1. Sharifzadeh etal (1989) considered a manufacturing process modeled as y =f
2. (x) +3. Response surfaces that are only based on gradients have also been used. Ho etal (1991) proposed a so-called Gradient SurfaceMethodology and used it for unconstrained optimization. \\tithin the optimization process, linear approximations are built for the gradients of a response function, i.e. approximations to the function itself are not considered. The approximations aredetermined using a standard least squares fit in terms of the gradients.
4. Toropov and co-workers (Malkov and Toropov, 1991; Toropov et al. 1993) used multi-point approximations in their optimization technique. The approximations are constructed for every cycle of the optimization process. In each cycle of the optimization a number of new function evaluations is carried out. The corresponding design variables can be viewed as a plan of experiments in the actual search sub-domain, with its dimensions and location controlled by amove-limit strategy. The approximation functions are fitted with function valuesand derivatives, if available, using a weighted least squares technique. In contrast to standard weighted least squares formulations, weights reflect the relative importance of data to the optimization process. Asanexample1points which are close to the boundary between feasible and infeasible design space get more weight as compared to points that lead to severe constraint violation. In this way it is attempted to achieve the best RSapproximations at those places of the sub-domain where the response function is most influential to the outcome of the optimization procedure. H design sensitivities are available, then this information is included in the RS construction. Normalization of the design sensitivities is done by means of the norm of the gradient. The relative influence of design sensitivities is controlled by a user-defined non-dimensional parameter. In this optimization strategy, designsensitivities are included to improveoverallefficiency. There are twoaspects that may improveefficiency. Firstly, more accurate and complex approximations might be built if sensitivities are available. Secondly, if design sensitivities may be evaluated cheaply, then the number ofdesignevaluations can be reduced as additional data is provided in terms of design sensitivities.