Robust Design Optimization Model Research Articles

Design optimization of continuous fiber composites with thermo-mechanical coupling and load uncertainties

This paper introduces a theoretical framework for the design optimization of continuous fiber composites reinforced with continuous fiber trajectories subject to thermo-mechanical coupling and load uncertainties. Different uniform temperature variations are applied in the structure to investigate the influence of ambient temperature change on the structural performance. To consider the external load uncertainties, a robust design optimization model is proposed where the loads are modeled as hybrid variables, namely magnitudes as random variables and directions as interval variables, with the robust objective determined through a hybrid orthogonal polynomial expansion method. Furthermore, we use a level-set function to represent the structural boundary, with its evolution driven by shape derivatives calculated based on uncertainty analysis. The continuous fiber paths are subsequently determined by the level-set isoline extracted from the structural boundary, which in turn influences the structural mechanical performance due to the material anisotropy of composites. The continuity of continuous fiber and the equal space between adjacent trajectories largely ensure the additive manufacturability of the composites. Three numerical examples are presented to demonstrate the effectiveness of the developed framework. The results show that the ambient temperature variations and load uncertainties largely impact the optimized topology and fiber infill patterns of composites, thus are important to be considered in the design stage. Moreover, the optimized structure can have a 5-fold stiffness per unit mass compared with the initial design thus largely increasing the material efficiency in carrying external uncertain loads.

Robust design modeling and optimization for dealing with a non-convex design space

Classic experimental designs effectively generate experimental design points under standard design spaces such as a circle, a cube, or a sphere. However, for non-convex design spaces, traditional experimental designs are not appropriate due to nonstandard experimental design conditions. No attention has been given to developing an algorithm to generate design points for a non-convex design space in the literature. This paper is three-fold. One, this paper presents a novel exchange algorithm based on an inner approximation approach in order to construct optimal design points where the design space is non-convex. Besides, the proposed algorithm efficiently produces experimental design points for non-convex design space. In addition, it is provided a fair comparison of the proposed algorithm performance. Two, the fitted response functions of the mean, standard deviation, and variance are found using the proposed regression model construction technique where the design space is non-convex. Three, a selected optimal design concept-based robust design optimization model is developed to find Pareto optimal solution settings of chosen design factors for the non-convex design space. Finally, an Industry 4.0 concept-based numerical example is provided to illustrate how to apply the proposed methodology effectively for the non-convex design space.

Multiple parameter optimization methodology by integrating a game theory principle into priority-based decision making

Mathematical model development for multivariate decision-making problems (i.e., multiple parameter and response optimization problems) has received significant attention and has been investigated by many researchers and practitioners. Although many different optimization models and methods, including priority and weight allocation problems, have been proposed in the literature, there is significant room for improvement. The majority of existing optimization methods may have difficulties in determining reliable priorities and weights for practical industrial situations. In addition, because they often focus on tradeoffs only among multiple output responses, these methods may not incorporate the multiple priority and/or weight effects directly from input factors to output responses (i.e., quality characteristics). To address these problems, the primary objective of this research is to propose a new multi-objective optimization approach by integrating a game theory principle (i.e., the Stackelberg leadership game) into a robust parameter design model to determine the optimal factor settings. First, a multi-response robust design optimization (RDO) problem was formulated using a mean squared error model and response surface methodology. A Stackelberg leadership game is then integrated into this RDO problem, where multiple responses play the role of game participants. Second, the integrated RDO model using the Stackelberg game-based multi-response (SGMR) formulation approach is analyzed by decomposition into various sequential optimization models in terms of different leader–follower relationships. Finally, non-dominated solutions are obtained from the proposed model by evaluating the overall quality loss (OQL). A pharmaceutical numerical example was performed to demonstrate the proposed integrated model and to examine whether this model can determine the most efficient solutions when the relative importance among multiple responses is unidentified. In addition, a comparative study associated with the conventional multi-objective optimization methods and the newly proposed RDO model is presented, and the proposed RDO model provided significantly better solutions than the conventional methods in the relevant comparative study.

