On inversely proportional hypermutations with mutation potential

Corus, Dogan; Oliveto, Pietro S.; Yazdani, D.

doi:10.1145/3321707.3321780

Cited by 6 publications

(6 citation statements)

References 21 publications

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“…The original motivation for using the HVL-Prime operator was that of making the smallest alterations possible to GP trees while respecting the key properties of the GP tree search space: variable length Algorithm 2: The HVL-Prime mutation operator Data: A binary syntax tree X. 1 Choose op ∈ {INS, DEL, SUB} uniformly at random; 2 if X is an empty tree then 3 Choose a literal l ∈ L uniformly at random; 4 Set l to be the root of X;…”

Section: Preliminariesmentioning

confidence: 99%

“…Such difficulties, naturally, impact the runtime analysis of GP considerably, where space complexity also comes into play. As a result, while nowadays the analysis of standard elitist [3,4] and nonelitist genetic algorithms [39,40,2] has finally become a reality, analyzing standard GP systems is far more prohibitive. Indeed, McDermott and O'Reilly [30] remarked that "due to stochasticity, it is arguably impossible in most cases to make formal guarantees about the number of fitness evaluations needed for a GP algorithm to find an optimal solution."…”

Section: Introductionmentioning

confidence: 99%

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Computational Complexity Analysis of Genetic Programming

Lissovoi

Oliveto

2019

Natural Computing Series

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Genetic programming (GP) is an evolutionary computation technique to solve problems in an automated, domain-independent way. Rather than identifying the optimum of a function as in more traditional evolutionary optimization, the aim of GP is to evolve computer programs with a given functionality. While many GP applications have produced human competitive results, the theoretical understanding of what problem characteristics and algorithm properties allow GP to be effective is comparatively limited. Compared with traditional evolutionary algorithms for function optimization, GP applications are further complicated by two additional factors: the variable-length representation of candidate programs, and the difficulty of evaluating their quality efficiently. Such difficulties considerably impact the runtime analysis of GP, where space complexity also comes into play. As a result, initial complexity analyses of GP have focused on restricted settings such as the evolution of trees with given structures or the estimation of solution quality using only a small polynomial number of input/output examples. However, the first computational complexity analyses of GP for evolving proper functions with defined input/output behavior have recently appeared. In this chapter, we present an overview of the state of the art.Algorithm 1: The (1+1) GP 1 Initialize a tree X;We will also consider the theoretical work on GSGP, where the variation operators used by the GP system are designed to modify program semantics rather than program syntax.This chapter presents an overview of the state of the art. It is structured as follows. In Section 2, we introduce the (1 + 1) GP, the GP system used for most of the available computational complexity analysis results. In Section 3, we present an overview of the analyses of GP systems for evolving tree structures with specific properties (the Order, Majority, and Sorting problems). In Section 4, we present results where GP systems evolve programs with limited functionality: the MAX problem is considered in Subsection 4.1, and the Identification problem in Subsection 4.2. Section 5 presents results for GP evolving proper Boolean functions of arity n. Section 6 presents a brief overview of the computational complexity results available for GSGP algorithms. Finally, Section 7 presents a summary of the presented results and discusses the open directions for future work.

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Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Computational Complexity Analysis of Genetic Programming

Lissovoi

Oliveto

2019

Natural Computing Series

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“…More recently, Corus et al [14] compared different variants of inversely fitness-proportional mutation potentials based on Hamming distance and fitness difference. They showed that a potential that increases exponentially with the Hamming distance to the optimum (called M expoHD ) is most promising and argued that using Hamming distance instead of fitness difference also comes with the advantage of robustness to scaling of the fitness function.…”

Section: Inversely Fitness-proportional Mutation Potentialsmentioning

confidence: 99%

“…Thus, the operator performed all n mutation steps and returned the best sampled search point instead of the first improved one. Later, Corus et al [14] demonstrated that their inversely fitness-proportional mutation potential (see Section 2.3.1) together with aging was able to optimize Cliff d with d = Θ(n) in expected polynomial time even if FCM is used.…”

Section: Opt-iamentioning

confidence: 99%

Theoretical Foundations of Immune-Inspired Randomized Search Heuristics for Optimization

Zarges

2019

Natural Computing Series

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Artificial immune systems are a class of nature-inspired algorithms based on the immune system of vertebrates. They have been used in a large number of different areas of application, most prominently learning, classification, pattern recognition, and (function) optimization. In the context of optimization, clonal selection algorithms are the most popular and constitute an interesting and promising alternative to evolutionary algorithms. While structurally similar, they offer very different features and capabilities. Over the last decade, significant progress has been made in the theoretical foundations of clonal selection algorithms. This chapter gives an overview of the state of the art in the theory of artificial immune systems with a focus on optimization. It provides pointers to corresponding articles where more details and proofs can be found. * This is a preliminary version of a chapter in the upcoming book "Theory of Evolutionary Computation: Recent Developments in Discrete Optimization", edited by Benjamin Doerr and Frank Neumann, to be published by Springer.

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“…However, the static HMP operator with FCM has also been proven to have runtimes of respectively Θ(n 2 log n) expected fitness evaluations for ONEMAX and Θ(n 3 ) for LEADINGONES. Recently, speed-ups in the exploitation phase have been shown for the Inversely Proportional HMP variant (INV HMP), that aims to decrease the mutation rate as the local and global optima are approached [11]. On one hand, while faster, INV HMP operators are still asymptotically slower than RLS and EAs for easy hillclimbing problems such as ONEMAX and LEADINGONES.…”

Section: Introductionmentioning

confidence: 99%