改进蜣螂算法优化工艺参数

doi:10.16183/j.cnki.jsjtu.2024.077

摘要/Abstract

摘要：

作为材料基因组工程的重要基础,材料数据库的建立及工艺参数优化研究对材料研发具有重要影响.针对目前传统关系型数据库无法较好地存储多源高维异构的合金数据,且材料研发模式亟需从传统的实验试错法转向数据驱动材料研究新模式等问题,提出了基于本体和图数据模型建立合金图数据库,在此基础上,通过改进蜣螂优化(IDBO)算法进行工艺参数组合寻优.利用反向学习初始化种群,再利用可变螺旋搜索策略改进觅食蜣螂位置更新方式,提高算法的全局搜索能力,最后在最优解位置处融合柯西变异扰动和混合策略,产生新解,避免算法陷入局部最优.为了验证所提出的改进蜣螂优化算法的性能,使用23个经典测试函数对IDBO算法进行评估,实验结果表明IDBO算法性能优于其他算法,显著提高了收敛速度和优化精度.同时,将IDBO算法应用于合金工艺参数优化研究,结果显示IDBO算法性能优于其他优化算法,并得到合金的最佳工艺参数组合,证明了其在工艺参数优化方面的优越性.

关键词: 合金数据库, 工艺参数优化, 蜣螂优化算法, 图数据模型, 多层感知机

Abstract:

As an important foundation of materials genome engineering, the establishment of materials database and the optimization of process parameter have an important impact on materials research and development. To address current challenges such as traditional relational databases being inadequate for storing multi-source, high-dimensional, and heterogeneous alloy data, and the urgent need to shift from the traditional trial-and-error experimentation to a data-driven research paradigm, this paper proposes to establish an alloy graph database based on ontology and graph data models. Based on this foundation, an improving dung beetle optimization (IDBO) algorithm is introduced to optimize combinations of process parameters. The algorithm enhances global search capability by initializing the population using inverse learning and updating dung beetle position using a variable spiral search strategy. To avoid local optima, Cauchy mutation perturbation and hybrid strategies are fused around the optimal solution to generate new candidates. To verify the performance of the proposed IDBO algorithm, it was tested on 23 classical benchmark functions, with results showing that IDBO algorithm outperforms other algorithms and significantly improves the convergence speed and optimization accuracy. Furthermore, when applied to the optimization of alloy process parameters, the IDBO algorithm not only demonstrated superior performance compared to other optimization algorithms but also successfully identified the optimal parameter combinations, validating its superiority in process parameter optimization.

Key words: alloy database, process parameter optimization, dung beetle optimization (DBO) algorithm, graph data model, multilayer perception machine (MLP)

中图分类号:

胡丹, 崔喻婷, 周海河, 刘英莉. 改进蜣螂算法优化工艺参数[J]. 上海交通大学学报, 2025, 59(12): 1901-1915.

HU Dan, CUI Yuting, ZHOU Haihe, LIU Yingli. Optimization of Process Parameters Using Improved Dung Beetle Algorithm[J]. Journal of Shanghai Jiao Tong University, 2025, 59(12): 1901-1915.