A fuzzy mixed-integer robust design optimization model to obtain optimum settings of both qualitative and quantitative input variables under uncertainty

Quality improvement is the most effective activity for the process and product development cycle, while minimizing the process and product variation. For this particular purpose, robust design models are proposed to reduce the process and product variance. However, the majority of robust design models in the literature deals with certain situations. This article has four objectives. First, an experimental design matrix is generated for both qualitative and quantitative input variables under uncertainty. Secondly, triangular fuzzy numbers are used to measure the values of a response variable while dealing with an α-level cut strategy. Fitted fuzzy mean, standard deviation and variance response functions are also obtained. Thirdly, a fuzzy mixed-integer robust design optimization model is proposed to obtain the optimum operating conditions of input variables under uncertainty. Finally, a numerical example is presented to show the effectiveness of the proposed fuzzy-based methodology development for an uncertain environment.

Development of a bi-objective 0-1 mixed-integer nonlinear response surface-based robust design optimization model for unbalanced experimental data

The purpose of this paper is to develop a model to obtain the optimum operating conditions under special engineering situations. These special situations are: (1) both qualitative and quantitative input variables are considered, (2) a specific number of design points is required, (3) the experimental design space is irregular due to physical constraints, and (4) the unbalanced experimental data is collected due to resource limitations and focusing on certain treatment combinations. Although such situations may occur in many processes, there has been little research on this subject. To address these research gaps, first, an I-optimal experimental design is selected to construct a design matrix by using a modified exchange algorithm. Second, a weighted least squares method is presented to deal with the unbalanced experimental data. Third, a bi-objective 0-1 mixed-integer nonlinear programming-based robust design model and its solution procedures are proposed to obtain optimum settings of both qualitative and quantitative variables. Finally, a case study, along with the comparative study, is presented.

A Robust Design Optimization Method Considering Correlated Intervals

In the robust design, correlations of uncertain parameters exist widely and have an influence on the results in most cases. It is essential to develop a robust design optimization method considering parametric correlation to future improve the analysis accuracy and engineering applicability. In this paper, a robust design optimization method based on multidimensional parallelepiped convex model is presented. Considering the effects of the interval uncertainties and their correlations, a robust design optimization model considering correlated intervals is established. In the established model, the average performance and robustness of the system response of concern are taken as the design optimization objectives, and the correlations among interval parameters are quantified by integrating the multidimensional parallelepiped convex model. And then, through an independence transforming procedure it can be converted into an independent interval model, which is ultimately converted into a deterministic multi-objective optimization model by using the interval possibility degree to cope with the uncertain constraints. Finally, the deterministic multi-objective optimization model is treated by coupling an efficient micro multi-objective genetic algorithm with the first order Taylor expansion. The feasibility and practicability of the proposed method are demonstrated by the numerical and engineering examples.

Stochastic Reliability Measurement and Design Optimization of an Inventory Management System

Inventory management systems and dynamic reliability measures and controls remain challenging at every stage, especially when time variances and operating conditions are considered. An inventory management system must maintain its adeptness over time while coping with the uncertainty of inventory flow. Unexpected delays during inventory movement can harm the reliability and robustness of the entire system. This paper introduces a method of quantifying the reliability of an inventory management system. Also, a novel, reliability-based robust design optimization model has been developed to optimally allocate and schedule time while considering uncertainty associated with inventory movement. The processes involved include purchasing, shipping, receiving, tracking, warehousing, storage, and turnover. A case study of a furniture company in Saudi Arabia is presented to demonstrate the efficacy of the model.

Cost efficient robust global supply chain system design under uncertainty

Brutal competitions in today’s global supply chain have forced business enterprises to focus attention on their supply chains. These issues have guided this research to introduce a supply chain service level measure and develop a novel robust design optimization (RDO) approach to assure service level rate requirements and minimize total service level costs. A supply chain system design must maintain its efficiency over time while coping with the uncertainty in production and transportation. Unexpected delay in the product flow can render the supply chain system inefficient with respect to service level costs. Analytical models for the determination of the risk involved in a supply chain system design are difficult to derive when uncertainty is involved in the supply chain. In this paper, the service level rate measure approach is detailed first. Then, the methodology for the robust design optimization-based approach is provided. Two case studies are performed to demonstrate the effectiveness of the proposed service level measure and developed robust design optimization model. Results from the two case studies have shown that by implementing the developed robust design optimization approach, a system is able to achieve a 90 % service level rate while minimizing performance cost and uncertainty impact.

