Multiple Response Optimization Research Articles

A modified tabu search strategy for multiple-response grinding process optimisation

Multiple-response grinding process is usually too complex to optimise, requiring a large number of interacting process variables and responses. Experimentation techniques, such as factorial design, fractional factorial design and Response Surface Methodology (RSM) that may be used for this process are too difficult to implement for production lines involving grinding and other necessary operations. For grinding process involving continuous variable, non-linear and multiple-response optimisation problem, the potential of Tabu Search (TS) strategy needs to be explored either in its original form or its variant. In this paper, integrating Artificial Neural Network (ANN) and composite desirability function with a Modified Tabu Search (MTS) strategy, based on Mahalanobis multivariate distance approach to identify tabu move, with scatter search intensification scheme is proposed for the above-mentioned problem. Computational results show that MTS provides better consistency in terms of sample mean and standard deviation of composite desirability measures than that of real-coded GA.

Multiple response optimization analysis for pretreatments of Tequila’s stillages for VFAs and hydrogen production

The objective of this work was study the effect of three pretreatments (alkalinization, thermical treatment, and sonication) on Tequila’s stillages hydrolysis process in acidogenesis stage, through the following response variables: soluble chemical oxygen demand (CODs), total sugar and volatile fatty acids profile and the hydrogen production at the time. The stillages were subject to these pretreatments (according to a 2 3 factorial design); afterward they were transferred to a batch reactor at 35 °C and inoculated with an anaerobic digestor sludge. Multiple response optimization (MRO) analysis was done to find the global optimum for the response variables described above. This optimum is able to maximize simultaneously all these variables. It was found adequate to be useful hydrolyzing the organic matter present in Tequila’s stillages. Mathematical models were fitted to observe the estimated effects of pretreatments on each response variable, then the MRO was applied.

Optimization of multiple quality characteristics for CNC turning under cryogenic cutting environment using desirability function

This paper optimizes multiple characteristics (tool life, cutting force, surface roughness and power consumption) in CNC turning of AISI P-20 tool steel using liquid nitrogen as a coolant. Four controllable factors of the turning process viz. cutting speed, feed, depth of cut and nose radius, were studied. Face centered central composite design was used for experimentation. Response surface methodology was used for modeling the responses. Desirability function was used for single and multiple response optimization.

Optimization of Physical Conditions for Caviar Analog Preparation Using Calcium-alginate Gel Capsules

High prices, overfishing, and contamination have limited the availability of natural caviar as a food product. We attempted to apply encapsulation by calcium-alginate gel membranes to caviar analog preparation in an effort to produce a high-quality replacement for natural caviar. Physical conditions of stirring speed and gelation time as the independent variables for gelation were optimized by response surface methodology. Sphericity , diameter , membrane thickness , rupture strength , and rupturing deformation were used as the dependent variables to compare characteristics of the capsules for caviar analogs with natural caviar. The values of the independent variables as evaluated by multiple response optimization were (278 rpm) and (12.2 min), respectively. Predicted values of the four dependent variables were . Membrane thickness was eliminated from the dependent variables for multiple response optimization because it could not be measured with an image analyzer. The experimental values prepared under the optimal conditions for verification nearly coincided with the predicted values and satisfied the conditions of natural caviar.

Effect of Arabic gum, xanthan gum and orange oil on flavor release from diluted orange beverage emulsion

The influence of main emulsion components namely Arabic gum (13–20% w/w), xanthan gum (0.3–0.20% w/w) and orange oil (10–14% w/w) on semi-quantitative headspace analysis of target volatile flavor compounds released from a model orange beverage (diluted orange beverage emulsion) was evaluated by using a three-factor circumscribed central composite design (CCCD). For optimization procedure, the peak area of 13 volatile flavor compounds (i.e. ethyl acetate, α-pinene, ethyl butyrate, β-pinene, 3-carene, myrcene, limonene, γ-terpinene, octanal, decanal, linalool, neral and geranial) were considered as response variables. The response surface analysis exhibited that the significant ( p < 0.05) second-order polynomial regression equations were successfully fitted for all response variables except for ethyl butyrate. A satisfactory coefficient of determination ( R 2) ranged from 0.831 to 0.969 (>0.8) was obtained for the response variables studied. No significant ( p > 0.05) lack of fit was indicated for the reduced models except for the models fitted for limonene and linalool. This observation confirmed an accurate fitness of the reduced response surface models to the experimental data. The multiple response optimizations indicated that an orange beverage emulsion containing 15.87% (w/w) Arabic gum, 0.5% (w/w) xanthan gum and 10% (w/w) orange oil was predicted to provide the minimum overall flavor release.

