<p>The optimization of Latin hypercube designs (LHDs) as a complex design structure has become increasingly critical in enhancing computational efficiency and solution accuracy. From a space-filling point of view, this study introduces the Aquila optimization–genetic algorithm (AOGA), an innovative hybrid optimization technique tailored to address the challenges of high-dimensional LHD problems. AOGA introduces two novel mechanisms—the shuffle window (SW) and crossover window (CW) operators—specifically designed to perturb and recombine LHD permutations while preserving structural integrity. These operators work in tandem with three dynamic adaptation rates: a diversification rate to periodically inject new solutions and avoid stagnation, a decay rate to guide convergence toward elite permutations, and an adaptive mutation rate to balance exploration–exploitation trade-offs across optimization phases. Our findings from the ablation study reveal that intermediate shuffle and crossover window sizes significantly improve optimization stability and convergence despite variations in initial populations and stochastic perturbations. Further analysis of AOGA’s robustness highlights stable dynamics (Lyapunov exponents near-zero/negative) and consistent convergence (low standard deviation (STD) across runs). Statistical validation (ANOVA: F = 4.71, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$p$</EquationSource> <EquationSource Format="MATHML"><math> <mi>p</mi> </math></EquationSource> </InlineEquation>=0.014; Tukey HSD: AOGA vs. LSGA <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$p$</EquationSource> <EquationSource Format="MATHML"><math> <mi>p</mi> </math></EquationSource> </InlineEquation>=0.024, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$p$</EquationSource> <EquationSource Format="MATHML"><math> <mi>p</mi> </math></EquationSource> </InlineEquation>=0.024, AOGA vs. MESE <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$p$</EquationSource> <EquationSource Format="MATHML"><math> <mi>p</mi> </math></EquationSource> </InlineEquation>=0.017) underscores AOGA’s superiority, achieving 2%–20% improvements in <InlineEquation ID="IEq5"> <EquationSource Format="TEX">${\phi }_{p}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ϕ</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> and Maxmin across LHD sizes. With computational complexity comparable to pure GA/AO, AOGA excels in large-scale designs (e.g., 15 × 50 and 18 × 80), demonstrating high-quality sampling.</p>

Aquila-genetic optimization with shuffle windows for the latin hypercube design problem

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发表日期：

2025年10月24日

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M. Masoudian,
R. Hajian,
S. H. Erfani

摘要

The optimization of Latin hypercube designs (LHDs) as a complex design structure has become increasingly critical in enhancing computational efficiency and solution accuracy. From a space-filling point of view, this study introduces the Aquila optimization–genetic algorithm (AOGA), an innovative hybrid optimization technique tailored to address the challenges of high-dimensional LHD problems. AOGA introduces two novel mechanisms—the shuffle window (SW) and crossover window (CW) operators—specifically designed to perturb and recombine LHD permutations while preserving structural integrity. These operators work in tandem with three dynamic adaptation rates: a diversification rate to periodically inject new solutions and avoid stagnation, a decay rate to guide convergence toward elite permutations, and an adaptive mutation rate to balance exploration–exploitation trade-offs across optimization phases. Our findings from the ablation study reveal that intermediate shuffle and crossover window sizes significantly improve optimization stability and convergence despite variations in initial populations and stochastic perturbations. Further analysis of AOGA’s robustness highlights stable dynamics (Lyapunov exponents near-zero/negative) and consistent convergence (low standard deviation (STD) across runs). Statistical validation (ANOVA: F = 4.71, $p$ $p$ =0.014; Tukey HSD: AOGA vs. LSGA $p$ $p$ =0.024, $p$ $p$ =0.024, AOGA vs. MESE $p$ $p$ =0.017) underscores AOGA’s superiority, achieving 2%–20% improvements in ${\phi }_{p}$ $ϕ_{p}$ and Maxmin across LHD sizes. With computational complexity comparable to pure GA/AO, AOGA excels in large-scale designs (e.g., 15 × 50 and 18 × 80), demonstrating high-quality sampling.