Constructing de Bruijn sequences by concatenating smaller universal cycles

Gabric, Daniel; Sawada, Joe

doi:10.1016/j.tcs.2018.06.039

Cited by 11 publications

(6 citation statements)

References 25 publications

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“…In order to avoid re-evaluating costly objective-function evaluations at equivalent blade arrangements, we propose to use the concept of necklace [22,23]. In combinatorics, a k-ary necklace of length n is an equivalence class of ncharacter strings over an alphabet k = {a 1 , a 2 , .…”

Section: The Necklace Distancementioning

confidence: 99%

“…We wish to restrict the search to distinct arrangements, thereby avoiding costly black-box objective-function evaluations at equivalent solutions. To that aim, we introduce the necklace distance, noted d neck , inspired from the concept of necklace in combinatorics [22,23], and we define a trust-region subproblem based on this new distance. Our main contribution is a new method, named DFOb-d neck , which includes the necklace distance for derivative-free mixed binary optimization with cyclic-symmetry problems.…”

Section: Introductionmentioning

confidence: 99%

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Derivative-free mixed binary necklace optimization for cyclic-symmetry optimal design problems

et al. 2021

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This paper presents an adapted trust-region method for computationally expensive black-box optimization problems with mixed binary variables that involve a cyclic symmetry property. Mixed binary problems occur in several practical optimal design problems, e.g., aircraft engine turbines, mooring lines of offshore wind turbines, electric engine stators and rotors. The motivating application for this study is the optimal design of helicopter bladed disk turbomachines. The necklace concept is introduced to deal with the cyclic symmetry property, and to avoid costly black-box objective-function evaluations at equivalent solutions. An adapted distance is proposed for the discretespace exploration step of the optimization method. A convergence analysis is presented for the trust-region derivative-free algorithm, DFOb-d H , extended to the mixed-binary case and based on the Hamming distance. The convergence proof is extended to the new algorithm, DFOb-d neck , which is based on the necklace distance. Computational comparison with state-of-the-art blackbox optimization methods is performed on a set of analytical problems and on a simplified industrial application.

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Section: The Necklace Distancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Derivative-free mixed binary necklace optimization for cyclic-symmetry optimal design problems

et al. 2021

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“…In order to detect similar blade arrangements, we introduce the concept of "necklace" [12,13]. In combinatorics, a k-ary necklace of length n is an equivalence class of n-character strings over an alphabet k = {a 1 , .…”

Section: Adapted Distance For Blade Design Applicationmentioning

confidence: 99%

Advanced Computational Methods for Knowledge Engineering

Nguyên

Do²,

Thi

2020

Advances in Intelligent Systems and Computing

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Numerous optimal design applications are black-box mixed integer nonlinear optimization problems: with objective function and constraints that are outputs of a black-box simulator involving mixed continuous and integer (discrete) variables. In this paper, we address an optimal design application for bladed disks of turbo-machines in aircraft. We discuss the formulation of an appropriate distance with respect to discrete variables which can deal with the cyclic symmetry property of the system under study. The necklace concept is introduced to characterize similar blade configurations and an adapted distance is proposed for discrete space exploration of a derivative-free optimization method. The results obtained with this method on a simplified industrial application are compared with results of state-of-the-art black-box optimization methods.

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“…The sequences generated by the CCR2 and CCR3 constructions can also be constructed by concatenation approaches [16] described later in this section; the equivalence of the shift-rules to their respective concatenation constructions has been confirmed up to n = 30, though no formal proof has been given. The Huang construction is a shift-rule based construction in [20].…”

Section: Computing the Discrepancy Of A De Bruijn Sequencementioning

confidence: 99%

“…For example, the following four columns are the co-necklace equivalence classes for n = 5: The periodic reduction of string α, denoted pr(α) is the smallest prefix β of α such that α = β t for some t ≥ 1. In [16], the following two de Bruijn sequence constructions CCR2 and CCR3 concatenate the periodic reductions of αα for given representatives α of each co-necklace equivalence class.…”

Section: Computing the Discrepancy Of A De Bruijn Sequencementioning

confidence: 99%

Investigating the discrepancy property of de Bruijn sequences

Gabric¹,

Sawada²

2020

Preprint

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The discrepancy of a binary string refers to the maximum (absolute) difference between the number of ones and the number of zeroes over all possible substrings of the given binary string. We provide an investigation of the discrepancy of known simple constructions of de Bruijn sequences. Furthermore, we demonstrate constructions that attain the lower bound of Θ(n) and a new construction that attains the previously known upper bound of Θ( 2 n √ n ). This extends the work of Cooper and Heitsch [Discrete Mathematics, 310 (2010)].

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Constructing de Bruijn sequences by concatenating smaller universal cycles

Cited by 11 publications

References 25 publications

Derivative-free mixed binary necklace optimization for cyclic-symmetry optimal design problems

Derivative-free mixed binary necklace optimization for cyclic-symmetry optimal design problems

Advanced Computational Methods for Knowledge Engineering

Investigating the discrepancy property of de Bruijn sequences

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