图/表 21

图1

图2

图3

图4

图5

图6

表1

图7

图8

图9

表2

经典测试函数详细信息

函数	维度	区间	最小值
f₁(x)=$\sum _{i=1}^{n}{x}_{i}^{2}$	30	[-100, 100]	0
f₂(x)=$\sum _{i=1}^{D}\left\|{x}_{i}\right\|$+$\prod _{i=1}^{D}\left\|{x}_{i}\right\|$	30	[-10, 10]	0
f₃(x)=$\sum _{i=1}^{n-1}$[100(x_i+1-${x}_{i}^{2}$)²+(x_i-1)²]	30	[-100, 100]	0
f₄(x)=$\sum _{i=1}^{n}$(x_i+0.5)²	30	[-100, 100]	0
f₅(x)=$\sum _{i=1}^{D}$100(${x}_{i+1}^{2}$-${x}_{i}^{2}$)²+(x_i-1)²	30	[-30, 30]	0
f₆(x)=$\sum _{i=1}^{D}{\left\|{x}_{i}+0.5\right\|}^{2}$	30	[-100, 100]	0
f₇(x)=$\frac{1}{4 000}\sum _{i=1}^{n}{x}_{i}^{2}$-$\prod _{i=1}^{n}$cos$\frac{{x}_{i}}{\sqrt{i}}$+1	30	[-1.28, 1.28]	0
f₈(x)=$\sum _{i=1}^{D}$-x_isin$\sqrt{\left\|{x}_{i}\right\|}$	30	[-500, 500]	-418.9D
f₉(x)=$\sum _{i=1}^{n}$-x_isin$\sqrt{\left\|{x}_{i}\right\|}$	30	[-5.12, 5.12]	0
f₁₀(x)=20+e-20exp$\left(-0.2\sqrt{\frac{1}{D}\sum _{i=1}^{D}{x}_{i}^{2}}\right)$-exp[$\frac{1}{D}\sum _{i=1}^{D}$(2πx_i)]	30	[-32, 32]	8.88×10^-16
f₁₁(x)=(x₁+2x₂-7)²+(2x₁+x₂-5)²	30	[-600, 600]	0
f₁₂(x)=$\frac{\pi }{D}\left\{10si{n}^{2}\left(\pi \right.{y}_{1})+\sum _{i-1}^{D-1}({y}_{i}{-1)}^{2}[1+10si{n}^{2}\left(\pi {y}_{i+1}\right)]+({y}_{D}-1)\right\}$+ $\sum _{i-1}^{D}$u(x_i, 10, 100, 4), y_i=1+$\frac{{x}_{i}+1}{4}$, u(x_i, 10, 100, 4)=$\left\{\begin{array}{ll}100({x}_{i}{-10)}^{4},& {x}_{i}10\\ 0,& -10x10\\ 100(-{x}_{i}{-10)}^{4},& {x}_{i}10\end{array}\right.$	30	[-50, 50]	0
f₁₃(x)=0.1{sin²(3πx_i)+$\sum _{i=1}^{D}$(x_i-1)²[1+sin²(3πx_i)]+ (x_D-1)²[1+sin²(2πx_D)]}+$\sum _{i-1}^{D}$u(x_i, 5, 100, 4)	30	[-50, 50]	0
f₁₄(x)=$\frac{1}{500}$+$\sum _{j=1}^{25}$[$\frac{1}{j+\sum _{i=1}^{2}({x}_{i}-{a}_{ij}{)}^{6}}$]^-1	2	[-65.53, 65.53]	0.998 004
f₁₅(x)=$\sum _{i=1}^{11}{\left[{a}_{i}-\frac{{x}_{1}({b}_{i}^{2}+{b}_{i}{x}_{2})}{{b}_{i}^{2}+{b}_{i}{x}_{3}+{x}_{4}}\right]}^{-1}$	30	[-5, 5]	0.003
f₁₆(x)=4${x}_{1}^{2}$-2.1${x}_{1}^{4}$+1/3${x}_{1}^{6}$+x₁x₂-4${x}_{2}^{2}$+${x}_{2}^{4}$	2	[-5, 5]	-1.031
f₁₇(x)=${\left({x}_{2}-\frac{5.1}{4{\pi }^{2}}{x}_{1}^{2}+\frac{5}{\pi }{x}_{1}-6\right)}^{2}$+10$\left(1-\frac{1}{8\pi }\right)$cos x₁+10	2	[-5, 10], [0, 15]	0.398
f₁₈(x)=[1+(x₁+x₂+1)²(19-14x₁+3${x}_{1}^{2}$-14x₂+6x₁x₂+3${x}_{2}^{2}$)]× [30+(2x₁-3x₂)²(18-32x₁+12${x}_{1}^{2}$+48x₂-36x₁x₂+27${x}_{2}^{2}$)]	30	[-5, 5]	3
f₁₉(x)=-$\sum _{i=1}^{4}${c_iexp[-$\sum _{j-1}^{3}$a_ij(x_j-p_ij)²]}	3	[0, 1]	-3.862
f₂₀(x)=-$\sum _{i=1}^{4}${c_iexp[-$\sum _{j-1}^{6}$a_ij(x_j-p_ij)²]}	6	[0, 1]	-3.32
f₂₁(x)=-$\sum _{i=1}^{5}$[(x-a_i)(x-a_i)^T+c_i]^-1	4	[0, 10]	-10.15
f₂₂(x)=-$\sum _{i=1}^{7}$[(x-a_i)(x-a_i)^T+c_i]^-1	4	[0, 10]	-10.40
f₂₃(x)=-$\sum _{i=1}^{10}$[(x-a_i)(x-a_i)^T+c_i]^-1	4	[0, 10]	-10.53

