Application of SVR,Taguchi loss function,and the artificial bee colony algorithm to resolve multiresponse parameter design problems: a case study on optimizing the design of a TIR lens

Multiresponse parameter design problems have become increasingly important and have received considerable attention from both researchers and practitioners since there are usually several quality characteristics that must be optimized simultaneously in most modern products/processes. This study applies support vector regression (SVR), Taguchi loss function, and the artificial bee colony (ABC) algorithm to develop a six-staged procedure that resolves these common and complicated parameter design problems. SVR is used to model the mathematical relationship between input control factors and output responses, and the ABC algorithm is used to find the optimal control factor settings by searching the well-constructed SVR models in which the Taguchi loss function is applied to evaluate the overall performance of a product/process. The feasibility and effectiveness of the proposed approach are demonstrated via a case study in which the design of a total internal reflection (TIR) lens is optimized while fabricating an MR16 light-emitting diode lamp. Experimental results indicate that the proposed solution procedure can provide highly robust design parameter settings for TIR lenses that can be directly applied in real manufacturing processes. Comparisons with the Taguchi method reveal that the Taguchi method is an undesirable and inappropriate method for resolving multiple-response parameter design problems, while the ABC algorithm can search the solution spaces in continuous domains modeled via SVR instead of in the limited discrete experiment levels, thus finding a more robust design than that obtained by the traditional analysis of variance. Consequently, the proposed integrated approach in this study can be considered feasible and effective and can be popularized as a useful tool for resolving general multiresponse parameter design problems in the real world.     

Improving the lighting performance of a 3535 packaged hi-power LED using genetic programming,quality loss functions and particle swarm optimization

The lighting performance of a 3535 packaged hi-power LED (light-emitting diode) is mainly influenced by its geometric design and the refractive properties of its materials. In the past, engineers often determined the settings of the geometric parameters and selected the refractive properties of the materials through a trial-and-error process based on the principles of optics and their own experience. This procedure was costly and time-consuming, and its use did not ensure that the settings of the design parameters were optimal. Therefore, this study proposed a hybrid approach based on genetic programming (GP), Taguchi quality loss functions, and particle swarm optimization (PSO) to solve the multi-response parameter design problems. The feasibility and effectiveness of the proposed approach was demonstrated by a case study on improving the lighting performance of an LED. The confirmation results showed that all of the key quality characteristics of an LED fulfill the required specifications, and the comparison found that the proposed hybrid approach outperforms the traditional Taguchi method in solving this multi-response parameter design problem. The proposed hybrid approach can be extended to solve parameter design problems with multiple responses in various application fields.     

Applying genetic programming and ant colony optimisation to improve the geometric design of a reflector

The lighting performance of an LED (light-emitting diode) flash is significantly influenced by the geometric form of a reflector. Previously, design engineers have usually determined the geometric design of a reflector according to the principles of optics and their own experience. Some real reflectors have then been created to verify the feasibility and performance of a certain geometric design. This, however, is a costly and time-consuming procedure. Furthermore, the geometric design of a reflector cannot be proven to be actually optimal. This study proposes a systematic approach based on genetic programming (GP) and ant colony optimisation (ACO), called the GP–ACO procedure, to improve the geometric design of a reflector. A case study is used to demonstrate the feasibility and effectiveness of the proposed optimisation procedure. The results show that all the crucial quality characteristics of an LED flash fulfil the required specifications; thus, the optimal geometric parameter settings of the reflector obtained can be directly applied to mass production. Consequently, the proposed GP–ACO procedure can be considered an effective method for resolving general multi-response parameter design problems.     

