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.

Keywords

• preferable probability
• multi–objective optimization
• finite sampling points
• simplifying evaluation
• uniform design method