Since response variables are different in some properties such as scale, measurement unit, type of optimality and their preferences, there are different approaches in model building and optimization of MRS problems. Moreover, optimizing the response surfaces considering dispersion effect variance of responses as objective function will increase reliability and robustness.
In this study, robust design and multiresponse optimization have been analyzed by MADM methods. Some earlier works in multiresponse optimization: Derringer and Suich applied a desirability function to optimize multi-response problems in a static experiment. Castillo et al. Layne presented a procedure that simultaneously considers three functions, the weighted loss function, the desirability function and a distance function, to determine the optimum parameter combination.
Khuri and Conlon proposed a procedure based on a polynomial regression model to simultaneously optimize several responses. Logothetis and Haigh also optimized a five response process by utilizing the multiple regression technique and the linear programming approach. Pignatiello utilized a variance component and a squared deviation-from-target to form an expected loss function to optimize a multiple response problem. This method is difficult to implement. The first reason is that a cost matrix must be initially obtained and the second reason is that it needs more experimental data.
Chapman proposed a co-optimization approach, which uses a composite response. Leon presented a method, which is based on the notions of a standardized loss function with specification limits, to optimize a multiresponse problem. However, only the nominal-the best NTB characteristic is suitable for this approach, which may limit the capability of this approach. Ames et al. The basic strategy is to describe the response surfaces with experimentally derived polynomials, which can be combined into a single loss function by using known or desired targets.
Next, minimizing the loss function with respect to process inputs locates the best operating conditions. Lai and Chang proposed a fuzzy multi-response optimization procedure to search for an appropriate combination of process parameter settings. A strategy of optimizing the most possible response values and minimizing the deviation from the most possible values is used when it considers not only the most possible value, but also the imprecision of the predicted responses.
Hsieh used neural network s to estimate relation between control variables and responses. Tong et al. Su and Tong also proposed a principle component analysis approach to perform the optimization of the multi-response problem. Initially, the quality loss of each response is standardized; principle component analysis is then applied to transform the primary quality responses into fewer quality responses. Finally, the optimum parameter combination can be obtained by maximizing the summation standardized quality loss.
Kezemzadeh proposed a general framework for multiresponse optimization problems based on goal programming. Their study proposes a general framework in MRS problems according to some existing study and some types of related decision makers and attempts to aggregate all of characteristics in one approach. Amiri et al. Their proposed method was combination of simulation approach, fuzzy goal programming and genetic algorithm.
In viewpoint of multiple objective decision making, Bashiri et al. RSM: Response Surface Methodology RSM is a collection of statistical and mathematical techniques useful for developing, improving and optimizing processes. RSM also has the ability to produce an approximate function using a smaller amount of data Yeh, However, most previous applications based on RSM have only dealt with a single-response problem and multi-response problems have received only limited attention.
Chang SI Some properties of multi-response D-optimal designs. We have strict control of our inventory, thus if a book is listed on the internet, it is available, with very, very few exceptions. View Toothacker, L. On the Lengths of the Confidence Intervals 5. The result is a design with high D-efficiency, given the constraints. Logothetis, N.
Studies have shown that the optimal factor settings for one performance characteristic are not necessarily compatible with those of other performance characteristics. In more general situations we might consider finding compromising conditions on the input variables that are somewhat favorable to all responses Koksoy, More details on RSM, related designs and optimization of response surfaces are given by Kleijnen , , Myers and Montgomery Three steps in these problems are:.
Dual Response Surface DRS is one of MRS problems in which the mean and variance of a special quality characteristic is estimated by a polynomial surface and in the optimization stage, both variance and mean are optimized simultaneously. The characteristics of MRS problems which it is necessary to attend to the model building and optimization stages are: different importance of responses, different measuring units, different scales and magnitude, different types of optimality, different direction, different preferences of responses and also different types of decision makers Kazemzadeh, MRO problems have been studied in several areas at different aspects.
We can categorize all viewpoints in the literature into three general categories:. Desirability viewpoints: In this category, researchers try aggregate information of each responses and get one response. Then optimization is performed on single objective called desirability function. Priority based a. Most popular methods in this group are: utility function method, global criterion method, bounded objective function method and lexicographic method that generate a set of Pareto optimal solution.
