Multi-objective optimization by a new hybridized method: applications to random mechanical systems
Hafid Zidani, Emmanuel Pagnacco, Rubens Sampaio, Rachid Ellaia, Eduardo Souza de Cursi · Engineering Optimization · 2012
In this article two linear problems with random Gaussian loading are transformed into multi-objective optimization problems. The first problem is the design of a pillar geometry with respect to a compressive random load process. The second problem is the design of a truss structure with respect to a vertical random load process for several frequency bands. A new algorithm, motivated by the Pincus representation formula hybridized with the Nelder–Mead algorithm, is proposed to solve the two multi-objective optimization problems. To generate the Pareto curve, the normal boundary intersection method is used to produce a series of constrained single-objective optimizations. The second problem, depending on the frequency band of excitation, can have as Pareto curve a single point, a standard Pareto curve, or a discontinuous Pareto curve, a fact that has been reported here for the first time in the literature, to the best of the authors’ knowledge.