Generalized jump functions

Bambury, Henry; Bultel, Antoine; Doerr, Benjamin

doi:10.1145/3449639.3459367

Cited by 26 publications

(11 citation statements)

References 43 publications

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“…Theorem 7. Let n ∈ N >0 be even, r ∈ [n/2], and let λ be as in equation (6). For sufficiently large n, the expected run time of RLS on MAJORITY r with uniform initialization is at most 6r • (λ r − 1)/(λ − 1) + n 1 + ln(r) /2.…”

Section: Theoretical Results For Rlsmentioning

confidence: 99%

“…b) Related work: Analyzing the performance of EAs on plateaus by theoretical means is a well-established concept. The arguably most studied benchmark function with a plateau is JUMP, existing in different variants, many of which were proposed recently [5], [6], [7], [8]. However, the problem posed by the plateau in JUMP is typically different than from crossing a plateau, as we discuss in the following.…”

Section: Introductionmentioning

confidence: 99%

“…This is in contrast to crossing a plateau, where the behavior of an EA on the plateau is very important. The main importance of jumping remains true for JUMP when shifting the global optimum [7] and/or increasing the number of global optima to jump to [6], [8]. However, the picture changes when considering EAs that apply crossover, that is, combining different solutions when creating new ones.…”

Section: Introductionmentioning

confidence: 99%

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Run Time Analysis for Random Local Search on Generalized Majority Functions

Doerr¹,

Krejca²

2022

Preprint

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Run time analysis of evolutionary algorithms recently makes significant progress in linking algorithm performance to algorithm parameters. However, settings that study the impact of problem parameters are rare. The recently proposed Wmodel provides a good framework for such analyses, generating pseudo-Boolean optimization problems with tunable properties.We initiate theoretical research of the W-model by studying how one of its properties-neutrality-influences the run time of random local search. Neutrality creates plateaus in the search space by first performing a majority vote for subsets of the solution candidate and then evaluating the smaller-dimensional string via a low-level fitness function.We prove upper bounds for the expected run time of random local search on this MAJORITY problem for its entire parameter spectrum. To this end, we provide a theorem, applicable to many optimization algorithms, that links the run time of MAJORITY with its symmetric version HASMAJORITY, where a sufficient majority is needed to optimize the subset. We also introduce a generalized version of classic drift theorems as well as a generalized version of Wald's equation, both of which we believe to be of independent interest.

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Section: Theoretical Results For Rlsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Run Time Analysis for Random Local Search on Generalized Majority Functions

Doerr¹,

Krejca²

2022

Preprint

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“…There is a large theory literature on how well algorithms handle 'jump functions', i.e. problems where there are local optima from which a jumps must be taken to reach the global optimum [3,13,86]. This subsection shows how expressive encodings can enable reliable jumps of maximal size-a useful feature for EAs in general.…”

Section: Special Case: Miracle Jumpsmentioning

confidence: 99%

“…The problems in this section all required jumps of size Θ(𝑛). Prior work with direct encodings has sought to tackle larger and larger jumps, but they are still generally sublinear [3,13]. The closest comparison [84] had jumps of size 𝑂 ( √ 𝑛), but required a representation that was a priori well-aligned for two-point crossover, and an island model with a number of islands dependent on the 𝑛.…”

Section: Extensionsmentioning

confidence: 99%

Simple Genetic Operators are Universal Approximators of Probability Distributions (and other Advantages of Expressive Encodings)

Meyerson,

Qiu,

Miikkulainen

2022

Preprint

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This paper characterizes the inherent power of evolutionary algorithms. This power depends on the computational properties of the genetic encoding. With some encodings, two parents recombined with a simple crossover operator can sample from an arbitrary distribution of child phenotypes. Such encodings are termed expressive encodings in this paper. Universal function approximators, including popular evolutionary substrates of genetic programming and neural networks, can be used to construct expressive encodings. Remarkably, this approach need not be applied only to domains where the phenotype is a function: Expressivity can be achieved even when optimizing static structures, such as binary vectors. Such simpler settings make it possible to characterize expressive encodings theoretically: Across a variety of test problems, expressive encodings are shown to achieve up to super-exponential convergence speed-ups over the standard direct encoding. The conclusion is that, across evolutionary computation areas as diverse as genetic programming, neuroevolution, genetic algorithms, and theory, expressive encodings can be a key to understanding and realizing the full power of evolution. CCS CONCEPTS• Computing methodologies → Genetic algorithms; Genetic programming; Neural networks.

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Stagnation Detection Meets Fast Mutation

Doerr

Rajabi

2022

Evolutionary Computation in Combinatorial Optimization

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Generalized jump functions

Cited by 26 publications

References 43 publications

Run Time Analysis for Random Local Search on Generalized Majority Functions

Run Time Analysis for Random Local Search on Generalized Majority Functions

Simple Genetic Operators are Universal Approximators of Probability Distributions (and other Advantages of Expressive Encodings)

Stagnation Detection Meets Fast Mutation

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