An integrated approach to optimise parameter design of multi-response processes based on Taguchi method and artificial intelligence

The Taguchi robust parameter design has been widely used over the past decade to solve many single-response process parameter designs. However, the Taguchi method is unable to deal with multi-response problems that are of main interest today, owing to increasing complexity of manufacturing processes and products. Several recent studies have been conducted in order to solve this problem. But, they did not effectively treat situations where responses are correlated and situations in which control factors have continuous values. This study proposed an integrated model for experimental design of processes with multiple correlated responses, composed of three stages which (1) use expert system, designed for selecting an inner and an outer orthogonal array, to design an actual experiment, (2) use Taguchi’s quality loss function to present relative significance of responses, and multivariate statistical methods to uncorrelate and synthesise responses into a single performance measure, (3) use neural networks to construct the response function model and genetic algorithms to optimise parameter design. The effectiveness of the proposed model is illustrated with three examples. Results of analysis showed that the proposed approach could yield a better solution in terms of the optimal parameters setting that results in a higher process performance measure than the traditional experimental design.     

An integrated neuro-genetic approach incorporating the Taguchi method for product design

Product design is a multidisciplinary activity that requires the integration of concurrent engineering approaches into a design process that secures competitive advantages in product quality. In concurrent engineering, the Taguchi method has demonstrated an efficient design approach for product quality improvement. However, the Taguchi method intuitively uses parameters and levels in measuring the optimum combination of design parameter values, which might not guarantee that the final solution is the most optimal. This work proposes an integrated procedure that involves neural network training and genetic algorithm simulation within the Taguchi quality design process to aid in searching for the optimum solution with more precise design parameter values for improving the product development. The concept of fractals in computer graphics is also considered in the generation of product form alternatives to demonstrate its application in product design. The stages in the general approach of the proposed procedures include: (1) use of the Taguchi experimental design procedure, (2) analysis of the neural network and genetic algorithm process, and (3) generation of design alternatives. An electric fan design is used as an example to describe the development and explore the applicability of the proposed procedures. The results indicate that the proposed procedures could enhance the efficiency of product design efforts by approximately 7.8%. It is also expected that the proposed design procedure will provide designers with a more effective approach to product development.     

Eulerian shape design sensitivity analysis and optimization with a fixed grid

Conventional shape optimization based on the finite element method uses Lagrangian representation in which the finite element mesh moves according to shape change, while modern topology optimization uses Eulerian representation. In this paper, an approach to shape optimization using Eulerian representation such that the mesh distortion problem in the conventional approach can be resolved is proposed. A continuum geometric model is defined on the fixed grid of finite elements. An active set of finite elements that defines the discrete domain is determined using a procedure similar to topology optimization, in which each element has a unique shape density. The shape design parameter that is defined on the geometric model is transformed into the corresponding shape density variation of the boundary elements. Using this transformation, it has been shown that the shape design problem can be treated as a parameter design problem, which is a much easier method than the former. A detailed derivation of how the shape design velocity field can be converted into the shape density variation is presented along with sensitivity calculation. Very efficient sensitivity coefficients are calculated by integrating only those elements that belong to the structural boundary. The accuracy of the sensitivity information is compared with that derived by the finite difference method with excellent agreement. Two design optimization problems are presented to show the feasibility of the proposed design approach.     

Accurate and efficient design technique for wideband substrate integrated waveguide directional couplers

In this article, we present an efficient technique for the accurate design of wideband substrate integrate waveguide directional couplers. By tapering the coupling section, the bandwidth of substrate integrated waveguide (SIW) directional couplers can be enlarged. Two design aspects are involved in this approach. First, the even‐mode propagation constant in the tapered coupling section is accurately extracted with the help of a numerical thru‐reflect‐line calibration technique. Then, it is fitted into the model of a uniform dielectric‐filled rectangular waveguide and thereafter extrapolated to the operation range of the odd mode. Second, equivalent circuit models of the waveguide bifurcation effects are also presented together with parametric values. Based on the results of extraction, a 90° 3‐dB directional coupler is developed to validate the proposed design approach. To achieve the reverse phasing at two output ports, the prototyped 90° 3‐dB directional coupler is subsequently integrated with a novel broadband fixed phase shifter developed with the SIW technology, of which a systematic synthesis procedure has been proposed in this article. Measured performance of both 90° and 180° 3‐dB couplers confirms the accuracy of our proposed design approach. This kind of wide‐band directional coupler can find applications in wideband power dividing/combining circuits within a single‐layer platform. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2012.     

