allowing the model structure, coefficients, and input variables to be searched simultaneously. Given that explainability and interpretability are key elements for integrating humans into the loop of learning in AI, increasing the capacity for data scientists to understand internal algorithmic processes and their resultant models has beneficial implications for the learning process as a whole.

This book represents a practical guide for industry professionals and students across a range of disciplines, particularly data science, engineering, and applied mathematics. Focused on state-of-the-art SR methods and providing ready-to-use recipes, this book is especially appealing to those working with empirical or semi-analytical models in science and engineering.

This multi-volume LNCS set, LNCS 15148-15151, constitutes the refereed proceedings of the 18th International Conference on Parallel Problem Solving from Nature, PPSN 2024, held in Hagenberg, Austria, in September 2024.

The 101 full papers presented in these proceedings were carefully reviewed and selected from 294 submissions. The papers presented in these four volumes are organized in the following topical sections:

Part I: Combinatorial Optimization; Genetic Programming; Fitness Landscape Modeling and Analysis.

Part II: Benchmarking and Performance Measures; Automated Algorithm Selection and Configuration; Numerical Optimization; Bayesian- and Surrogate-Assisted Optimization.

Part III: Theoretical Aspects of Nature-Inspired Optimization; (Evolutionary) Machine Learning and Neuroevolution; Evolvable Hardware and Evolutionary Robotics.

Part IV: Multi-Objective Optimization; Real-World Applications.

This multi-volume LNCS set, LNCS 15148-15151, constitutes the refereed proceedings of the 18th International Conference on Parallel Problem Solving from Nature, PPSN 2024, held in Hagenberg, Austria, in September 2024.

The 101 full papers presented in these proceedings were carefully reviewed and selected from 294 submissions. The papers presented in these four volumes are organized in the following topical sections:

Part I: Combinatorial Optimization; Genetic Programming; Fitness Landscape Modeling and Analysis.

Part II: Benchmarking and Performance Measures; Automated Algorithm Selection and Configuration; Numerical Optimization; Bayesian- and Surrogate-Assisted Optimization.

Part III: Theoretical Aspects of Nature-Inspired Optimization; (Evolutionary) Machine Learning and Neuroevolution; Evolvable Hardware and Evolutionary Robotics.

Part IV: Multi-Objective Optimization; Real-World Applications.

This multi-volume LNCS set, LNCS 15148-15151, constitutes the refereed proceedings of the 18th International Conference on Parallel Problem Solving from Nature, PPSN 2024, held in Hagenberg, Austria, in September 2024.

The 101 full papers presented in these proceedings were carefully reviewed and selected from 294 submissions. The papers presented in these four volumes are organized in the following topical sections:

Part I: Combinatorial Optimization; Genetic Programming; Fitness Landscape Modeling and Analysis.

Part II: Benchmarking and Performance Measures; Automated Algorithm Selection and Configuration; Numerical Optimization; Bayesian- and Surrogate-Assisted Optimization.

Part III: Theoretical Aspects of Nature-Inspired Optimization; (Evolutionary) Machine Learning and Neuroevolution; Evolvable Hardware and Evolutionary Robotics.

Part IV: Multi-Objective Optimization; Real-World Applications.

This multi-volume LNCS set, LNCS 15148-15151, constitutes the refereed proceedings of the 18th International Conference on Parallel Problem Solving from Nature, PPSN 2024, held in Hagenberg, Austria, in September 2024.

The 101 full papers presented in these proceedings were carefully reviewed and selected from 294 submissions. The papers presented in these four volumes are organized in the following topical sections:

Part I: Combinatorial Optimization; Genetic Programming; Fitness Landscape Modeling and Analysis.

Part II: Benchmarking and Performance Measures; Automated Algorithm Selection and Configuration; Numerical Optimization; Bayesian- and Surrogate-Assisted Optimization.

Part III: Theoretical Aspects of Nature-Inspired Optimization; (Evolutionary) Machine Learning and Neuroevolution; Evolvable Hardware and Evolutionary Robotics.

Part IV: Multi-Objective Optimization; Real-World Applications.

This book brings together some of the most impactful researchers in the field of genetic programming (GP), each one working on unique and interesting intersections of theoretical development and practical applications of this evolutionary-based machine learning paradigm. Topics of particular interest for this year´s book include powerful modeling techniques through GP-based symbolic regression, novel selection mechanisms that help guide the evolutionary process, modular approaches to GP, and applications in cybersecurity, biomedicine, and program synthesis, as well as papers by practitioner of GP that focus on usability and real-world results. In summary, readers will get a glimpse of the current state-of-the-art in GP research.