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An Introduction to Geometric Semantic Genetic Programming

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Book cover NEO 2015

Part of the book series: Studies in Computational Intelligence ((SCI,volume 663))

Abstract

For all supervised learning problems, where the quality of solutions is measured by a distance between target and output values (error), geometric semantic operators of genetic programming induce an error surface characterized by the absence of locally suboptimal solutions (unimodal error surface). So, genetic programming that uses geometric semantic operators, called geometric semantic genetic programming, has a potential advantage in terms of evolvability compared to many existing computational methods. This fosters geometric semantic genetic programming as a possible new state-of-the-art machine learning methodology. Nevertheless, research in geometric semantic genetic programming is still much in demand. This chapter is oriented to researchers and students that are not familiar with geometric semantic genetic programming, and are willing to contribute to this exciting and promising field. The main objective of this chapter is explaining why the error surface induced by geometric semantic operators is unimodal, and why this fact is important. Furthermore, the chapter stimulates the reader by showing some promising applicative results that have been obtained so far. The reader will also discover that some properties of geometric semantic operators may help limiting overfitting, bestowing on genetic programming a very interesting generalization ability. Finally, the chapter suggests further reading and discusses open issues of geometric semantic genetic programming.

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Notes

  1. 1.

    When the quality of a solution, or fitness, is equal to an error between calculated values and targets, like in the cases studied in this chapter, the terms error surface and fitness landscape are synonymous. The former term is generally used by the machine learning community, while the latter is more popular in the evolutionary computation terminology. In this chapter, these two terms will be used interchangeably.

  2. 2.

    The example in Sect. 3.4, contrarily to the previous examples, is a case of continuous optimization. Thus, it is practically impossible to find exactly the global optimum. From now on, when continuous optimization is considered, the term “solving” the problem will be used to indicate that it is possible to approximate a globally optimal solution with any prefixed precision.

  3. 3.

    In several references [49], the term ball mutation, instead of box mutation, can be found for indicating this operator. If the area of variation induced by this operator can geometrically be represented as a “box” or a “ball”, it depends on the particular metric used, as explained in [36]. In this simple example, we are considering the intuitive Euclidean distance and this is why we use the term box mutation.

  4. 4.

    The word “cono” actually means cone in several languages of Latin origin, among which Italian and Spanish.

  5. 5.

    How could it be otherwise? GP is working with a population of trees, so the genetic operators can only act on them!

  6. 6.

    Simple references to lookup table entries can be used in the implementation instead of real memory pointers (see [6, 49]). This makes the implementation possible also in programming languages that do not allow direct manipulation of memory pointers, like for instance Java or MatLab.

  7. 7.

    The term “ancestors” here is a bit abused to designate not only the parents but also the random trees used to build an individual by crossover or mutation.

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Acknowledgments

My heartfelt acknowledgment goes to Sara Silva and Mauro Castelli, who shared with me the work on geometric semantic genetic programming and much much more! I also dearly thank Leonardo Trujillo and Oliver Schütze for inviting me to the NEO 2015 workshop. It has been an unforgettable experience.

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  1. NOVA IMS, Universidade Nova de Lisboa, 1070-312, Lisboa, Portugal

    Leonardo Vanneschi

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  1. Leonardo Vanneschi
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Correspondence to Leonardo Vanneschi .

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  1. Departamento de Comput Cinvestav-IPN, Mexico, Mexico

    Oliver Schütze

  2. Posgrado en Ciencias de la Ingeniería, Instituto Tecnológico de Tijuana, Tijuana, Baja California, Mexico

    Leonardo Trujillo

  3. Université de Bordeaux, Bordeaux, France

    Pierrick Legrand

  4. Posgrado en Ciencias de la Ingeniería, Instituto Tecnológico de Tijuana, Tijuana, Mexico

    Yazmin Maldonado

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Vanneschi, L. (2017). An Introduction to Geometric Semantic Genetic Programming. In: Schütze, O., Trujillo, L., Legrand, P., Maldonado, Y. (eds) NEO 2015. Studies in Computational Intelligence, vol 663. Springer, Cham. https://doi.org/10.1007/978-3-319-44003-3_1

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