Approximation Models for Multi-Objective Optimization

Yeun, Y.S.,Yang, Y.S.,Jang, B.S.,Ruy, W.S. 대진대학교 생산기술연구소 2000 생산기술연구소 논문집 Vol.3 No.-

In engineering problems, computationally intensive high-fidelity models or expensive computer simulations hinder the use of standard optimization techniques because they should be invoked repeatedly during optimization, despite the alarming growth of computer capability. Therefore, these expensive analyses are often replaced with approximation models that can be evaluated nearly free. However, due to their limited accuracy, it is practically impossible to exactly find an actual optimum(or a set of actual noninferior solutions) of the original single(or multi-objective) optimization problem. Significant efforts have been made to overcome this problem, The model management framework is one of such endeavours. The approximation models are sequentially updated during the iterative optimization process in such a way that their capability to accurately model original functions especially in the region of our interests can be improved. The models are modified using one or several sample points generated by making good use of the predictive ability of the approximation models. However, theses approaches have been restricted to a single objective optimization problem. It seems that there is no reported management framework that can handle a multi-objective optimization problem. This paper will suggest strategies that can successfully treat not only a single objective but also multiple objectives by extending the concept of sequentially managing approximation models and combining this extended concept with the Genetic Algorithm which can treat multiple objective s(MOGA). Consequently, the number of exact analysis required to converge an actual optimum or to generate a sufficiently accurate Pareto set can be reduced considerably. Especially, the approach for multiple objectives will lead to the surprising reduction in the number. We will confirm these effects through several illustrating examples. Key words : optimization, approximation model, model management framework, multi-objective

Experimental validation of FE model updating based on multi-objective optimization using the surrogate model

Hwang, Yongmoon,Jin, Seung-seop,Jung, Ho-Yeon,Kim, Sehoon,Lee, Jong-Jae,Jung, Hyung-Jo Techno-Press 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.65 No.2

In this paper, finite element (FE) model updating based on multi-objective optimization with the surrogate model for a steel plate girder bridge is investigated. Conventionally, FE model updating for bridge structures uses single-objective optimization with finite element analysis (FEA). In the case of the conventional method, computational burden occurs considerably because a lot of iteration are performed during the updating process. This issue can be addressed by replacing FEA with the surrogate model. The other problem is that the updating result from single-objective optimization depends on the condition of the weighting factors. Previous studies have used the trial-and-error strategy, genetic algorithm, or user's preference to obtain the most preferred model; but it needs considerable computation cost. In this study, the FE model updating method consisting of the surrogate model and multi-objective optimization, which can construct the Pareto-optimal front through a single run without considering the weighting factors, is proposed to overcome the limitations of the single-objective optimization. To verify the proposed method, the results of the proposed method are compared with those of the single-objective optimization. The comparison shows that the updated model from the multi-objective optimization is superior to the result of single-objective optimization in calculation time as well as the relative errors between the updated model and measurement.

Experimental validation of FE model updating based on multi-objective optimization using the surrogate model

황용문,진승섭,정호연,김세훈,이종재,정형조 국제구조공학회 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.65 No.2

In this paper, finite element (FE) model updating based on multi-objective optimization with the surrogate model for a steel plate girder bridge is investigated. Conventionally, FE model updating for bridge structures uses single-objective optimization with finite element analysis (FEA). In the case of the conventional method, computational burden occurs considerably because a lot of iteration are performed during the updating process. This issue can be addressed by replacing FEA with the surrogate model. The other problem is that the updating result from single-objective optimization depends on the condition of the weighting factors. Previous studies have used the trial-and-error strategy, genetic algorithm, or user’s preference to obtain the most preferred model; but it needs considerable computation cost. In this study, the FE model updating method consisting of the surrogate model and multi-objective optimization, which can construct the Pareto-optimal front through a single run without considering the weighting factors, is proposed to overcome the limitations of the single-objective optimization. To verify the proposed method, the results of the proposed method are compared with those of the single-objective optimization. The comparison shows that the updated model from the multi-objective optimization is superior to the result of single-objective optimization in calculation time as well as the relative errors between the updated model and measurement.

