The aim of this article is to discuss the application of multi-task regression (MTR) in multi-objective optimization of automobile crashworthiness and lightweight. The applicability of MTR in such tasks is assessed by comparing the fitting accuracy of single-task regression (STR) and MTR. Two typical cases were selected for the study: an automotive front-end structure (frontal rigid wall crash) and a battery pack system (side rigid column crush). A surrogate is constructed using a multi-layer perceptron (MLP), and comprehensive correlation coefficient is used for feature screening and Bayesian optimization is used for hyper-parameter optimization. This study finds that MTR has higher prediction accuracy for objectives with poor STR performance when the STR surrogate’s performance is disparate between objectives. In the three-objective case, combining with two better-performing objectives brings more significant improvement than combining with a single objective. Ultimately, multi-task regression-based multi-objective optimization is solved using the U-NSGA-III algorithm and a compromise solution is selected using the Entropy-Gray method. It is shown that MTR has the potential to improve the efficiency and effectiveness of optimization in crashworthiness and lightweight multi-objective optimization tasks.
KianiMShiozakiHMotoyamaK. Simulation-based design optimisation to develop a lightweight body-in-white structure focusing on dynamic and static stiffness. Int J Veh Des2015; 67(3): 219–236.
2.
WangDXieC. Contribution analysis of the cab-in-white for lightweight optimization employing a hybrid multi-criteria decision-making method under static and dynamic performance. Eng Optim2020; 52(10–12): 1903–1922.
3.
LiSWangDWangS, et al. Structure–connection–performance integration lightweight optimisation design of multi-material automotive body skeleton. Struct Multidiscipl Optim2023; 66(9): 198.
4.
LiSZhouDPanA. Integrated lightweight optimization design of wall thickness, material, and performance of automobile body side structure. Struct Multidiscipl Optim2024; 67(6): 95.
5.
GoelTHaftkaRTShyyW, et al. Ensemble of surrogates. Struct Multidiscipl Optim2007; 33: 199–216.
6.
AcarERais-RohaniM. Ensemble of metamodels with optimized weight factors. Struct Multidiscipl Optim2009; 37(3): 279–294.
7.
ForresterASobesterAKeaneA. Engineering design via surrogate modelling: a practical guide. New York, NY: John Wiley & Sons, 2008.
8.
LiRPanYZhangX, et al. Mechanical safety prediction of a battery-pack system under low speed frontal impact via machine learning. Eng Anal Bound Elem2024; 160: 65–75.
9.
ZhangQHanSAbedAM, et al. Enhancing battery pack safety against cone impact using machine learning techniques and Gaussian noise. Process Saf Environ Prot2024; 191: 448–465.
10.
ZhangXXiongYPanY, et al. Deep-learning-based inverse structural design of a battery-pack system. Reliab Eng Syst Saf2023; 238: 109464.
11.
NakanoRSatohS. Mixture of multilayer perceptron regressions. In: ICPRAM 2019 - proceedings of the 8th international conference on pattern recognition applications and methods, ICPRAM - Volume 1, Prague, Czech Republic, 2019, pp. 509–516.
12.
LiZZhangDZhaoX, et al. A temporally smoothed MLP regression scheme for continuous knee/ankle angles estimation by using multi-channel sEMG. IEEE Access2020; 8: 47433–47444.
13.
LeeJJeongHKangS. Derivative and GA-based methods in metamodeling of back-propagation neural networks for constrained approximate optimization. Struct Multidiscipl Optim2008; 35: 29–40.
14.
García-SeguraTYepesVFrangopolDM. Multi-objective design of post-tensioned concrete road bridges using artificial neural networks. Struct Multidiscipl Optim2017; 56: 139–150.
15.
SunGWangS. A review of the artificial neural network surrogate modeling in aerodynamic design. Proc IMechE, Part G: J Aerospace Engineering2019; 233: 5863–5872.
16.
GomesWJDS. Shallow and deep artificial neural networks for structural reliability analysis. ASME J Risk Uncertainty Part B2020; 6: 041006.
17.
AghayanINoiiNKuntMM. Extended traffic crash modeling through precision and response time using fuzzy clustering algorithms compared with multi-layer perceptron. Promet2012; 24(6): 455–467.
18.
