Multi-objective optimal design of submerged arches using extreme learning machine and evolutionary algorithms

The design of funicular (or momentless) submerged arches has a great application in the fields of the building construction and the civil engineering. Traditional approaches in this field have been based on the resolution of ordinary differential equations that govern the structural behavior of the submerged arches. Indeed, these approaches only consider a design parameter and they are computationally expensive. For intermediate depth ratios, the funicular shape of the arch lays about halfway between the geometric forms of the parabola and the ellipse. Actually, the arch centerline could be modeled as a parametric linear function of these two conical shapes where different parameters are established, opening new opportunities for the optimization in the design of such structures, which also consider several design parameters. In this article, we propose a methodology to optimize several parameters in the design of submerged arches. Specifically, we focus on the reduction of the arch bending moment, which is a critical factor in the design cost of the structure, and also the maximization of the airspace enclosed by the arch, which is of particular interest in the serviceability of recreational submerged installations. Our methodology is based on a multi-objective evolutionary algorithm, which uses artificial neural networks with extreme learning machine (ELM) to predict the level of bending stresses at the submerged arch under different shape configurations and also reduce the overall computational cost. Two groups of test examples, corresponding to deep and shallow waters, are developed to compare the numerical results obtained by multi-objective optimization with the theoretical curves predicted by the traditional funicular analysis. Our experimental results offer good accuracy (R2 up to 93%) in the fitness evaluation using ELM. After the multi-objective optimization procedure, our results show optimal arch-shapes with minimum bending stress (i.e., minimum cost) and maximum airspace; thus, the functionality of the underwater installation is also optimal.