Real Royal Road Functions for Constant Population Size

Storch, Tobias; Wegener, Ingo

doi:10.1007/3-540-45110-2_14

Cited by 26 publications

(22 citation statements)

References 3 publications

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“…In the past decade or so theoreticians have started to apply computational complexity techniques to a variety of EAs. Precise bounds on the expected run time for a variety of EAs have been obtained by using such techniques [116][117][118][119][120][121][122][123]. Typically, this has been done only for specific classes of functions although there are some exceptions where run-time bounds have been derived for more general combinatorial optimisation problems [124][125][126][127][128][129][130][131].…”

Section: Convergence Proofs and Computational Complexitymentioning

confidence: 99%

Theoretical results in genetic programming: the next ten years?

Poli

Vanneschi

Langdon

et al. 2010

Genet Program Evolvable Mach

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We consider the theoretical results in GP so far and prospective areas for the future. We begin by reviewing the state of the art in genetic programming (GP) theory including: schema theories, Markov chain models, the distribution of functionality in program search spaces, the problem of bloat, the applicability of the no-free-lunch theory to GP, and how we can estimate the difficulty of problems before actually running the system. We then look at how each of these areas might develop in the next decade, considering also new possible avenues for theory, the challenges ahead and the open issues.

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Section: Convergence Proofs and Computational Complexitymentioning

confidence: 99%

Theoretical results in genetic programming: the next ten years?

Poli

Vanneschi

Langdon

et al. 2010

Genet Program Evolvable Mach

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“…However, studies so far have eluded the most fundamental setting of building-block functions. Crossover was proven to be superior to mutation only on constructed artificial examples like Jump k [9,12] and "Real Royal Road" functions [10,18], the H-IFF problem [2], coloring problems inspired by the Ising model from physics [5,19], and the all-pairs shortest path problem [3,22,17]. H-IFF [2] and the Ising model on trees [19] consist of hierarchical building blocks.…”

Section: Introductionmentioning

confidence: 99%

Crossover speeds up building-block assembly

Sudholt

2012

Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation

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We re-investigate a fundamental question: how effective is crossover in combining building blocks? Although this has been discussed controversially for decades, we are still lacking a rigorous and intuitive answer. We provide such answers for royal road functions and OneMax, where every bit is a building block. For the latter we prove that a simple GA with uniform crossover is twice as fast as the fastest EA using only standard bit mutation, up to small-order terms. The reason is that crossover effectively turns neutral mutations into improvements by combining the right building blocks at a later stage. Compared to mutation-based EAs, this makes multi-bit mutations more useful. Introducing crossover changes the optimal mutation rate on OneMax from 1/n to (1 + √ 5)/2 · 1/n ≈ 1.618/n. Similar results are proved for k-point crossover. Experiments and statistical tests confirm that our findings apply to a broad class of building-block functions.

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“…However, examples with reverse run-times are also given. In 2003 Storch and Wegener introduced new royal road functions for which the same previous results can be obtained but with the minimum population size of 2 individuals [38] . He and Yao, in 2002, presented another paper proving how a population may be beneficial over single individuals on all sorts of pseudo boolean toy problems [24] .…”

Section: When Populations Are Beneficialmentioning

confidence: 58%

Time complexity of evolutionary algorithms for combinatorial optimization: A decade of results

Oliveto

Yao

2007

Int J Automat Comput

188

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Computational time complexity analyzes of evolutionary algorithms (EAs) have been performed since the mid-nineties. The first results were related to very simple algorithms, such as the (1+1)-EA, on toy problems. These efforts produced a deeper understanding of how EAs perform on different kinds of fitness landscapes and general mathematical tools that may be extended to the analysis of more complicated EAs on more realistic problems. In fact, in recent years, it has been possible to analyze the (1+1)-EA on combinatorial optimization problems with practical applications and more realistic population-based EAs on structured toy problems. This paper presents a survey of the results obtained in the last decade along these two research lines. The most common mathematical techniques are introduced, the basic ideas behind them are discussed and their elective applications are highlighted. Solved problems that were still open are enumerated as are those still awaiting for a solution. New questions and problems arisen in the meantime are also considered.

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Real Royal Road Functions for Constant Population Size

Cited by 26 publications

References 3 publications

Theoretical results in genetic programming: the next ten years?

Theoretical results in genetic programming: the next ten years?

Crossover speeds up building-block assembly

Time complexity of evolutionary algorithms for combinatorial optimization: A decade of results

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