An efficient local search-based genetic algorithm for constructing optimal Latin hypercube design

Shang, Xiaobing; Chao, Tao; Ma, Ping; Yang, Ming

doi:10.1080/0305215x.2019.1584618

Cited by 30 publications

(11 citation statements)

References 36 publications

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“…On the other hand, the Latin hypercube sampling provides a stratified sampling framework for improved coverage of the k-dimensional input space (e.g. McKay et al, 2000;Helton and Davis, 2003;Iman, 2008;Clifford et al, 2014;Shields and Zhang, 2016;Shang et al, 2020). Conditioned Latin hypercube sampling is an attempt to draw a sample that captures the variation of multiple environmental variables.…”

Section: Uncertainties In Global Mean Temperaturementioning

confidence: 99%

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Ilyas

2021

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Instrumental temperature records are derived from the network of in situ measurements of land and sea surface temperatures. This observational evidence is seen as fundamental to climate science. Therefore, the accuracy of these measurements is of prime importance for the analysis of temperature variability. There are spatial gaps in the distribution of instrumental temperature measurements across the globe. This lack of spatial coverage introduces coverage error. An approximate Bayesian computation based multi-resolution lattice kriging is developed and used to quantify the coverage errors through the variance of the spatial process at multiple spatial scales. It critically accounts for the variation in the parameters of this advanced spatial statistics model itself, thereby providing for the first time a full description of both the spatial coverage uncertainties along with the uncertainties in the modelling of these spatial gaps. These coverage errors are combined with the existing estimates of uncertainties due to observational issues at each station location. It results in an ensemble of 100,000 monthly temperatures fields over the entire globe that samples the combination of coverage, parametric and observational uncertainties from 1850 till 2018 over a 5 • × 5 • grid.

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Section: Uncertainties In Global Mean Temperaturementioning

confidence: 99%

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Ilyas

2021

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“…Additionally, the Monte Carlo samples can contain some points clustered closely, while other intervals within the space obtain no sample. On the other hand, the Latin hypercube sam-pling provides a stratified sampling framework for improved coverage of the k-dimensional input space (e.g., McKay et al, 2000;Helton and Davis, 2003;Iman, 2008;Clifford et al, 2014;Shields and Zhang, 2016;Shang et al, 2020). Conditioned Latin hypercube sampling is an attempt to draw a sample that captures the variation in multiple environmental variables.…”

Section: Subsample Of Hyperparameter Ensemble Datamentioning

confidence: 99%

Global ensemble of temperatures over 1850–2018: quantification of uncertainties in observations, coverage, and spatial modeling (GETQUOCS)

et al. 2021

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Abstract. Instrumental global temperature records are derived from the network of in situ measurements of land and sea surface temperatures. This observational evidence is seen as being fundamental to climate science. Therefore, the accuracy of these measurements is of prime importance for the analysis of temperature variability. There are spatial gaps in the distribution of instrumental temperature measurements across the globe. This lack of spatial coverage introduces coverage error. An approximate Bayesian computation based multi-resolution lattice kriging is developed and used to quantify the coverage errors through the variance of the spatial process at multiple spatial scales. It critically accounts for the uncertainties in the parameters of this advanced spatial statistics model itself, thereby providing, for the first time, a full description of both the spatial coverage uncertainties along with the uncertainties in the modeling of these spatial gaps. These coverage errors are combined with the existing estimates of uncertainties due to observational issues at each station location. It results in an ensemble of 100 000 monthly temperatures fields over the entire globe that samples the combination of coverage, parametric and observational uncertainties from 1850 to 2018 over a 5∘×5∘ grid.

