Robust and multi-objective optimization applied in I-beam using non-dominated sorting genetic algorithm

Abstract

The I-Beam problem is a multi-objective optimization which originally consists of minimizing the cross-sectional area and the vertical deflection of the beam. When uncertainty is considered in the production of the beam, the I-beam problem becomes a robust optimization problem where the mean and variance of a sample around the neighborhood of a solution are taken as the objective functions. In this paper, we present robust optimization applied in I-beam using Nondominated Sorting Genetic Algorithm (NSGA). While the main objective of the optimization is to find the robust optimum cross-sectional area of the beam, we parameterize the NSGA for the optimization of other objective functions such as the beam deflection and bending stress.