차량 현가 부품의 근사 다목적 설계 최적화에 대한 메타모델 영향도

송창용(Chang Yong Song),최하영(Ha-Young Choi),변성광(Sung-Kwang Byon) 한국기계가공학회 2019 한국기계가공학회지 Vol.18 No.3

Herein, we performed a comparative study on approximate multi-objective design optimization, to realize a structural design to improve the weight and vibration performances of the knuckle—a car suspension component—considering various load conditions and vibration characteristics. In the approximate multi-objective optimization process, a regression meta-model was generated using the response surfaces method (RSM), while Kriging and back-propagation neural network (BPN) methods were applied for interpolation meta-modeling. The Pareto solutions, multi-objective optimal solutions, were derived using the non-dominated sorting genetic algorithm (NSGA-II). In terms of the knuckle design considered in this study, the characteristics and influence of the meta-model on multi-objective optimization were reviewed through a comparison of the approximate optimization results with the meta-models and the actual optimization.

Balanced Allocation of Bridge Deck Maintenance Budget Through Multi-objective Optimization

심형섭,이승현 대한토목학회 2017 KSCE Journal of Civil Engineering Vol.21 No.4

Multi-objective optimization method for the allocation of bridge deck Maintenance, Repair, and Rehabilitation (MR&R) budget is proposed using Bridge Management System (BMS) models. In single-objective optimization method, the objective function is usually either total annual MR&R budget or structurally deficient deck area which must be minimized with given annual budget. These objective functions are minimized with constraints, and the solution methods are well-known for the most cases. In multiobjective optimization, objective functions can be the structurally deficient deck area as well as annual MR&R budget. Since structurally deficient deck area and level of annual deck MR&R budget are closely interrelated, State agencies need the method to balance the investment-deck improvement trade-off. This paper uses multi-objective optimization technique with linearly weighted sum method to find balanced MR&R alternatives for the network of bridge decks. Data obtained from Wyoming Department of Transportation (WYDOT) are used to validate the feasibility of application of multi-objective optimization for the maintenance of bridge decks.

Effectiveness of meta-models for multi-objective optimization of centrifugal impeller

Sayed Ahmed Imran Bellary,Afzal Husain,Abdus Samad 대한기계학회 2014 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.28 No.12

The major issue of multiple fidelity based analysis and optimization of fluid machinery system depends upon the proper constructionof low fidelity model or meta-model. A low fidelity model uses responses obtained from a high fidelity model, and the meta-model isthen used to produce population of solutions required for evolutionary algorithm for multi-objective optimization. The Pareto-optimalfront which shows functional relationships among the multiple objectives can produce erroneous results if the low fidelity models are notwell-constructed. In the present research, response surface approximation and Kriging meta-models were evaluated for their effectivenessfor the application in the turbomachinery design and optimization. A high fidelity model such as CFD technique along with the metamodelswas used to obtain Pareto-optimal front via multi-objective genetic algorithm. A centrifugal impeller has been considered as casestudy to find relationship between two conflicting objectives, viz., hydraulic efficiency and head. Design variables from the impellergeometry have been chosen and the responses of the objective functions were evaluated through CFD analysis. The fidelity of each metamodelhas been discussed in context of their predictions in entire design space in general and near optimal region in particular. Exploitationof the multiple meta-models enhances the quality of multi-objective optimization and provides the information pertaining to fidelityof optimization model. It was observed that the Kriging meta-model was better suited for this type of problem as it involved less approximationerror in the Pareto-optimal front.