Loss function: In this category, based on loss function represented by Taguchi all responses value are aggregated and convert to single one. There were wide range of researches, have been studied to develop and generalize taguchi loss function with respect to special trait of its cases. Overview of MADM methods: Multiple attribute decision making methods are developed for selecting, ranking or rating or sometimes categorizing several alternative according to have several attribute which be maximized, minimized or reach a goal.
Application of these methods helps us to product one score from several responses representing aggregate score of each experiment. Summary of each algorithms are shown below:. Furthermore, the thresholds of preference p , indifference q and veto v have been introduced, so that relations are not expressed mistakenly due to differences that are less important.
If it is assumed that the objective functions of all criteria should be maximized, the concordance matrix is defined with the elements:. The discordance matrix can be calculated as long as the veto threshold v j has been defined; then credibility matrix is built from concordance and discordance matrixes. The determination of the hierarchy rank is achieved by calculating the superiority ratio for each alternative. The numerator represents the total dominance of the specific alternative over the rest and the denominator the dominance of the remaining alternatives over the former.
Therefore this fraction is the score of each alternative which be maximized Papadopoulos and Karagiannidis, The basic principle is that the chosen alternative should have the shortest distance from the ideal solution and the farthest distance from the negative-ideal solution. It determines the compromise ranking-list, the compromise solution and the weight stability intervals for preference stability of the compromise solution obtained with the initial given weights.
This method focuses on ranking and selecting from a set of alternatives in the presence of conflicting criteria. It introduces the multicriteria ranking index based on the particular measure of closeness to the ideal solution. Assuming that each alternative is evaluated according to each criterion function, the compromise ranking could be performed by comparing the measure of closeness to the ideal alternative. The multicriteria measure for compromise ranking is developed from the L p -metric used as an aggregating function in a compromise programming method. In single response surface, regression model is built from relation between controllable variables and response values but in multiresponse surface, regression model must be fitted for each response individually.
In most methods such as desirability function and weighted sum combination of several response applied to find single response. The aim of this study is to use scores of MADM methods as one response instead of several responses achieved from experiments. Advertisement Hide. A hierarchical method for evaluating products with quantitative and sensory characteristics.
This process is experimental and the keywords may be updated as the learning algorithm improves. This is a preview of subscription content, log in to check access. Beebe-Center, J. Journal of Psychology , 39 , — Google Scholar. Biles, W.
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Journal of Experimental Psychology , 42 , — Harrington, Jr. Industrial Quality Control , 21 10 , 94— Jacobs, B. Kaufmann, E. American Journal of Psychology , 62 , — The optimal output of any process can be achieved through simultaneous optimization of multiple responses. In this study, multiple responses were optimized using the desirability function as proposed by Harrington in 30 and modified by Derringer and Suich in It is a statistical procedure that can be used in any second order response surface designs like BBD, in which multiple goals can be set simultaneously and the desirable product quality can be ensured.
Desirability is an objective function which converts each individual response into a single desirability function ranging from 0 to 1. A value of zero for desirability function indicates the least desired hatching output and a value of one represents the most desired hatching output. The most desired hatching output in this study was measured in terms of maximum hatching percentage and minimum hatching time. As a first step, individual desirability function for hatching percentage and hatching time was calculated and a simultaneous objective function, a function which combines the individual desirability function was calculated by finding geometric mean of all individual desirability functions.
The formula used for desirability D is as follows:. To achieve the goal of maximising hatching percentage and minimizing hatching time the desirability function was modified by differential weighting in the function to provide added emphasis to target variables i.
In present study nil value is given for the input variables and value one is given for responses Weights range from a minimum of zero to a maximum of ten. With a weight of one, desirability function varies linearly. Any value below one gives less importance to that particular goal during calculation of the multiple desirability function while weights above one adds more importance to that goal.
The desirability function was calculated based on the settings given in Table 2. This setting ensured economical operation of the hatching process.
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Manuscript revision and experimental setup was done by B. Correspondence to Neelam Saharan. This work is licensed under a Creative Commons Attribution 4. Aquaculture Land By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate. Article metrics. Advanced search. Skip to main content. Subjects Ichthyology Marine biology Statistical methods.
Introduction Aquaculture experiments often adopt a unifactorial approach i.