Computational complexity analysis of simple genetic programming on two problems modeling isolated program semantics

Durrett, Greg; Neumann, Franz‐Josef; O’Reilly, Una-May

doi:10.1145/1967654.1967661

Cited by 32 publications

(78 citation statements)

References 21 publications

(30 reference statements)

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“…For instance, Durrett et al [5] analyzed the probabilities of improvement and time bounds for solving majority and order problems using a simplified variant of GP. However, in absence of two distance metrics, one in fitness function and the other underlying a search operator, these and other non-GSGP works do not directly relate of this study.…”

Section: Related Workmentioning

confidence: 99%

Progress properties and fitness bounds for geometric semantic search operators

Pawlak

Krawiec

2015

Genet Program Evolvable Mach

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Metrics are essential for geometric semantic genetic programming. On one hand, they structure the semantic space and govern the behavior of geometric search operators; on the other, they determine how fitness is calculated. The interactions between these two types of metrics are an important aspect that to date was largely neglected. In this paper, we investigate these interactions and analyze their consequences. We provide a systematic theoretical analysis of the properties of abstract geometric semantic search operators under Minkowski metrics of arbitrary order. For nine combinations of popular metrics (city-block, Euclidean, and Chebyshev) used in fitness functions and of search operators, we derive pessimistic bounds on fitness change. We also define three types of progress properties (weak, potential, and strong) and verify them for operators under those metrics. The analysis allows us to determine the combinations of metrics that are most attractive in terms of progress properties and deterioration bounds.

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Section: Related Workmentioning

confidence: 99%

Progress properties and fitness bounds for geometric semantic search operators

Pawlak

Krawiec

2015

Genet Program Evolvable Mach

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“…Note that it does not work with a tree structure as the tree-based genetic programming approach analyzed by Durrett et al [2]. We are rather interested in how the right coefficients can be learned for the given class of functions.…”

Section: Problem and Algorithmsmentioning

confidence: 99%

“…The computational complexity analysis of genetic programming has just been started by Durrett et al [2]. In their paper, they focus on simple problems such as ORDER and MAJORITY introduced by Goldberg and O'Reilly [6] and analyze the time to achieve an exact solution for these given problems.…”

Section: Introductionmentioning

confidence: 99%

PAC learning and genetic programming

Kötzing

Neumann

Spöhel

2011

Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation

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Genetic programming (GP) is a very successful type of learning algorithm that is hard to understand from a theoretical point of view. With this paper we contribute to the computational complexity analysis of genetic programming that has been started recently. We analyze GP in the well-known PAC learning framework and point out how it can observe quality changes in the the evolution of functions by random sampling. This leads to computational complexity bounds for a linear GP algorithm for perfectly learning any member of a simple class of linear pseudo-Boolean functions. Furthermore, we show that the same algorithm on the functions from the same class finds good approximations of the target function in less time.

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“…Due to the difficulty of analysing GP, there is only very initial work on its runtime analysis. Durrett et al [5] present the runtime analysis of a mutation-based GP with a tree representation on very simplified problems, in which trees do not represent functions (i.e., objects that return different output values for different input values) but, rather, structures (i.e., objects whose fitness depends on some structural properties of the tree representation). This deviates quite significantly from the very essence of GP, which is about evolving functions.…”

Section: Introductionmentioning

confidence: 99%

Runtime analysis of mutation-based geometric semantic genetic programming on boolean functions

Moraglio

Mambrini

Manzoni

2013

Proceedings of the Twelfth Workshop on Foundations of Genetic Algorithms XII

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Geometric Semantic Genetic Programming (GSGP) is a recently introduced form of Genetic Programming (GP), rooted in a geometric theory of representations, that searches directly the semantic space of functions/programs, rather than the space of their syntactic representations (e.g., trees) as in traditional GP. Remarkably, the fitness landscape seen by GSGP is always -for any domain and for any problemunimodal with a linear slope by construction. This has two important consequences: (i) it makes the search for the optimum much easier than for traditional GP; (ii) it opens the way to analyse theoretically in a easy manner the optimisation time of GSGP in a general setting. The runtime analysis of GP has been very hard to tackle, and only simplified forms of GP on specific, unrealistic problems have been studied so far. We present a runtime analysis of GSGP with various types of mutations on the class of all Boolean functions.

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Computational complexity analysis of simple genetic programming on two problems modeling isolated program semantics

Cited by 32 publications

References 21 publications

Progress properties and fitness bounds for geometric semantic search operators

Progress properties and fitness bounds for geometric semantic search operators

PAC learning and genetic programming

Runtime analysis of mutation-based geometric semantic genetic programming on boolean functions

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