Development and optimization of a novel oral controlled delivery system for tamsulosin hydrochloride using response surface methodology

The purpose of this study was to develop and optimize oral controlled-release formulations for tamsulosin hydrochloride using a combination of two cellulose ester derivatives, hydroxypropyl methylcellulose (HPMC) and hydroxypropyl methylcellulose phthalate (HPMCP), with Surelease ® as a coating material. A three-factor, three-level Box-Behnken design was used to prepare systematic model formulations, which were composed of three formulation variables, the content of HPMC ( X 1 ) and HPMCP ( X 2 ) and the coating level ( X 3 ), as independent variables. The response surface methodology (RSM) and multiple response optimization utilizing the polynomial equation were used to search for the optimal coating formulation with a specific release rate at different time intervals. The drug release percentages at 2, 3 and 5 h were the target responses and were restricted to 15–30% ( Y 1), 50–65% ( Y 2) and 80–95% ( Y 3), respectively. The optimal coating formulation was achieved with 10% HPMC and 20% HPMCP at a coating level of 25%, and the observed responses coincided well with the predicted values from the RSM optimization technique. The drug release from pellets coated with the optimized formulation showed a controlled-release pattern (zero-order), in comparison with a commercial product (Harunal ® capsule). In conclusion, a novel, oral, controlled-release delivery system for tamsulosin hydrochloride was successfully developed by incorporating HPMC and HPMCP as coating additives into Surelease ® aqueous ethylcellulose dispersion.

Application of grey relational analysis in sheet metal forming for multi-response quality characteristics

The theory of grey systems is a new technique for performing prediction, relational analysis and decision making in many areas. In this paper, the use of grey relational analysis for optimizing the square hole flanging process parameters with considerations of the multiple response (the average flanging height, regular flanging and maximum strain) is introduced. Various flanging parameters, such as the blank inner radius rb, blank inner width B0, are considered. An orthogonal array is used for the experimental design. Multiple response values are obtained using finite element analysis (FEA). Optimal process parameters are determined by the grey relational grade obtained from the grey relational analysis for multi-performance characteristics (flanging height, regular flanging and maximum strain). Analysis of variance (ANOVA) for the grey relational grade is implemented. The results showed good agreement with the experiment result. Grey relational analysis can be applied in multiple response optimization designs.

Optimization of the Bacillus thuringiensis var. kurstaki HD-1 δ-endotoxins production by using experimental mixture design and artificial neural networks

An experimental mixture design coupled with data analysis by means of both response surface methodology (RSM) and artificial neural networks (ANNs) followed by multiple response optimization through a desirability function, was applied to the production of δ-endotoxins from Bacillus thuringiensis var. kurstaki. The composition of a culture medium was defined by testing three regional effluents: milky effluent, beer wastewater and sugar cane molasses. Both RSM and ANNs accomplished the goal pursued in this work, by predicting the optimal mixture of the effluents. ANNs provided more reliable results due to the complexity of the models to be fitted. The optimal selected blend was: 74%, 26% and 0%, respectively for each the above-mentioned effluents.

Evaluation of Optimal Parametric Combination in Submerged Arc Double Pass Butt Welding

In the present paper, application of Taguchi method with grey relational analysis has been highlighted for solving multiple response optimization problem in submerged arc welding (SAW). A grey relational grade evaluated from the grey relational analysis has been adopted to reveal an optimal parameter combination in order to obtain acceptable features of weld quality characteristics in submerged arc butt welding.

Optimization in Multiple Response Model with Modified Desirability Function

The desirability function approach to multiple response optimization is a useful technique for the analysis of experiments in which several responses are optimized simultaneously. But the existing methods have some defects, and have to be modified to some extent. This paper proposes a new method to combine the individual desirabilities.

