• Journal of the Korean Operations Research and Management Science Society
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• v.32 no.2
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• pp.99-107
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• 2007

We consider (worst-case) robust optimization versions of the Economic Order Quantity (EOQ) model with decreasing cost functions. Two variants of the EOQ model are discussed, in which the purchasing costs are decreasing power functions in either the order quantity or demand rate. We develop the corresponding worst-case robust optimization models of the two variants, where the parameters in the purchasing cost function of each model are uncertain but known to lie in an ellipsoid. For the robust EOQ model with the purchasing cost being a decreasing function of the demand rate, we derive the analytical optimal solution. For the robust EOQ model with the purchasing cost being a decreasing function of the order quantity, we prove that it is a convex optimization problem, and thus lends itself to efficient numerical algorithms.

• Journal of Electrical Engineering and Technology
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• v.13 no.6
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• pp.2262-2267
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• 2018

In electric machine design, there is a large computation cost for finite element analyses (FEA) when analyzing nonlinear characteristics in the machine Therefore, for the optimal design of an electric machine, designers commonly use an optimization algorithm capable of excellent convergence performance. However, robustness consideration, as this factor can guarantee machine performances capabilities within design uncertainties such as the manufacturing tolerance or external perturbations, is essential during the machine design process. Moreover, additional FEA is required to search robust optimum. To address this issue, this paper proposes a computationally efficient robust optimization algorithm. To reduce the computational burden of the FEA, the proposed algorithm employs a useful technique which termed static analysis assisted technique (SAAT). The proposed method is verified via the effective robust optimal design of electric machine to reduce cogging torque at a reasonable computational cost.

• Management Science and Financial Engineering
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• v.18 no.2
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• pp.23-27
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• 2012

The problem of jointly determining a robust optimal bundle of price and order quantity for a retailer in a single-retailer, single supplier, single-product supply chain is considered. Demand is modeled as a decreasing power function of product price, and unit purchasing cost is modeled as a decreasing power function of order quantity and demand. Parameters defining the two power functions are uncertain but their possible values are characterized by ellipsoids. We extend a previous study in two ways; the purchasing cost function is generalized to take into account the economies of scale realized by higher product demand in addition to larger order quantity, and an exact transformation into an equivalent convex optimization program is developed instead of a geometric programming approximation scheme proposed in the previous study.

• Computers and Concrete
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• v.23 no.6
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• pp.433-444
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• 2019

As rice husk ash (RHA) is not produced in controlled manufacturing process like cement, its properties vary significantly even within the same lot. In fact, properties of Rice Husk Ash Based Concrete (RHABC) are largely dictated by uncertainty leading to huge deviations from their expected values. This paper proposes a Robust Cost Optimization (RCO) procedure for RHABC, which minimizes such unwanted deviation due to uncertainty and provides guarantee of achieving desired strength and workability with least possible cost. The RCO simultaneously minimizes cost of RHABC production and its deviation considering feasibility of attaining desired strength and workability in presence of uncertainty. RHA related properties have been modeled as uncertain-but-bounded type as associated probability density function is not available. Metamodeling technique is adopted in this work for generating explicit expressions of constraint functions required for formulation of RCO. In doing so, the Moving Least Squares Method is explored in place of conventional Least Square Method (LSM) to ensure accuracy of the RCO. The efficiency by the proposed MLSM based RCO is validated by experimental studies. The error by the LSM and accuracy by the MLSM predictions are clearly envisaged from the test results. The experimental results show good agreement with the proposed MLSM based RCO predicted mix properties. The present RCO procedure yields RHABC mixes which is almost insensitive to uncertainty (i.e., robust solution) with nominal deviation from experimental mean values. At the same time, desired reliability of satisfying the constraints is achieved with marginal increment in cost.