Design Optimization for the Robustness of Dimensional Tolerance by Using Evidence Theory

The design optimization of tolerance is researched to improve the robustness of plane dimension chain. The nonlinear functional relationship between the closed loop and the component loops of a dimension chain is formulated. The tolerances of component loops are regarded as design variables. The total manufacturing costs of the component loops and the success rate of assembly of the closed loop are treated as constraint conditions. Then, a robust design optimization model is established to minimize the variance of the closed loop and to make the mean value of the closed loop approach to target value. The evidence theory is used to deal with the constraint condition on the success rate of assembly. The dimension chain of a gear box is taken as an example to illustrate the proposed method and the example shows that the proposed method is effective.

Lexicographical dynamic goal programming approach to a robust design optimization within the pharmaceutical environment

The primary objective of this paper is to develop a new robust design (RD) optimization procedure based on a lexicographical dynamic goal programming (LDGP) approach for implementing time-series based multi-responses, while the conventional experimental design formats and frameworks may implement static responses. First, a parameter estimation method for time-dependent pharmaceutical responses (i.e., drug release and gelation kinetics) is proposed using the dual response estimation concept that separately estimates the response functions of the mean and variance, as a part of response surface method. Second, a multi-objective RD optimization model using the estimated response functions of both the process mean and variance is proposed by incorporating a time-series components within a dynamic modeling environment. Finally, a pharmaceutical case study associated with a generic drug development process is conducted for verification purposes. Based on the case study results, we conclude that the proposed LDGP approach effectively provides the optimal drug formulations with significantly small biases and MSE values, compared to other models.

A pharma-robust design method to investigate the effect of PEG and PEO on matrix tablets

Even though polyethyleneoxide (PEO)–polyethyleneglycol (PEG) blends have been used widely for sustained release matrix tablets, evaluations of the effects of PEG or PEO on the matrix properties have been limited. In order to evaluate gelling behavior and drug release profiles of PEG, various contents of the polymers were investigated through a robust experimental design method. When exposed to an aqueous environment, the PEO–PEG matrix hydrated slowly and swelled, causing a thick gel layer to form on the surface, the thickness of which increased significantly depending on the PEG contents. Since polyacrylate plates were used for the study, the matrix was not completely hydrated and gelled even after 5 h. However, the results could be applied to the time-oriented responses RD (robust design) models to obtain optimal settings and responses for the observed times. The optimal settings of PEO and PEG were 94.26 and 140.04 mg, respectively (PEG rate of 148.57%). Moreover, as the amount of PEG increased, the release rate also increased. When the formulation contained more than 150% of PEG, most of the drug loaded in the tablet was released in about 12 h. When the amount of PEG was less than 100%, the drug release rate was sustained significantly. Based on the RD optimization model for drug release, the optimal settings were PEG and PEO of 124.3 and 110 mg, respectively (PEG rate of 88.50%). Therefore, PEG rate of about 90–150% is suggested for matrix tablet formulations, and the exact ratio could be formulated according to the resulting tablet's properties.

Development of a multidisciplinary–multiresponse robust design optimization model

Robust design is an efficient process improvement methodology that combines experimentation with optimization to create systems that are tolerant to uncontrollable variation. Most traditional robust design models, however, consider only a single quality characteristic, yet customers judge products simultaneously on a variety of scales. Additionally, it is often the case that these quality characteristics are not of the same type. To addresses these issues, a new robust design optimization model is proposed to solve design problems involving multiple responses of several different types. In this new approach, noise factors are incorporated into the robust design model using a combined array design, and the results of the experiment are optimized using a new approach that is formulated as a nonlinear goal programming problem. The results obtained from the proposed methodology are compared with those of other robust design methods in order to examine the trade-offs between meeting the objectives associated with different optimization approaches.