Hyper-heuristic Optimization and Decision-making of Hobs and Control Parameters

doi:10.3969/j.issn.1004-132X.2026.04.009

Abstract

Abstract:

To address the issues of automatic selection of heuristic algorithms in hobbing tools and control parameter optimization， as well as parameter decision-making under the fuzzy expression of users' emphasis on machining performance， a method for optimizing and deciding hobbing tools and control parameters was proposed based on an improved hyper-heuristic algorithm and fuzzy TOPSIS. The spectral clustering algorithm was used to determine the upper and lower limits of parameters based on historical machining datas. With carbon emissions， cutting time， and quality as optimization objectives， an improved multi-objective hyper-heuristic algorithm was used to obtain optimized hobbing parameters （non-dominated solutions）. Based on the user's emphasis on machining performance， fuzzy TOPSIS was employed to rank the optimized hobbing parameters and select the parameters that best met the user's requirements. Experiments verified the feasibility and effectiveness of the proposed method.

Key words: gear hobbing, hob and control parameter, multi-objective optimization, decision-making, hyper-heuristic

摘要：

为研究滚齿刀具和控制参数优化中的启发式算法自动选择问题以及用户对加工性能看重程度模糊表达下的参数决策问题，提出了一种基于改进超启发算法和模糊优劣解距离法（TOPSIS ）的滚齿刀具和控制参数优化与决策方法。使用谱聚类算法根据历史加工数据确定滚齿参数的上下限；以碳排放量、切削时间和质量为优化目标，使用改进的多目标超启发算法获取优化滚齿参数（非支配解）；采用模糊TOPSIS对优化滚齿参数进行排序以获取最符合用户要求的参数。最后通过实验验证了方法的可行性和有效性。

关键词: 滚齿, 刀具和控制参数, 多目标优化, 决策, 超启发

CLC Number:

TH166

CAO Weidong, WANG Yuanshuo, LI Minrong, CHEN Fuqi, CHEN Xingzheng, WU Dianjian, HU Kexin. Hyper-heuristic Optimization and Decision-making of Hobs and Control Parameters[J]. China Mechanical Engineering, 2026, 37(4): 846-854.

曹卫东, 汪袁烁, 李闽榕, 陈富祺, 陈行政, 吴电建, 胡可心. 滚齿刀具和控制参数超启发优化与决策[J]. 中国机械工程, 2026, 37(4): 846-854.

Figures/Tables 12

Tab.1 Attribute description

问题属性	描述	滚齿参数	描述
f₁	工件模数/mm	p₁	滚刀外径/mm
f₂	工件压力角/rad	p₂	滚刀头数
f₃	工件齿数	p₃	主轴转速/（r·min $- 1$ ）
f₄	工件螺旋角/rad	p₄	轴向进给/（mm·r $- 1$ ）
f₅	工件外径/mm
f₆	工件齿宽/mm
f₇	切削深度/mm

Tab.1 Attribute description

问题属性	描述	滚齿参数	描述
f₁	工件模数/mm	p₁	滚刀外径/mm
f₂	工件压力角/rad	p₂	滚刀头数
f₃	工件齿数	p₃	主轴转速/（r·min $- 1$ ）
f₄	工件螺旋角/rad	p₄	轴向进给/（mm·r $- 1$ ）
f₅	工件外径/mm
f₆	工件齿宽/mm
f₇	切削深度/mm