Multiple response optimization using Taguchi methodology and neuro‐fuzzy based model

PurposeTo provide a good insight into solving a multi‐response optimization problem using neuro‐fuzzy model and Taguchi method of experimental design.Design/methodology/approachOver the last few years in many manufacturing organizations, multiple response optimization problems were resolved using the past experience and engineering judgment, which leads to increase in uncertainty during the decision‐making process. In this paper, a four‐step procedure is proposed to resolve the parameter design problem involving multiple responses. This approach employs the advantage of both artificial intelligence tool (neuro‐fuzzy model) and Taguchi method of experimental design to tackle problems involving multiple responses optimization.FindingsThe proposed methodology is validated by revisiting a case study to optimize the three responses for a double‐sided surface mount technology of an electronic assembly. Multiple signal‐to‐noise ratios are mapped into a single performance statistic through neuro‐fuzzy based model, to identify the optimal level settings for each parameter. Analysis of variance is finally performed to identify parameters significant to the process.Research limitations/implicationsThe proposed model will be validated in future by conducting a real life case study, where multiple responses need to be optimized simultaneously.Practical implicationsIt is believed that the proposed procedure in this study can resolve a complex parameter design problem with multiple responses. It can be applied to those areas where there are large data sets and a number of responses are to be optimized simultaneously. In addition, the proposed procedure is relatively simple and can be implemented easily by using ready‐made neural and statistical software like Neuro Work II professional and Minitab.Originality/valueThis study adds to the literature of multi‐optimization problem, where a combination of the neuro‐fuzzy model and Taguchi method is utilized hand‐in‐hand.

Crossed mixture design and multiple response analysis for developing complex culture media used in recombinant protein production

A crossed mixture design coupled with data analysis by means of response surface methodology (RSM) and multiple response optimization through a Desirability function ( D) was applied for the first time to the area of development and optimization of culture media for the production of recombinant proteins in mammalian cells. A mixture of three hexoses (H1, H2 and H3) was evaluated combined with a mixture of three energy-provider compounds (E1, E2 and E3) to determine the optimal proportion of these components in the culture medium. Response surfaces were generated according to two different analyses of empirical data. In the first approach, a model (linear, quadratic or special cubic) dependent on hexose composition was fitted for each response, at each different energy provider mixture. Alternatively, the second approach fitted a quadratic × quadratic product model for every response. In the first analysis, the best empirically tested combination of the E compounds was selected, and the optimal proportions of the hexoses were predicted at this point. On the other hand, following the product model analysis allowed the prediction of the optimal blend of all six components being studied. The high values obtained for function D (0.59, 0.61 and 0.62) are very significant since this function was demanded to satisfy five simultaneous requirements. The predicted mixtures of compounds are expected to maximize cell growth, specific productivity and biological activity of the produced molecule, while minimizing the accumulation of potentially inhibitory by-products.

Multiple response optimisation based on desirability functions of a microwave-assisted extraction method for the simultaneous determination of chloroanisoles and chlorophenols in oak barrel sawdust

A microwave-assisted extraction (MAE) method was optimised for extracting 2,4,6-trichloroanisole (TCA), 2,3,4,6-tetrachloroanisole (TeCA), pentachloroanisole (PCA), 2,4,6-trichlorophenol (TCP), 2,3,4,6-tetrachlorophenol (TeCP) and pentachlorophenol (PCP) from oak barrels. The method was optimised by using a central composite experimental design with extraction time, temperature and solvent volume as influential parameters. A desirability function was then employed in addition to the simultaneous optimisation of the compounds. The optimal conditions identified were temperature 130 °C, solvent volume 35 mL and extraction time 50 min. The compounds were determined by gas chromatography with electron-capture detection. MAE was compared with conventional Soxhlet extraction; the results obtained with MAE were in good agreement with those obtained by Soxhlet extraction.

Optimization of multiple responses considering both location and dispersion effects

An integrated modeling approach to simultaneously optimizing both the location and dispersion effects of multiple responses is proposed. The proposed approach aims to identify the setting of input variables to maximize the overall minimal satisfaction level with respect to both location and dispersion of all the responses. The proposed approach overcomes the common limitation of the existing multiresponse approaches, which typically ignore the dispersion effect of the responses. Several possible variations of the proposed model are also discussed. Properties of the proposed approach are revealed via examples.