表2

表3

表4

经典测试函数优化结果对比

函数	参数	IDBO	DBO	PSO	GWO	WOA
F1	Mean	9.91×10^-140	5.88×10^-46	3.26×10⁺⁰⁴	1.81×10^-27	2.92×10^-80
	Std	5.33×10^-139	2.11×10^-45	1.07×10⁺⁰⁴	4.40×10^-27	1.47×10^-79
F2	Mean	2.16×10^-75	9.17×10^-22	1.11×10⁺⁰¹	8.95×10^-17	3.99×10^-51
	Std	1.15×10^-74	2.16×10^-75	2.40×10⁺⁰¹	5.02×10^-17	2.07×10^-50
F3	Mean	1.05×10^-127	7.40×10^-08	3.90×10⁺⁰⁴	5.61×10^-06	2.88×10⁺⁰³
	Std	5.68×10^-127	3.65×10^-07	1.17×10⁺⁰⁴	1.13×10^-05	5.46×10⁺⁰³
F4	Mean	7.95×10^-69	5.06×10^-08	4.07×10⁺⁰¹	6.11×10^-07	1.36×10^-09
	Std	4.28×10^-68	2.25×10^-07	2.40×10⁺⁰¹	7.81×10^-07	7.20×10^-09
F5	Mean	2.71×10⁺⁰¹	2.82×10⁺⁰²	1.17×10⁺⁰⁸	2.71×10⁺⁰¹	1.43×10⁺⁰¹
	Std	0.74×10⁺⁰⁰	0.54×10⁺⁰⁰	9.34×10⁺⁰⁷	0.78×10⁺⁰⁰	1.35×10⁺⁰¹
F6	Mean	0.81×10⁺⁰⁰	1.89×10⁺⁰⁰	2.57×10⁺⁰⁴	0.71×10⁺⁰⁰	0.09×10⁺⁰⁰
	Std	1.81×10⁺⁰⁰	0.55×10⁺⁰⁰	1.03×10⁺⁰⁴	0.27×10⁺⁰⁰	0.18×10⁺⁰⁰
F7	Mean	0.00×10⁺⁰⁰	0.00×10⁺⁰⁰	5.18×10⁺⁰¹	0.00×10⁺⁰⁰	0.00×10⁺⁰⁰
	Std	0.00×10⁺⁰⁰	0.00×10⁺⁰⁰	3.53×10⁺⁰¹	0.00×10⁺⁰⁰	0.00×10⁺⁰⁰
F8	Mean	-1.25×10⁺⁰⁴	-1.25×10⁺⁰⁴	-7.17×10⁺⁰²	-6.23×10⁺⁰³	-1.23×10⁺⁰⁴
	Std	5.74×10⁺⁰⁰	1.14×10⁺⁰⁰	9.53×10⁺⁰²	7.28×10⁺⁰²	6.93×10⁺⁰²
F9	Mean	0.00×10⁺⁰⁰	1.21×10⁺⁰⁰	2.28×10⁺⁰²	1.71×10⁺⁰⁰	0.00×10⁺⁰⁰
	Std	0.00×10⁺⁰⁰	6.48×10⁺⁰⁰	4.62×10⁺⁰¹	2.20×10⁺⁰⁰	0.00×10⁺⁰⁰
F10	Mean	4.44×10⁺⁰⁰	5.62×10⁺⁰⁰	1.99×10⁺⁰¹	9.39×10⁺⁰⁰	2.22×10⁺⁰⁰
	Std	0.00×10⁺⁰⁰	6.37×10⁺⁰⁰	0.01×10⁺⁰⁰	1.68×10⁺⁰⁰	1.77×10⁺⁰⁰
F11	Mean	0.00×10⁺⁰⁰	0.00×10⁺⁰⁰	2.79×10⁺⁰²	0.00×10⁺⁰⁰	0.00×10⁺⁰⁰
	Std	0.00×10⁺⁰⁰	0.00×10⁺⁰⁰	1.15×10⁺⁰²	0.00×10⁺⁰⁰	0.00×10⁺⁰⁰
F12	Mean	0.01×10⁺⁰⁰	0.18×10⁺⁰⁰	3.22×10⁺⁰⁸	0.04×10⁺⁰⁰	0.00×10⁺⁰⁰
