Construction of maximin distance Latin squares and related Latin hypercube designs

Xiao, Qian; Xu, Hongquan

doi:10.1093/biomet/asx006

Cited by 33 publications

(20 citation statements)

References 13 publications

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“…In such situations, space-filling designs are ideal due to their robustness. [20][21][22][23][24] Maximin distance designs are ideal for kriging models, as any unobserved point will not be too far from observed design points and thus the prediction error will not be too big. An interesting topic for the future research is how space-filling designs, especially maximin distance designs, perform under kriging models in drug combination studies.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Application of kriging models for a drug combination experiment on lung cancer

Xiao

Wang

2018

Statistics in Medicine

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Combinatorial drugs have been widely applied in disease treatment, especially chemotherapy for cancer, due to its improved efficacy and reduced toxicity compared with individual drugs. The study of combinatorial drugs requires efficient experimental designs and proper follow-up statistical modeling techniques. Linear and nonlinear models are often used in the response surface modeling for such experiments. We propose the use of kriging models to better depict the response surfaces of combinatorial drugs. We illustrate our method via a drug combination experiment on lung cancer and further show how proper experimental designs can reduce the necessary run size. We demonstrate that only 27 runs are needed to predict all 512 runs in the original experiment and achieve better precision than existing analyses.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Application of kriging models for a drug combination experiment on lung cancer

Xiao

Wang

2018

Statistics in Medicine

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“…, 30 and n = φ(N). Table 2 compares LHDs generated by the linear permutation, the Williams transformation, R package SLHD provided by Ba, Myers and Brenneman (2015) and the Gilbert and Golomb methods proposed by Xiao and Xu (2017). The SLHD package adopts the L 2 -distance measure, so we ran the command maximinSLHD with option t = 1 and default settings for 100 times, and chose the design with the largest L 1 -distance.…”

Section: Williams' Transformationmentioning

confidence: 99%

“…be an m × m LHD from the modified Williams transformation. Table 5 compares LHDs generated by the modified Williams transformation, the R package SLHD and the Welch, Gilbert and Golomb methods from Xiao and Xu (2017). The modified Williams transformation always provides better designs than any other methods.…”

Section: Modified Williams' Transformationmentioning

confidence: 99%

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Optimal maximin $L_{1}$-distance Latin hypercube designs based on good lattice point designs

Wang¹,

Xiao²,

Xu³

2018

Ann. Statist.

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Maximin distance Latin hypercube designs are commonly used for computer experiments, but the construction of such designs is challenging. We construct a series of maximin Latin hypercube designs via Williams transformations of good lattice point designs. Some constructed designs are optimal under the maximin L 1 -distance criterion, while others are asymptotically optimal. Moreover, these designs are also shown to have small pairwise correlations between columns.

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“…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%

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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Construction of maximin distance Latin squares and related Latin hypercube designs

Cited by 33 publications

References 13 publications

Application of kriging models for a drug combination experiment on lung cancer

Application of kriging models for a drug combination experiment on lung cancer

Optimal maximin $L_{1}$-distance Latin hypercube designs based on good lattice point designs

Modified Algorithms for Fast Construction of Optimal Latin-Hypercube Design

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