Optimal Deployment of Water Resources Based on Multi-Objective Genetic Algorithm

Yong Liu,Yongrui Zhuang,Nan Lu 보안공학연구지원센터 2016 International Journal of u- and e- Service, Scienc Vol.9 No.12

Freshwater is limited resource and it is shrinking rapidly due to the urbanization, contamination and climate change impacts. As a result, raising water demands and insufficient freshwater resources become the main reasons of water conflicts. Optimal water allocation model would be an effective method to achieve the optimal allocation of limited water resources, in terms of the conjunctive use planning and management. In this paper, a multi-objective optimal water resources allocation model is proposed and the social, economic and environmental benefits are regarded as the optimal objective functions. The presented model is applied to a case of planning water resources management in China. Furthermore, simulations and optimization modeling methods have been conducted to solve the allocation model. The Gray Model has been used to predict the fresh water demand and storage of different user parts in 2025 and the Genetic Algorithm technique has been employed to solve the multi-objective problem. The obtained results illustrate how to allocate the quantity of different water resource to different users while achieving maximum social, economic and environmental benefits, which is valuable and helpful to develop a water resources optimal allocation strategy.

Multi-objective optimization of drive gears for power split device using surrogate models

Jixin Wang,Wanghao Shen,Zhongda Wang,Mingyao Yao,Xiaohua Zeng 대한기계학회 2014 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.28 No.6

Power split device (PSD) is a key component in the energy coupling and decoupling of parallel-series hybrid electric vehicle. This paperproposes a multi-objective optimization method to achieve optimal balance solution among the volume, contact stress, and frictionalenergy dissipation of PSD drive gears, some of which are implicit with respect to design variables. To avoid the time-consuming problemof finite element analysis used to solve nonlinear responses, surrogate models are adopted to generate approximate expressions of designvariables. Pareto-optimal solutions of PSD are obtained using multi-island genetic algorithm (GA), non-dominated sorting GA-II(NSGA-II), and multi-objective particle swarm optimization algorithm. The performances of PSD before and after optimization are compared. Results indicate that the proposed method is effective, and NSGA-II achieves higher optimizing efficiency in solving the multiobjectiveoptimization problem of PSD than the other algorithms.

Multi-objective optimization of sheet metal forming die using FEA coupled with RSM

Parviz Kahhal,Seyed Yousef Ahmadi Brooghani,Hamed Deilami Azodi 대한기계학회 2013 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.27 No.12

Present study describes the approach of applying response surface methodology (RSM) with a Pareto-based multi-objective genetic algorithm to assist engineers in optimization of sheet metal forming. In many studies, finite element analysis and optimization technique have been integrated to solve the optimal process parameters of sheet metal forming by transforming multi objective problem into a singleobjective problem. This paper aims to minimize objective functions of fracture and wrinkle simultaneously. Design variables are blankholding force and draw-bead geometry (length and diameter). Response surface model has been used for design of experiment and finding relationship between variables and objective functions. Forming limit diagram (FLD) has been used to define objective functions. Finite element analysis applied for simulating the process. Proposed approach has been investigated on a cross-shaped cup drawing case and it has been observed that it is more effective and accurate than traditional finite element analysis method and the ‘trial and error’ procedure.

Multi-objective reliability-based topology optimization of structures using a fuzzy set model

Suwin Sleesongsom,Sujin Bureerat 대한기계학회 2020 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.34 No.10

This research proposes a multi-objective reliability-based topology optimization (MORBTO) for structural design, which considers uncertain structural parameters based on a fuzzy set model. The new technique is established in the form of multi-objective optimization where the equivalent possibilistic safety index (EPSI) is included as one of the objective functions along with mass, and compliance. This technique can reduce complexity due to a doubleloop nest problem used previously due to performing single objective optimization. The present technique can accomplish within one optimization run using a multi-objective approach. Two design examples are used to demonstrate the present technique, which have the objectives as structural mass and compliance with the constraint of structural strength. The results show the proposed technique is effective and simple compared to previous techniques.