A new second-order approximation method for optimum design of structures

Ahmadvand, Hosein; Habibi, Alireza

doi:10.1080/14488353.2020.1798039

Cited by 2 publications

(4 citation statements)

References 78 publications

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“…The proposed algorithm was validated using four engineering optimization problems: the welded beam design problem [64], tension/compression spring design problem [65], pressure vessel design problem, and three bar truss design problem. The proposed methods were implemented for 30 independent runs.…”

Section: Engineering Problemsmentioning

confidence: 99%

A Novel Hybrid Hunger Games Search Algorithm With Differential Evolution for Improving the Behaviors of Non-Cooperative Animals

Chen

et al. 2021

IEEE Access

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Inspired by the behaviors of animals in the state of starvation, hunger games search algorithm (HGS) is proposed. HGS has shown competitive performance among other meta-heuristic (MH) algorithms. However, HGS tends to stagnate in local optimal for some complex optimization problems and remains premature convergence. Therefore, to solve these problems and enhance the diversity of the population, a modified HGS based on the operators of the differential evolution algorithm (DE), chaotic local search (CLS) strategies, and evolutionary population dynamics technique (EPD) is proposed (named DECEHGS). The proposed DECEHGS algorithm consists of two stages: in the first stage, based on the animals' behaviors, we use different evolutionary methods to update animals' positions; in the second stage, the CLS strategy and EPD technique are combined to prevent premature convergence and stagnation in a local optimum. The proposed algorithm was evaluated using IEEE CEC2014 and IEEE CEC2017 mathematical functions and four engineering problems. The experimental results demonstrate that DECEHGS has competitive performance in global optimization tasks and engineering problems compared with state-ofthe-art algorithms.

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Section: Engineering Problemsmentioning

confidence: 99%

A Novel Hybrid Hunger Games Search Algorithm With Differential Evolution for Improving the Behaviors of Non-Cooperative Animals

Chen

et al. 2021

IEEE Access

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“…Based on this brief concerning sensitivity analysis, we can establish a convenient strategy to reduce the computational effort of a second-order study. The significant effort involving the adjoint method is related to the solution of Equations ( 7) and (10), whereas the direct method requires the solution of Equations ( 7) and (8). Thus, based on this comparative evaluation, even considering the diagonal particularization, the adjoint method is still preferable.…”

Section: ⏞⏞⏞ D𝜔 I Ds Lmentioning

confidence: 99%

“…Although desirable in second‐order algorithms, the Hessian information is in general difficult to handle; the mathematical complexity and the computational costs 7 hinder the practical usage of such methods in large models. Thus, many studies reported the use of Hessian approximations based on the calculation of the diagonal terms 8‐10 . Fleury 11 studied the trade‐off between computational cost and accuracy or convergence by using the diagonal terms in structural optimization.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, many studies reported the use of Hessian approximations based on the calculation of the diagonal terms. [8][9][10] Fleury 11 studied the trade-off between computational cost and accuracy or convergence by using the diagonal terms in structural optimization. Etman et al 12 developed a sequential convex programming algorithm based on diagonal quadratic subproblems.…”

Section: Introductionmentioning

confidence: 99%

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Second‐order design sensitivity analysis using diagonal hyper‐dual numbers

Endo

Fancello

Muñoz-Rojas

2021

Numerical Meth Engineering

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Although sensitivity analysis provides valuable information for structural optimization, it is often difficult to use the Hessian in large models since many methods still suffer from inaccuracy, inefficiency, or limitation issues. In this context, we report the theoretical description of a general sensitivity procedure that calculates the diagonal terms of the Hessian matrix by using a new variant of hyper‐dual numbers as derivative tool. We develop a diagonal variant of hyper‐dual numbers and their arithmetic to obtain the exact derivatives of tensor‐valued functions of a vector argument, which comprise the main contributions of this work. As this differentiation scheme represents a general black‐box tool, we supply the computer implementation of the hyper‐dual formulation in Fortran. By focusing on the diagonal terms, the proposed sensitivity scheme is significantly lighter in terms of computational costs, facilitating the application in engineering problems. As an additional strategy to improve efficiency, we highlight that we perform the derivative calculation at the element‐level. This work can contribute to many studies since the sensitivity scheme can adapt itself to numerous finite element formulations or problem settings. The proposed method promotes the usage of second‐order optimization algorithms, which may allow better convergence rates to solve intricate problems in engineering applications.

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A new second-order approximation method for optimum design of structures

Cited by 2 publications

References 78 publications

A Novel Hybrid Hunger Games Search Algorithm With Differential Evolution for Improving the Behaviors of Non-Cooperative Animals

A Novel Hybrid Hunger Games Search Algorithm With Differential Evolution for Improving the Behaviors of Non-Cooperative Animals

Second‐order design sensitivity analysis using diagonal hyper‐dual numbers

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