Simultaneous optimization of multi-response problems in the Taguchi method using genetic algorithm

The optimization of multiple responses (or performance characteristics) has received increasing attention over the last few years in many manufacturing organizations. Most previous applications of the Taguchi method only emphasize the single-response problems, while the multi-response problems have received relatively little attention. Many Taguchi practitioners have employed past experience and engineering knowledge or judgement when dealing with multiple responses. The approach presented in this paper takes advantage of both the Taguchi method and genetic algorithm, which forms a robust and practical methodology in tackling multiple response optimization problems. The paper also presents a case study to illustrate the potential of this powerful integrated approach for tackling multiple response optimization problems. The variance analysis is also an integral part of the study, which identifies the most critical and statistically significant parameters.

Use of grey relational analysis to assess and optimize small biomass boilers

This paper presents a new methodology for the evaluation of the environmental and economic feasibility of combustion of different biomass fuels in small boilers. The study focuses on pellets as the basic co-firing product and forest residues as the complementary product. Although the co-firing of forest residues can be economically profin, it is difficult to evaluate the general economic advantages due to the worsening of combustion in terms of performance and emissions caused by the presence of the forest residues in the fuel mixture. The grey relational analysis of different energetic and emission variables and also residue prices allows for the definition of a new single variable called the grey relational grade. Thus, evaluation and optimization of complicated multiple responses can be converted into the optimization of a standardised single variable. Experimental analyses by means of the Grey theory of different forest residues have revealed the possibility of co-firing crust of pine combined with wood pellets as a way of reducing fuel costs, keeping performance and emissions within average standards in small pellet boilers.

Multiple response optimization applied to the development of a capillary electrophoretic method for pharmaceutical analysis

Multiple response simultaneous optimization by using the desirability function was used for the development of a capillary electrophoresis method for the simultaneous determination of four active ingredients in pharmaceutical preparations: vitamins B 6 and B 12, dexamethasone and lidocaine hydrochloride. Five responses were simultaneously optimized: the three resolutions, the analysis time and the capillary current. This latter response was taken into account in order to improve the quality of the separations. The separation was carried out by using capillary zone electrophoresis (CZE) with a silica capillary and UV detection (240 nm). The optimum conditions were: 57.0 mmol l −1 sodium phosphate buffer solution, pH 7.0 and voltage = 17.2 kV. Good results concerning precision (CV lower than 2%), accuracy (recoveries ranged between 98.5 and 102.6%) and selectivity were obtained in the concentration range studied for the four compounds. These results are comparable to those provided by the reference high performance liquid chromatography (HPLC) technique.

The MM-Estimator in Response Surface Methodology

In this article, a robust regression technique called MM-estimator is proposed to model the responses in response surface methodology (RSM). Model fitting based on the MM-estimator allows practitioners to find a better optimal setting in dual-response surface optimization and multiple-response optimization when the responses are considerably nonnormal and/or contain some outliers. The MM-estimator is one of the robust regression techniques that can dampen the effect of the outliers. An example from the Roman catapult experiment is used to illustrate our proposal.

A New Approach for Multiple-Response Optimization

The desirability of a response that increases in a linear manner from the lower specification limit to the target value and decreases in a linear manner from the target value to the upper specification limit results in a breakpoint (nondifferentiable point) at the target value of its desirability function. Thus, modified desirability functions were proposed to solve this breakpoint problem so that the generalized reduced gradient can be applied. The modified desirability functions require the fitting of a quartic polynomial in the vicinity of the target. However, the fitting of the quartic polynomial needs to satisfy five conditions and involves numerous computations. Therefore, an approach with less computations and yet that is simple to implement is proposed in this article. This approach is applicable when the lower specification limit, the target value, and the upper specification limit of a response are available. In addition, this approach also allows practitioners to assign different degrees of importance to the responses. An example from the original paper of modified desirability functions is used to illustrate this approach.

Index C*pm in Multiple Response Optimization

The index used in process capability is proposed as an optimization criterion in this article. This index can be viewed as an extension of mean squared error (MSE). Thus, the index allows practitioners to find an optimal setting with the mean responses close to their respective target values, T i , while the standard deviations (or variance) of the responses are kept small. The index as an optimization criterion is applicable when upper specification limits, target values, and lower specification limits of mean responses are available. However, it also can be applied to mean responses with only target values and lower specification limits (or upper specification limits) in specific situations. An example will be used to illustrate this proposal.