Application of finite sampling points in probability based multi: Objective optimization by means of the uniform experimental design

Abstract

Introduction/purpose: An approximation for assessing a definite integral is continuously an attractive topic owing to its practical needs in scientific and engineering areas. An efficient approach for preliminarily calculating a definite integral with a small number of sampling points was newly developed to get an approximate value for a numerical integral with a complicated integrand. In the present paper, an efficient approach with a small number of sampling points is combined to the novel probability-based multi-objective optimization (PMOO) by means of uniform experimental design so as to simplify the complicated definite integral in the PMOO preliminarily. Methods: The distribution of sampling points within its single peak domain is deterministic and uniform, which follows the rules of the uniform design method and good lattice points; the total preferable probability is the unique and deterministic index in the PMOO. Results: The applications of the efficient approach with finite sampling points in solving typical problems of PMOO indicate its rationality and convenience in the operation. Conclusion: The efficient approach with finite sampling points for assessing a definite integral is successfully combined with PMOO by means of the uniform design method and good lattice points.