Optimization of parameter design: An intelligent approach using neural network and simulated annealing

Parameter design optimization problems have found extensive industrial applications, including product development, process design and operational condition setting. The parameter design optimization problems are complex because non-linear relationships and interactions may occur among parameters. To resolve such problems, engineers commonly employ the Taguchi method. However, the Taguchi method has some limitations in practice. Therefore, in this work, we present a novel means of improving the effectiveness of the optimization of parameter design. The proposed approach employs the neural network and simulated annealing, and consists of two phases. Phase 1 formulates an objective function for a problem using a neural network method to predict the value of the response for a given parameter setting. Phase 2 applies the simulated annealing algorithm to search for the optimal parameter combination. A numerical example demonstrates the effectiveness of the proposed approach.     

Rapid surrogate‐assisted design optimization of minimum‐size broadband branch‐line couplers with variable topology

This work discusses simulation‐driven design of miniaturized wideband branch‐line couplers with a variable topology. Size reduction is enabled here by replacing uniform transmission lines of the original coupler with slow‐wave structures in the form of cascaded compact cells and meander lines. The primary goal is to determine a number of cells in the cascade and particular cell dimensions for which the minimum size of the coupler as well as its required operating conditions are ensured. To this end, we employ a surrogate‐assisted technique involving a trust‐region gradient search framework. Computational efficiency of the design process stems from estimating the Jacobian of circuit responses at the level of a low‐fidelity model of the cascade. The latter is composed in a circuit simulator from duplicated EM‐evaluated data blocks of a single cell and is well correlated with the corresponding high‐fidelity model. The key advantage of this work is the utilization of a reconfigurable, cheap, and well‐aligned low‐fidelity model. The proposed approach is demonstrated through design of a minimum‐size two‐section branch‐line coupler with quasi‐periodic dumbbell‐shaped cells and meander lines. Excellent circuit performance as well as its small size showcase the reliability and usefulness of the presented method. Experimental verification is also provided.     

Adjustment of high‐order sliding‐mode controllers

Long‐lasting problems of high‐order sliding‐mode (HOSM) design are solved. Only local uncertainty suppression was previously obtained in the case when the dynamic system uncertainties are unbounded. This restriction is removed in this paper. A universal method is proposed for the proper controller parameter adjustment based on the homogeneity approach. The method allows making the finite‐time convergence arbitrarily fast or slow. In addition, a HOSM regularization procedure is proposed diminishing chattering. Computer simulation confirms the theoretical results. Copyright © 2008 John Wiley & Sons, Ltd.     

Artificial neural network based approach for dynamic parameter design

The Taguchi parameter design method has been recognized as an important tool for improving the quality of a product or a process. However, the statistical methods and optimization procedures proposed by Taguchi have much room for improvement. For instance, the two-step procedure proposed by Taguchi may fail to identify an optimum design condition if an adjustment parameter does not exist, the optimal setting of a design parameter is determined only among the levels included in the parameter design experiment, and, for the dynamic parameter design, the signal parameter is assumed to follow a uniform rather than a general distribution. This paper develops an artificial neural network based dynamic parameter design approach to overcome the shortcomings of the Taguchi and existing alternative approaches. First, an artificial neural network is trained to map the relationship between the characteristic, design, noise and signal parameters. Second, Latin hypercube samples of the signal and noise parameters are obtained and used to estimate the slope between the signal parameter and characteristic as well as the variance of the characteristic at each set of design parameter settings. Then, the dynamic parameter design problem is formulated as a nonlinear optimization problem and solved to find the optimal settings of the design parameters using sequential quadratic programming. The effectiveness of the proposed approach is illustrated with an example.     

