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Multiple response optimization (MRO) problems are usually solved in three phases that include experiment design, modeling, and optimization. Committee machine (CM) as a set of some experts such as some artificial neural networks (ANNs) is used for modeling phase. Also, the optimization phase is done with different optimization techniques such as genetic algorithm (GA). The current paper is a development of recent authors' work on application of CM in MRO problem solving. In the modeling phase, the CM weights are determined with GA in which its fitness function is minimizing the RMSE. Then, in the optimization phase, the GA specifies the final response with the object to maximize the global desirability. Due to the fact that GA has a stochastic nature, it usually finds the response points near to optimum. Therefore, the performance the algorithm for several times will yield different responses with different GD values. This study includes a committee machine with four different ANNs. The algorithm was implemented on five case studies and the results represent for selected cases, when number of performances is equal to five, increasing in maximum GD with respect to average value of GD will be eleven percent. Increasing repeat number from five to forty-five will raise the maximum GD by only about three percent more. Consequently, the economic run number of the algorithm is five.

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Many industrial problems need to be optimized several responses simultaneously. These problems are named multiple response optimization (MRO) and they can have different objectives such as Target, Minimization or Maximization. Committee machine (CM) as a set of some experts such as some artificial neural networks (ANNs) in combination with genetic algorithm (GA) is applied for modeling and optimization of MRO problems. In addition, optimization usually is done on Global Desirability (GD) function. Current article is a development for recent authors' work to determine economic run number for application of CM and GA in MRO problem solving. This study includes a committee machine with four different ANNs. The CM weights are determined with GA which its fitness function is minimizing the RMSE. Then, another GA specifies the final solution with object maximizing the global desirability. This algorithm was implemented on five case studies and the results represent the algorithm can get higher global desirability by repeating the runs and economic run number (ERN) depends on the MRO problem objective. ERN is ten for objective “Target”. This number for objectives which are mixture of minimization and maximization ERN is five. The repetition are continued until these ERN values have considerable increased in maximum GD with respect to average value of GD. More repetition from these ERN to forty five numbers cause a slight raise in maximum GD.

Submerged arc welding (SAW) is a well-known method to weld seam in manufacturing of large diameters steel pipes in oil and gas industry. The main subject of SAW design is selection of the optimum combination of input variables for achieving the desired output variables of weld. Input variables include voltage, amperage and speed of welding and output variables include residual stresses due to welding. On the other hand, main target in multi response optimization (MRO) problem is to find input variables values to achieve to desired output variables. Current study is a combination and modification of some works of authors in MRO and SAW subjects. This study utilizes an experiment design according to Taguchi arrays. Also a committee machine (CM) modeling the problem by CM using two approaches. The first CM consists eight experts with traditional approach in computation and second CM includes elite experts. Genetic algorithm was applied to find CM weights and desired responses. Results show that proposed approach in CM has a smaller root mean squire error (RMSE) than traditional approach. The validation of CM model is done by comparison of results with simulation of SAW process and residual stresses in a finite element environment. Finally, the results show few differences between the real case responses and the proposed algorithm responses.