Sequential sampling approach to energy‐based multi‐objective design optimization of steel frames with correlated random parameters

Abstract

This work presents a novel sequential sampling approach to the multi-objective reliability-based design optimization of moment-resisting steel frames subjected to earthquake excitation. The optimization problem is formulated with two objective functions, namely, the total mass and the energy dissipated by beam members of the frame, and subject to uncorrelated probabilistic constraints on dynamic responses under the effects of correlated random parameters of floor masses, external loads, and material properties. The dynamic responses for a small number of designs are found by nonlinear response history analysis and further approximated by Gaussian process (GP) models to mitigate the computational burden during the optimization process. Approximate solutions sorted among existing candidate solutions are updated after each optimization iteration using discrete random local and global searches. The GP models are also refined after each optimization iteration by specifying new sampling points that lie on the Pareto front of a bi-objective deterministic maximization problem formulated for the improvement in the current approximate solutions and the feasibility of the new sampling points. As demonstrated in a test problem, the new sampling points tend to distribute in the neighborhood of the exact solutions, thereby underpinning a quick termination as well as the robustness of the proposed method. Optimization results from the test problem and a design example show that good approximate solutions are always obtained as the solution quality converges.

Multiobjective Optimization Design of Green Building Energy Consumption Based on Inorganic Thermal Insulation Nanomaterials

“…Liu et al applied AANS to cost prediction and verified the feasibility of the model through multiple regression analysis [8]. Do and Ohsaki put forward a mixed integer optimization model to maximize the score of construction projects in LEED evaluation under the constraints of budget and design [9].…”

Proximal-exploration multi-objective Bayesian optimization for inverse identification of cyclic constitutive law of structural steels

“…The third step for improving Ω is to formulate a hypervolume-based acquisition function that intelligently guides MOBO (Do and Ohsaki, 2022b;Do et al, 2021). This formulation is natural because (1) the acquisition function, a key ingredient of BO, directs the algorithm toward better solutions by mapping our belief about an improvement in the current solutions to a measure of how promising each parameter vector in the parameter space is if it is specified in the next optimization iteration; and (2) the hypervolume (HV) measure is often used in the field of multi-objective design to assess the quality of different sets of solutions (Emmerich et al, 2006).…”

“…Maximizing the improvement of Ω, therefore, coincides with maximizing the difference of the HV defined by the union of f(x) and Ω, and that defined by Ω, where f(x) is evaluated at an arbitrary vector x in the parameter space. This difference is further represented by the following hypervolume improvement (HVI) indicator (Do and Ohsaki, 2022b;Do et al, 2021):…”

“…However, the calculation of the expected HVI using such an integral is not advantageous for quickly finding x s+1 (Roussel et al, 2021). Thus, we replaced HV(f(x) ∪ Ω, f R ) with HV(µ f (x) ∪ Ω, f R ) (Do and Ohsaki, 2022b;Do et al, 2021), leading to an expected measure of HVI as illustrated by the hatched area in Fig. 1(a), where µ f (x) is the Gaussian mean vector of the error functions at x given in Eqs.…”

“…Such an exploration is referred to as proximal exploration. It can also make the improvement of HV more stable than that observed when using only HVI to guide MOBO (Do and Ohsaki, 2022b). Moreover, although x = x 0 maximizes the exponential, we do not reselect x 0 because the HVI at x 0 equals zero.…”