Author(s)

SANTIAGO HERNÁNDEZ, FÉLIX NIETO

Abstract

Multi-objective optimization is a formulation of engineering design that considers several properties of the prototype to be optimized where there is conflict amongst them. Namely, increasing the quality of one produces worsening in others. This is why a surface coined Pareto front is created, composed of Pareto points that are trade-off values of the objective functions. Multi-objective optimization algorithms usually transform the initial formulation in a single objective optimization with an objective function that is a combination of the complete set. Each process produces a Pareto point, thus reducing the number of single optimizations and increasing the information on the Pareto points are very important metrics for an algorithm. Two techniques with that aim are presented. One associated with the description of the unconstrained and constrained Pareto points and how they shape the Pareto front. The other describes a new type of sensitivity analysis at the Pareto points, namely the sensitivity between objective functions, the sensitivity analysis of the design variables in relation to the objective functions. Two application examples are presented, namely portal frames with two objective functions (volume of material and flexibility) subject to stress constraints. One has the Pareto front composed of unconstrained Pareto points while the other is almost entirely composed of constrained Pareto points.

Keywords

multi-objective optimization, Pareto front, sensitivity analysis, structural design, constrained and unconstrained Pareto points