Robust flight control system design using H∞ loop-shaping and recessive trait crossover genetic algorithm

A proposed approach to robust controller design is introduced. This approach combines the recessive trait crossover genetic algorithm with the loop-shaping design procedure using H_∞ synthesis. The requirements, design and simulation of a flight control system for precision tracking task are considered. The proposed method is applied to design a control system for the F-16 fighter aircraft model. The flight simulations reveal that the desired performance objectives are achieved and that the controller provides acceptable performance in spite of modeling errors and plant parameter variations.     

A balanced solution of a fuzzy soft set based decision making problem in medical science

The purpose of this paper is two folded. Firstly, the concept of mean potentiality approach (MPA) has been developed and an algorithm based on this new approach has been proposed to get a balanced solution of a fuzzy soft set based decision making problem. Secondly, a parameter reduction procedure based on relational algebra with the help of the balanced algorithm of mean potentiality approach has been used to reduce the choice parameter set in the parlance of fuzzy soft set theory and it is justified to the problems of diagnosis of a disease from the myriad of symptoms from medical science. Moreover the feasibility of this proposed method is demonstrated by comparing with Analytical Hierarchy Process (AHP), Naive Bayes classification method and Feng's method.     

A novel physical based meta-heuristic optimization method known as Lightning Attachment Procedure Optimization

In this article, A novel nature-inspired optimization algorithm known as Lightning Attachment Procedure Optimization (LAPO) is proposed. The proposed approach mimics the lightning attachment procedure including the downward leader movement, the upward leader propagation, the unpredictable trajectory of lightning downward leader, and the branch fading feature of lightning. Final optimum result would be the lightning striking point. The proposed method is free from any parameter tuning and it is rarely stuck in the local optimum points. To evaluate the proposed algorithm, 29 mathematical benchmark functions are employed and the results are compared to those of 9 high quality well-known optimization methods The results of the proposed method are compared from different points of views, including quality of the results, convergence behavior, robustness, and CPU time consumption. Superiority and high quality performance of the proposed method are demonstrated through comparing the results. Moreover, the proposed method is also tested by five classical engineering design problems including tension/compression spring, welded beam, pressure vessel designs, Gear train design, and Cantilever beam design and a high constraint optimization problem known as Optimal Power Flow (OPF) which is a high constraint electrical engineering problem. The excellence performance of the proposed method in solving the problems with large number of constraints and also discrete optimization problems are also concluded from the results of the six engineering problem.     

A data mining approach to dynamic multiple responses in Taguchi experimental design

To simultaneously optimize the parameter robust design of dynamic multiple responses is difficult due to product complexity; however, the design is what determines most of the production time, cost, and quality. Although several methods tackling this problem have been published, they have proven unable to effectively resolve the situation if a system has continuous control factors. This work proposes a data mining approach, consisting of four stages based on artificial neural networks (ANN), desirability functions, and a simulated annealing (SA) algorithm to resolve the problems of dynamic parameter design with multiple responses. An ANN is employed to build a system’s response function model. Desirability functions are used to evaluate the performance measures of multiple responses. A SA algorithm is applied to obtain the best factor settings through the response function model. By using the proposed approach, the obtained best factor settings can be any values within their upper and lower bounds so that the system’s multiple responses have the least sensitivity to noise factors along the magnitude of the signal factor. An example from the literature is illustrated to confirm the feasibility and effectiveness of the proposed approach.     

The use of simulation in discrete-event dynamic systems design

The use of simulation as a tool to design complex stochastic systems is often inhibited by cost. We present a procedure for estimating a value for the controllable input parameter which generates a desirable output. Since the output has to be matched by varying the input parameter, an iterative method of solution is applied. The proposed solution algorithm is based on Newton's method using a single-run simulation approach to estimate the needed derivative. The major contribution of this paper is to provide a framework for arriving at a target value for product, process and service attributes through Monte Carlo experiments. The effectiveness of the proposed procedure is demonstrated by determining a desirable service rate in a queueing system with known analytical solution.     

