Surrogate modelling and computational experience with the optimisation problem

Surrogate modelling is becoming a necessary modelling tool in engineering analysis and synthesis. This is, especially, true when mathematical models are not available. The capability of response surface methodology is explored with single unconstrained/constrained linear and non-linear problems. Problems with special features or with highly non-linear nature are dealt with. A further development with multi-objective problems starts with bi-objective functions and continues to deal with higher number of objective functions. A simple multi-objective problem is taken to initiate the development. Orthogonal arrays and response surface models are combined and used to explore the sets of Pareto Frontiers. One important result is that various array sizes are able to explore the Pareto set at no or little cost change with comparable accuracy. Except for one array, the optimum solution is typical for all arrays employed. One development is using the first derivative of the two objective functions to obtain the starting point for model construction. Design of experiments and analysis of variance (ANOVA) are employed to verify the relative significance of variables. Results of ANOVA guide the modeller in the model building process. We attempt to achieve a 'local accurate model' rather than a 'global accurate model'. Computational experience with different classes of problems is given.