Abstract
We present an improved Pareto Genetic Algorithm (PGA), which finds solutions to problems of robust design in multi-response systems with 4 responses and as many as 10 control and 5 noise factors. Because some response values might not have been obtained in the robust design experiment and are needed in the search process, the PGA uses Response Surface Methodology (RSM) to estimate them. Not only the PGA delivered solutions that adequately adjusted the response means to their target values, and with low variability, but also found more Pareto efficient solutions than a previous version of the PGA. This improvement makes it easier to find solutions that meet the trade-off among variance reduction, mean adjustment and economic considerations. Furthermore, RSM allows estimating outputs’ means and variances in highly non-linear systems, making the new PGA appropriate for such systems.
Highlights
Parameter Design (PD) is a two-stage method for executing robust design (RD) interventions, which tries to set controllable input factors of a production or service system, so that the system’s outputs stay as stable as possible
To find solutions that achieve both objectives of PD and to be able to assess the relative merit of setting different control factors to reduce variability and obtain mean adjustment, the use of a Pareto Genetic Algorithm (PGA) has been proposed (Canessa, Bielenberg & Allende, 2014)
The following subsections present some parts of the previous PGA (PGA1) and concepts related to Response Surface Methodology (RSM) necessary for understanding the changes made to PGA1
Summary
Parameter Design (PD) is a two-stage method for executing robust design (RD) interventions, which tries to set controllable input factors of a production or service system, so that the system’s outputs stay as stable as possible. The PGA delivers Pareto efficient solutions and it exposes the trade-off between reducing variability and getting mean adjustment Using such solutions, the engineer incorporates other considerations The PGA presented here will automatically calculate the RSM and use it in the estimation of missing values of responses This last point is important, given that to lower the cost of PD studies, generally, engineers use highly fractioned experimental designs (Maghsoodloo, Jordan & Huang, 2004; Roy, 2001; Taguchi, 1991). A good estimate of these values will in turn enhance the search capabilities of the PGA and allow the PGA to obtain a good approximation to the Pareto frontier
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