Compact cell topology selection for size‐reduction‐oriented design of microstrip rat‐race couplers

In this work, we address the problem of compact cell topology selection for miniaturization of rat‐race couplers. The principal objective of the design process is to achieve the smallest possible footprint of the coupler, while maintaining the required levels of electrical parameters imposed on its components. Our approach permits identification of the minimum achievable coupler area, provided that the circuit is composed of a given compact cell and folded lines. This allows for the quantitative assessment of a set of considered cells with respect to the miniaturization capabilities they exhibit under certain design specifications. The proposed method is validated using 6 different cells with unified parameterization to identify the smallest rectangular‐like rat‐race coupler described by 2 design specifications. The obtained results attest that circuit topology and electrical parameters of the reference design are critical factors determining the final miniaturization rate. The proof‐of‐concept prototype devices occupy merely 8% of the conventional coupler area, while preserving fractional bandwidths (20% and 13.5%) of their conventional counterparts. The experimental results confirm the claims inferred from the numerical data.     

Neuro-genetic approach to optimize parameter design of dynamic multiresponse experiments

Engineers have widely applied the Taguchi method, a traditional approach for robust experimental design, to a variety of quality engineering problems for enhancing system robustness. However, the Taguchi method is unable to deal with dynamic multiresponse owing to increasing complexity of the product or design process. Although several alternative approaches have been presented to resolve this problem, they cannot effectively treat situations in which the control factors have continuous values. This study incorporates desirability functions into a hybrid neural network/genetic algorithm approach to optimize the parameter design of dynamic multiresponse with continuous values of parameters. The objective is to find the optimal combination of control factors to simultaneously maximize robustness of each response. The proposed approach is based on three stages which (1) use neural networks for constructing a response function model of a dynamic multiresponse system, (2) use exponential desirability functions for evaluating overall performance of a specific factor combination, and (3) use a genetic algorithm to optimize parameter design. Effectiveness of the proposed approach is illustrated with a simulated example. Analysis results reveal that the approach has higher performance than the traditional experimental design.     

Penalty function approach for the mixed discrete nonlinear problems by particle swarm optimization

In this paper, the basic characteristics of particle swarm optimization (PSO) for the global search are discussed at first, and then the PSO for the mixed discrete nonlinear problems (MDNLP) is suggested. The penalty function approach to handle the discrete design variables is employed, in which the discrete design variables are handled as the continuous ones by penalizing at the intervals. As a result, a useful method to determine the penalty parameter of penalty term for the discrete design variables is proposed. Through typical mathematical and structural optimization problems, the validity of the proposed approach for the MDNLP is examined.     

The sample solution approach for determination of the optimal shape parameter in the Multiquadric function of the Kansa method

The Kansa method with the Multiquadric-radial basis function (MQ-RBF) is inherently meshfree and can achieve an exponential convergence rate if the optimal shape parameter is available. However, it is not an easy task to obtain the optimal shape parameter for complex problems whose analytical solution is often a priori unknown. This has long been a bottleneck for the MQ-Kansa method application to practical problems. In this paper, we present a novel sample solution approach (SSA) for achieving a reasonably good shape parameter of the MQ-RBF in the Kansa method for the solution of problems whose analytical solution is unknown. The basic assumption behind the SSA is that the optimal shape parameter is considered to be largely depended on the shape of computational domain, the type of the boundary conditions, the number and distribution of nodes, and the governing equation. In the procedure of the SSA, we set up a pseudo-problem as the sample solution whose solution is known. It is not difficult to obtain the optimal parameter of the MQ-RBF in the numerical solution of the pseudo-problem. The SSA suggests that the optimal shape parameter of the pseudo-problem can also achieve an approximately optimal accuracy in the solution of the original problem. Numerical examples and comparisons are provided to verify the proposed SSA in terms of accuracy and stability in solving homogeneous problems and non-homogeneous modified Helmholtz problems in several complex domains even using chaotic distribution of collocation points.