Multiple response optimization, non-dominated solutions, artificial neural networks, epsilon constraint, and genetic algorithm.
Simultaneous optimization of multiple response problems is an important problem in manufacturing cases. Polynomial regression is a common method for finding the relationship between controllable factors and responses. Some researchers have showed that artificial neural networks have better performance when the relationships are far too complex. In the multiple response problems, determination of non-dominated solutions is more valuable than finding only one solution as an optimum treatment, while this solution is one of the obtained non-dominated solutions. Unlike other existing research into using neural networks for multiple response problems, in the proposed method, responses are assumed as inputs, and controllable factors are assumed as targets of the neural network. This kind of input and target definition for neural networks helps us to determine non-dominated solutions by employing a neural network, an epsilon constraint technique and a genetic algorithm. The proposed method includes three major steps: 1) modeling the relation between responses and controllable factors by employing a neural network, 2) finding non-dominated solutions using an epsilon constraint and a genetic algorithm, 3) sieving solutions obtained from the last step and determining strong non-dominated solutions. For showing the efficiency of the proposed method, non-dominated solutions for a numerical example from the literature are determined by using the proposed approach. Comparing the results shows that obtained non-dominated solutions obtained by the proposed method for the example, are often better than other research results for the same example.
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