Multiobjective reliability-based design optimization formulations solved combining NSGA-II and first order reliability method

Abstract

A. Uncertainties are inherent in realistic structural optimization problems. For example, geometric variables and material properties are uncertain parameters and have to be accounted to ensure safety and quality. A manner of considering uncertainties in structural design is using constraints written in terms of probability of failure or reliability index in the optimization problem. Usually structural optimization problems consider constraints as restrictions and optimize the cost or the weight of the structures. However, several types of problems can be formulated in the field of Optimization under Uncertainty. This paper presents a computer program to solve two type of problems: In the first one, a bi-objective problem is solved, where the probability of system failure has been added as the second objective to the original cost objective. The second problem consists in optimising simultaneously two more performances or objective functions subject to reliability constraints. This formulation is named Multiobjective Reliability Based Design Optimization (MO-RBDO). Reliability analysis is carried out using a gradient based First Order Reliability Method (FORM). This structural reliability assessment method has shown efficient. An analytical example and a classical ten bar truss illustrate the application of this algorithm.