Fig.1 Improved multi-objective selection based hyper heuristic algorithm

Fig.2 YS3120CNC6

Tab.2 Historical processed sample set［2］

l_i	问题属性							滚齿参数
l_i	f₁	f₂	f₃	f₄	f₅	f₆	f₇	p₁	p₂	p₃	p₄
l₁	2.50	0.401	46	0.436	128.55	13.50	5.815	80	3	380	1.5
l₂	2.00	0.305	44	0.611	110.00	12.60	5.742	80	3	360	1.5
l₃	1.86	0.279	30	0.628	73.90	13.80	5.784	80	2	360	1.8
l₄	1.80	0.297	33	0.576	76.30	14.50	5.782	80	2	360	2.0
l₅	1.89	0.288	39	0.576	93.55	13.70	6.321	80	2	360	1.8
l₆	1.75	0.305	31	0.576	67.80	14.50	5.297	80	2	400	2.0
l₇	2.50	0.333	17	0.578	59.80	30.40	7.150	80	1	380	1.6
l₈	1.81	0.286	47	0.579	106.22	18.00	4.000	70	3	450	1.5
l₉	2.75	0.436	18	0.486	62.45	38.00	6.200	80	1	360	1.6
l₁₀	2.77	0.349	34	0.339	109.81	18.50	6.453	80	2	360	1.5
l₁₁	3.00	0.524	17	0	56.30	40.40	4.020	110	1	230	2.5
l₁₂	2.00	0.307	45	0.550	109.68	13.80	6.000	70	3	410	1.5
l₁₃	2.00	0.346	53	0.463	123.20	13.20	5.400	70	3	400	1.5
l₁₄	1.63	0.288	35	0.607	74.28	13.70	5.300	70	2	395	1.8
l₁₅	1.89	0.288	36	0.576	86.80	13.00	6.085	80	2	360	2.0
l₁₆	2.40	0.349	69	0.524	194.10	25.50	6.734	80	4	350	1.2
l₁₇	2.54	0.333	17	0.578	59.80	30.40	7.150	80	1	380	1.6
l₁₈	2.75	0.436	18	0.486	62.45	38.00	6.200	80	1	360	1.6
l₁₉	2.77	0.349	34	0.339	109.81	18.50	6.453	80	2	360	1.5
l₂₀	1.86	0.279	40	0.628	96.70	11.90	5.812	76	3	375	1.8
l₂₁	1.73	0.305	31	0.576	67.80	14.50	5.295	80	2	360	2.0
l₂₂	1.80	0.297	32	0.576	74.15	14.00	5.778	80	2	360	2.0
l₂₃	1.89	0.288	39	0.576	93.55	13.70	6.321	80	2	360	1.8
l₂₄	2.50	0.401	26	0	72.00	14.15	4.700	80	2	360	1.8
l₂₅	2.65	0.428	26	0	74.75	15.00	5.448	80	2	360	1.8
l₂₆	2.00	0.340	21	0.532	54.30	16.90	5.957	80	2	360	1.8
l₂₇	2.40	0.349	17	0.524	54.10	29.10	6.745	80	1	360	1.8
l₂₈	2.50	0.332	71	0.497	207.70	29.00	6.997	80	4	350	1.2
l₂₉	2.02	0.253	31	0.583	79.10	18.00	5.524	80	2	360	2.0

Fig.3 Pareto front

Fig.4 Pareto front of each method

Tab.3 Results of SP

第i次运行	HF	H1	H2	H3	H4
1	0.273	1.442	0.404	0.393	0.390
2	0.211	5.055	0.283	1.346	8.287
3	0.273	1.427	0.885	0.196	8.914
4	0.252	1.559	0.757	8.740	1.037
5	0.278	0.812	0.751	0.883	1.723

Fig.5 Violin plot of SP

Fig.6 Coverage rate

Tab.4 Score obtained via TOPSIS

第i次运行	HF	H1	H2	H3	H4
1	0.7238	0.6664	0.7154	0.7246	0.7228
2	0.7239	0.6685	0.7156	0.7246	0.7229
3	0.7240	0.6704	0.7164	0.7248	0.7239
4	0.7313	0.6721	0.7187	0.7351	0.7241
5	0.7413	0.6979	0.7202	0.7392	0.7241

Fig.7 Pareto frontier search comparison

Fig.8 Comparison of the target values of each method over five runs

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