ANN-based Lagrange optimization for RC circular columns having multiobjective functions

Abstract

Structural engineers must encounter multiobjective optimization (MOO) problems in designs including a design of reinforced concrete (RC) columns, where several design objectives must be satisfied to meet contractors’ interests and produce a sustainable design. MOO applications in structural engineering practice are uncommon despite their high demand. Multiobjective population methods have been mainly investigated. However, previous studies have mostly neglected the stopping criteria and convergence of these algorithms. This study proposes a novel gradient-based algorithm – ANN-based Lagrange optimization and its implementation in designs of circular reinforced concrete columns where three objectives, such as cost, CO2 emissions, and column weight, are minimized simultaneously. This study integrates each single-objective function extracted from an artificial neural network (ANN) into a global Lagrange function, a unified function of objectives (UFO), using the trade-off fractions. The Lagrange multiplier method is adopted to deal with constrained conditions by using Newton–Raphson iteration to solve Karush-Kuhn-Tucker (KKT) conditions. The proposed algorithm brought in a set of optimal results capturing multiple objectives, known as a Pareto frontier, which are compared with those obtained using the Nondominated Sorting Genetic Algorithm – II (NSGA-II), showing that two algorithms calibrated to each other. Overall, the ANN-based Lagrange optimization algorithm exhibited better convergence than NSGA-II.

Keywords

• gradient-based multiobjective optimization algorithm
• unified function of objectives
• weighted sum method
• lagrange multiplier method
• pareto frontier