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“…According to publication [31], population sizes were 20 × dimensions for small size LHDs, 10 × dimensions for medium and large size LHDs, respectively, in PermGA, while elite size, crossover and mutation rates were 5, 0.8, 0.05 [15], respectively. For LSGA, the author of literature [25] suggested that population number P, mutation probability m p , parameters max p , min p and distance ratio c were 10, 0.2, 0.3, 0.01 and 0.5, respectively, while there was no parameter settings for ILS.…”

Section: A Experimental Settingmentioning

confidence: 99%

“…Husslage et al [28] made a comparison of simulated annealing (SA), ESE and PermGA algorithms and the results showed that the ESE algorithm found better results than SA and PermGA algorithms for almost all of the cases. Moreover, the performance of ESE algorithm for establishment of OLHD with high space-filling quality was further validated in literatures [14], [22], [23] and [25] through comparing with SOBSA, GA, SLE, SLHD, LSGA and a novel extension algorithms. The results revealed that the ESE algorithm is a significantly efficient and robust algorithm for optimizations of LHDs within 10 dimensions.…”

Section: Introductionmentioning

confidence: 97%

“…Hence, the balance between time costs and optimality of solution in the global optimization of LHD interests and challenges researchers. Thus, many outstanding efforts for improving efficiency in construction of LHDs with high space-filling quality were made, which include enhancement of enhanced stochastic evolutionary (EESE) algorithm (Chantarawong et al [11]), successive local enumeration (SLE) algorithm (Zhu et al [12]), particle swarm optimization (PSO) algorithm (Chen et al [13]), sequencing optimization based on simulated annealing (SOBSA) algorithm (Pholdee, and S. Bureera [14]), a new DOE framework based on PermGA (Kianifar et al [15]), PermGA based on chromosome-length-expansion (CLE) scheme (Mahmoudi and Zimmermann [16]), slice latin-hypercube design (SLHD) (Ba et al [17]), maximum projection design (Joseph et al [18] and [19]), sequential-successive local enumeration (S-SLE) algorithm (Long et al [20]), inflate, expand and stack (IES) algorithm (GuiBan et al [21]), an efficient method for constructing space-filling and nearorthogonality Sequential LHD (Wu,et al [22]), a novel extension algorithm (Li et al [23]), maximin distance latin squares and related latin-hypercube design based on Costas arrays and the Welch, Gilbert and Golomb methods (Xiao and Xu [24]) and local search-based genetic algorithm (LSGA) (Shang et al [25]). Additionally, in publications, we noticed a quite efficient algorithm, the latin-hypercube via translational propagation (TPLHD), was developed by Grosso et al [26] to faster construct a near high-quality design.…”

Section: Introductionmentioning

confidence: 99%

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Modified Algorithms for Fast Construction of Optimal Latin-Hypercube Design

et al. 2020

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As accuracy of optimization can not be guaranteed without high-quality samples, the distribution of a finite number of evaluation points where experiments should be conducted in design space is an important issue, particularly when the experiment to obtain sample is expensive. To utilize limited number of evaluation points to represent the design space, optimal latin-hypercube design (OLHD), with considerable space-filling quality, is widely used as a methodology in design of experiments (DOE). However, OLHD generation requires significant time. This study focuses on further improvement of efficiency in generation of OLHD in terms of both time and latin-hypercube design (LHD) optimization. Two modified algorithms, namely the modified enhanced stochastic evolutionary (MESE) and translational propagation modified enhanced stochastic evolutionary (TPMESE) algorithms, based on existing algorithms, are proposed. The MESE algorithm is modified from the enhanced stochastic evolutionary (ESE) algorithm by using a new update method for "temperature," while the TPMESE algorithm optimizes the LHD via translational propagation (TPLHD) instead of optimizing a random LHD like the MESE algorithm does. Their performance is evaluated by comparison with several famous heuristic algorithms and each original algorithm using optimization tests of LHDs with various sizes. For all cases, proposed algorithms show better performance of convergence than other heuristic algorithms participated in our comparison. For large and medium LHDs, the MESE algorithm faster converges to a solution with the same level as original algorithm (ESE). For large LHDs, the TPMESE algorithm is the most time efficient algorithm in obtaining near-optimal or sufficient near-optimal designs. INDEX TERMS Optimal latin-hypercube design, design of experiments, evolutionary algorithm, translational propagation

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An efficient local search-based genetic algorithm for constructing optimal Latin hypercube design

Cited by 30 publications

References 36 publications

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Global ensemble of temperatures over 1850–2018: quantification of uncertainties in observations, coverage, and spatial modeling (GETQUOCS)

Modified Algorithms for Fast Construction of Optimal Latin-Hypercube Design

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