Optimization of Process Parameters Using Improved Dung Beetle Algorithm

doi:10.16183/j.cnki.jsjtu.2024.077

Abstract

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)

CLC Number:

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.

Figures/Tables 21

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Tab.1

Fig.7

Fig.8

Fig.9

Tab.2

Details of classical test function

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

Tab.2

Tab.3

Tab.4

Comparison of optimization results of classic test functions

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

Tab.4

Fig.10

Fig.11

Tab.5

Fig.12

Fig.13

Fig.14

Tab.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