	Std	0.08×10⁺⁰⁰	0.25×10⁺⁰⁰	2.18×10⁺⁰⁸	0.02×10⁺⁰⁰	0.00×10⁺⁰⁰
F13	Mean	1.57×10⁺⁰⁰	2.50×10⁺⁰⁰	6.72×10⁺⁰⁸	0.62×10⁺⁰⁰	0.04×10⁺⁰⁰
	Std	0.91×10⁺⁰⁰	0.32×10⁺⁰⁰	4.15×10⁺⁰⁸	0.28×10⁺⁰⁰	0.04×10⁺⁰⁰
F14	Mean	1.79×10⁺⁰⁰	2.30×10⁺⁰⁰	2.41×10⁺⁰⁰	3.28×10⁺⁰⁰	2.44×10⁺⁰⁰
	Std	1.12×10⁺⁰⁰	0.85×10⁺⁰⁰	1.72×10⁺⁰⁰	3.26×10⁺⁰⁰	1.90×10⁺⁰⁰
F15	Mean	0.00×10⁺⁰⁰	0.00×10⁺⁰⁰	0.00×10⁺⁰⁰	0.00×10⁺⁰⁰	0.00×10⁺⁰⁰
	Std	0.00×10⁺⁰⁰	0.00×10⁺⁰⁰	0.00×10⁺⁰⁰	0.00×10⁺⁰⁰	0.00×10⁺⁰⁰
F16	Mean	-1.03×10⁺⁰⁰	-1.03×10⁺⁰⁰	-1.03×10⁺⁰⁰	-1.03×10⁺⁰⁰	-1.03×10⁺⁰⁰
	Std	2.95×10⁺⁰⁰	2.32×10⁺⁰⁰	4.38×10⁺⁰⁰	2.43×10⁺⁰⁰	9.29×10⁺⁰⁰
F17	Mean	0.39×10⁺⁰⁰	0.40×10⁺⁰⁰	0.39×10⁺⁰⁰	0.39×10⁺⁰⁰	0.39×10⁺⁰⁰
	Std	0.00×10⁺⁰⁰	0.05×10⁺⁰⁰	0.00×10⁺⁰⁰	0.00×10⁺⁰⁰	0.00×10⁺⁰⁰
F18	Mean	3.00×10⁺⁰⁰	3.00×10⁺⁰⁰	8.39×10⁺⁰⁰	5.70×10⁺⁰⁰	9.33×10⁺⁰⁰
	Std	0.00×10⁺⁰⁰	3.93×10⁺⁰⁰	2.02×10⁺⁰¹	1.45×10⁺⁰¹	1.14×10⁺⁰¹
F19	Mean	-3.86×10⁺⁰⁰	-3.85×10⁺⁰⁰	-3.86×10⁺⁰⁰	-3.86×10⁺⁰⁰	-3.76×10⁺⁰⁰
	Std	0.00×10⁺⁰⁰	0.00×10⁺⁰⁰	0.00×10⁺⁰⁰	0.00×10⁺⁰⁰	0.00×10⁺⁰⁰
F20	Mean	-3.08×10⁺⁰⁰	-2.87×10⁺⁰⁰	-3.18×10⁺⁰⁰	-3.24×10⁺⁰⁰	-3.06×10⁺⁰⁰
	Std	0.37×10⁺⁰⁰	0.51×10⁺⁰⁰	0.13×10⁺⁰⁰	0.10×10⁺⁰⁰	0.16×10⁺⁰⁰
F21	Mean	-9.64×10⁺⁰⁰	-4.70×10⁺⁰⁰	-4.67×10⁺⁰⁰	-8.97×10⁺⁰⁰	-7.65×10⁺⁰⁰
	Std	1.80×10⁺⁰⁰	2.70×10⁺⁰⁰	1.43×10⁺⁰⁰	2.66×10⁺⁰⁰	2.84×10⁺⁰⁰
F22	Mean	-9.88×10⁺⁰⁰	-6.16×10⁺⁰⁰	-4.28×10⁺⁰⁰	-1.04×10⁺⁰¹	-7.39×10⁺⁰⁰
	Std	1.90×10⁺⁰⁰	3.27×10⁺⁰⁰	2.48×10⁺⁰⁰	0.00×10⁺⁰⁰	2.88×10⁺⁰⁰
F23	Mean	-1.05×10⁺⁰¹	-7.13×10⁺⁰⁰	-5.94×10⁺⁰⁰	-1.05×10⁺⁰¹	-7.70×10⁺⁰⁰
	Std	1.51×10⁺⁰⁰	2.60×10⁺⁰⁰	3.44×10⁺⁰⁰	0.00×10⁺⁰⁰	2.77×10⁺⁰⁰

