Multi-objective optimization algorithm assisted by metamodels with applications in aerodynamics problems

Abstract

The optimization algorithms when used in real engineering problems involving high fidelity numeric simulations often require a large number of numerical assessments to achieve a good approximation of the optimal solution. The computational time needed to find this solution may be unfeasible in these problems. The metamodel assisted algorithms have been used to accelerate optimization problems using different strategies to find the optimum. For single objective problems, CORS (Constrained Optimization using Response Surfaces) was developed with basis on the iterative generation of distance constraints to explore and exploit the design space, such that convergence to a global optimum is mathematically guaranteed. In this paper, a multi-objective optimization strategy based on metamodel construction using radial basis functions, MO-CORS, is presented. It takes the advantage of the CORS strategy in multi-objective problems to perform the effective detection of the non-dominated set extreme points, for the subsequent filling of empty spaces between these extremes. Metamodels are used strategically in an iterative sampling process to guide the search for better solutions and to determine where in the domain the next objective function evaluations should be performed. The evaluations carried out on the expensive functions also allow improving metamodel construction in the promising regions at each iteration. Results obtained in test problems and in aerodynamic problems applications show that the developed algorithm is an effective tool to accelerate single and multi-objective optimization problems and that the use of the CORS strategy inside MO-CORS was relevant in helping it to attain solutions not found by other optimization algorithms.