NiyogisubizoJLiaoLLinY, et al. A novel stacking framework based on hybrid of gradient boosting-adaptive boosting-multilayer perceptron for crash injury severity prediction and analysis. In: 2021 IEEE 4th international conference on electronics and communication engineering (ICECE), Xi’an, China, 17–19 December 2021.
19.
ZendePDalirH. Multi-objective optimization of composite square tube for minimizing peak crushing force and maximizing specific energy absorption using artificial neural network and genetic algorithm. In: ASME international mechanical engineering congress and exposition, proceedings (IMECE), Columbus, OH, USA, 30 October–3 November 2022.
20.
PasqualeAChampaneyVKimY, et al. A parametric metamodel of the vehicle frontal structure accounting for material properties and strain-rate effect: application to full frontal rigid barrier crash test. Heliyon2022; 8(12): e12397.
21.
ZhangYYangQ. An overview of multi-task learning. Nat Sci Rev2018; 5: 30–43.
22.
ZhangYYangQ. A survey on multi-task learning. IEEE Trans Knowl Data Eng2022; 34(12): 5586–5609.
23.
BrarASSinghK. A multi-objective stacked regression method for distance based colour measuring device. Sci Rep2024; 14(1): 5530.
24.
IlbertRTiomokoMLouartC, et al. Analysing multi-task regression via random matrix theory with application to time series forecasting. Adv Neural Inf Process Syst2024; 37: 115021–115057.
25.
RashedAJawedSRehbergJ, et al. A deep multi-task approach for residual value forecasting. In: BrefeldUFromontEHothoA, et al. (eds) Machine learning and knowledge discovery in databases. Cham: Springer International Publishing, 2020, pp.467–482.
26.
LeangISistuGBürgerF, et al. Dynamic task weighting methods for multi-task networks in autonomous driving systems. In: 2020 IEEE 23rd international conference on intelligent transportation systems (ITSC), Rhodes, Greece, 20–23 September 2020, pp.1–8. New York: IEEE.
27.
XingYHuZMoX, et al. Driver steering behaviour modelling based on neuromuscular dynamics and multi-task time-series transformer. Automot Innov2024; 7(1): 45–58.
28.
SunLJiYPengT. Multi-task regression with process knowledge-based forest learners in process industries. In: 2023 IEEE international conference on automation science and engineering (CASE), Auckland, New Zealand, 26–30 August 2023.
29.
SchreiberJSickB. Emerging relation network and task embedding for multi-task regression problems. In: Proceedings - international conference on pattern recognition, Milan, Italy, 10–15 January 2021.
30.
NoyNWaldYElidanG, et al. Robust multitask elliptical regression (ROMER). In: 2019 IEEE 8th international workshop on computational advances in multi-sensor adaptive processing, CAMSAP 2019 - proceedings, Le Gosier, Guadeloupe, 15–18 December 2019.
CCSA. 2010Toyota Yaris finite element model validation coarse mesh. 2013.
33.
SpearmanC. General intelligence, objectively determined and measured. Am J Psychol1904; 15(2): 201–292.
34.
AkibaTSanoSYanaseT, et al. Optuna: a next-generation hyperparameter optimization framework. In: Proceedings of the 25th ACM SIGKDD international conference on knowledge discovery & data mining, Anchorage, AK, USA, 4–8 August 2019, pp.2623–2631. New York: Association for Computing Machinery.
35.
BlankJDebKRoyPC. Investigating the normalization procedure of NSGA-III. In: DebKGoodmanECoelloCA, et al. (eds) Evolutionary multi-criterion optimization. Cham: Springer International Publishing, 2019, pp.229–240.
36.
DebKPratapAAgarwalS, et al. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput2002; 6(2): 182–197.
37.
SeadaHDebK. U-NSGA-III: a unified evolutionary optimization procedure for single, multiple, and many objectives: proof-of-principle results. In: Gaspar-CunhaAHenggeler AntunesCCoelloC (eds) Evolutionary multi-criterion optimization. Cham: Springer International Publishing, 2015, pp.34–49.
38.
DasIDennisJE. Normal-boundary intersection: a new method for generating the pareto surface in nonlinear multicriteria optimization problems. SIAM J Optim1998; 8(3): 631–657.
39.
DengJ. Introduction to Grey system theory. J Grey Syst1989; 1: 1–24.
40.
AndwariAMPesiridisARajooS, et al. A review of Battery Electric Vehicle technology and readiness levels. Renew Sustain Energy Rev2017; 78: 414–430.
