ANN-based optimized design of doubly reinforced rectangular concrete beams based on multi-objective functions

Abstract

In the structural engineering field, multi-objective optimization is a difficult task as demands of objective functions in structural designs are sometimes conflicting, such as costs and structural weight. Some previous studies which are mainly based on metaheuristics have investigated multi-objective optimizations to deal with such conflicts. However, the optimized results obtained by the populations-based methods do not present the tradeoff ratios contributed by each objective function. This study provides a five-step multi-objective optimization that can be used by structural engineers and decision-makers who are not familiar with optimization algorithms. The unified function of objectives (UFO) is optimized to derive the Pareto frontier. Design requirements are imposed by equality and equality constraints. The multiple design variables are obtained using Newton-Raphson iterations which solves huge differential equations representing Jacobi equations of UFO. The five steps to optimize the design of a doubly reinforced concrete beam proposed in this study are based on an ANN-based Lagrange optimization algorithm developed in previous studies by the authors. Optimized designs are presented and verified, showing trade-off ratios of objective functions. An example of decision-making based on the UFO is presented, which engineers and decision-makers can use as a guide throughout a preliminary design stage.