表4

图10

图11

表5

图12

图13

图14

表6

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节点1	描述	关系	节点2	描述
paper	文献	文献连接	paper	文献
paper	文献	包含_成分	composition	成分
paper	文献	包含_制备工艺	fabrication	制备工艺
paper	文献	包含_微观结构	microstructure	微观结构
paper	文献	包含_性能	property	性能
composition	成分	影响	microstructure	微观结构
composition	成分	表征	property	性能
fabrication	制备工艺	处理	microstructure	微观结构
fabrication	制备工艺	制造	property	性能
microstructure	微观结构	表征	property	性能

分类	参数	范围
成分	Si, c₁/%	[0.5, 65]
	Fe, c₂/%	[0.1, 8.5]
	Mg, c₃/%	[0.16, 2.9]
	Ni, c₄/%	[1, 7.5]
制备工艺过程	固溶温度,f₁/℃	[2, 711]
	固溶时间,f₂/h	[0.16, 15]
	时效温度,f₃/℃	[2, 215]
	时效时间,f₄/h	[0.1, 48]
	挤压比,f₅	[0.12, 38]
微观组织结构	等效直径,m/μm	[1.78, 65]

分类	参数	取值
合金成分	c₁/%	9.3
	c₂/%	1.5
	c₃/%	0.8
	c₄/%	2.3
制备工艺参数	f₁/℃	158
	f₂//h	2.3
	f₃/℃	20.7
	f₄/h	6.8
	f₅	3.8
微观组织结构	m/μm	17.6