• International Journal of Automotive Technology
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• v.4 no.4
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• pp.193-201
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• 2003

The problem of brake judder is typically caused by defects of quality manufacturing. DFSS (Design for six sigma) is a design process for quality improvement. DFSS will result in more improved but less expensive quality products. This paper presents an implementation of DFSS for quality improvement of the brake judder of heavy-duty trucks. Carrying out 5 steps of DFSS, the major reasons for defects of quality are found. The numerical approximation of the brake system is derived by means of the response surface method. Its quality for brake judder is improved by using the sigma based robust design methodology. Results are compared between the conventional deterministic optimal design and the proposed sigma based robust design. The proposed one shows that manufacturing cost may increase as the quality level increase. The proposed one, however, is more economical in aspect of the overall cost since the probability of failure dramatically goes down.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.40-43
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• 1996

To design high quality products at low cost is one of very important task for engineers Design optimization for performances can be one solution in this task. This is robust design which has been proved effectively in many field of engineering design. In this paper, the concept of robust design is introduced and combined to fuzzy optimization and nonsingleton fuzzy logic system. The optimum parameter set points were obtained by the fuzzy optimization method and nonsingleton fuzzy logic system. These methods are applied to a filter circuit, a part of the audio circuit of mobile radio transceiver. The results are compared each other.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.46 no.3
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• pp.15-21
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• 2009

In this paper, we consider the design problem of robust stabilization and robust guaranteed cost state feedback controller for discrete-time singular systems with parameter uncertainties by LMI(linear matrix inequality) approach without semi-definite condition and decomposition of system matrices. The objective of robust stabilization controller is to construct a state feedback controller such that the closed-loop system is regular, causal, and stable. In the case of robust guaranteed cost control, the optimal value of guaranteed cost and controller design method are presented on the basis of robust stabilization control technique. Finally, a numerical example is provided to show the validity of the design methods.

• Korean Management Science Review
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• v.24 no.2
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• pp.73-80
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• 2007

Robust Design(RD) is a cost-effective methodology to determine the optimal settings of control factors that make a product performance insensitive to the influence of noise factors. To better facilitate the robust design optimization, a dual response surface approach, which models both the process mean and standard deviation as separate response surfaces, has been successfully accepted by researchers and practitioners. However, the construction of response surface approximations has been limited to problems with only a few variables, mainly due to an excessive number of experimental runs necessary to fit sufficiently accurate models. In this regard, an innovative response surface approach has been proposed to investigate robust design optimization problems with larger number of variables. Response surfaces for process mean and standard deviation are partitioned and estimated based on the multi-level approximation method, which may reduce the number of experimental runs necessary for fitting response surface models to a great extent. The applicability and usefulness of proposed approach have been demonstrated through an illustrative example.

• Journal of Magnetics
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• v.19 no.4
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• pp.385-392
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• 2014

Uncertainties in loads, materials and manufacturing quality must be considered during electromagnetic devices design. This paper presents an effective methodology for robust optimization design based on the variance decomposition in order to keep higher accuracy of the robustness prediction. Sobol' theory is employed to estimate the response variance under some specific tolerance in design variables. Then, an optimal design is obtained by adding a criterion of response variance upon typical optimization problems as a constraint of the optimization. The main contribution of this paper is that the proposed method applies the variance decomposition to obtain a more accurate variance of the response, as well save the computational cost. The performance and robustness of the proposed algorithms are investigated through a numerical experiment with both an analytic function and the TEAM 22 problem.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.38 no.5
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• pp.535-543
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• 2014

In the robust optimization field, the robustness of the objective function emphasizes an insensitive design. In general, the robustness of the objective function can be achieved by reducing the change of the objective function with respect to the variation of the design variables and parameters. However, in conventional methods, when an insensitive design is emphasized, the performance of the objective function can be deteriorated. Besides, if the numbers of the design variables are increased, the numerical cost is quite high in robust optimization for nonlinear programming problems. In this research, the robustness index for the objective function and a process of robust optimization are proposed. Moreover, a method using the supremum of linearized functions is also proposed to reduce the computational cost. Mathematical examples are solved for the verification of the proposed method and the results are compared with those from the conventional methods. The proposed approach improves the performance of the objective function and its efficiency.