A derivative-free level-set method for topology optimization

Guirguis, David; Mahmood, Mahmood A.

doi:10.1016/j.finel.2016.06.002

Cited by 32 publications

(20 citation statements)

References 42 publications

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“…Next, the details of GEF technique are seen in [8,18,19]. Later, a method for solving checkerboard pattern was presented by Guirguis and Aly [20]. They proposed that derivative-free level-set method for solving structural topology can solve the checkerboard problem.…”

Section: Topological Designs With Ground Element Filteringmentioning

confidence: 99%

Topology Optimisation Using MPBILs and Multi-Grid Ground Element

Sleesongsom

Bureerat

2018

Applied Sciences

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This paper aims to study the comparative performance of original multi-objective population-based incremental learning (MPBIL) and three improvements of MPBIL. The first improvement of original MPBIL is an opposite-based concept, whereas the second and third method enhance the performance of MPBIL using the multi and adaptive learning rate, respectively. Four classic multi-objective structural topology optimization problems are used for testing the performance. Furthermore, these topology optimization problems are improved by the method of multiple resolutions of ground elements, which is called a multi-grid approach (MG). Multi-objective design problems with MG design variables are then posed and tackled by the traditional MPBIL and its improved variants. The results show that using MPBIL with opposite-based concept and MG approach can outperform other MPBIL versions.

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Section: Topological Designs With Ground Element Filteringmentioning

confidence: 99%

Topology Optimisation Using MPBILs and Multi-Grid Ground Element

Sleesongsom

Bureerat

2018

Applied Sciences

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“…Furthermore, as a mathematical aspect, the gradient-based optimization could possibly fall into local optima, e.g. optimized results may differ due to the selection of starting point [18,19,20]. In contrast, the non-gradient approaches rely only on the calculation of the objective function and do not require gradient information.…”

Section: Introductionmentioning

confidence: 99%

“…The binary particle swarm algorithm in the work of Luh et al [19] imitates the social behavior of animals when they collaborate to search for food. Guirguis and Aly [20] combined level set method and pattern search algorithm to develop a derivative-free tool for topology optimization. Critically, the global search of non-gradient approaches does not guarantee a global optimum, as pointed out in some works [19,21].…”

Section: Introductionmentioning

confidence: 99%

“…Critically, the global search of non-gradient approaches does not guarantee a global optimum, as pointed out in some works [19,21]. Another drawback is the large number of function evaluation during the stochastic search, which quickly scales up corresponding to the problem size [20,21]. Therefore, both gradient-and non-gradient approaches have their own strengths and weaknesses.…”

Section: Introductionmentioning

confidence: 99%

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A Non-Gradient Approach for Three Dimensional Topology Optimization

Nguyen

Tran

2021

JST

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The present work is devoted to the extension of the non-gradient approach, namely Proportional Topology Optimization (PTO), for compliance minimization of three-dimensional (3D) structures. Two schemes of material interpolation within the framework of the solid isotropic material with penalization (SIMP), i.e. the power function and the logistic function are analyzed. Through a comparative study, the efficiency of the logistic-type interpolation scheme is highlighted. Since no sensitivity is involved in the approach, a density filter is applied instead of sensitivity filter to avoid checkerboard issue

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“…The primary bottleneck of EM-driven design closure is its high computational cost. Even local optimization (both gradient-based [14] and derivative-free [15]) typically involves dozens or hundreds of EM analyses. Whereas global search using population-based metaheuristics (evolutionary algorithms [16], particle swarm optimizers [17], differential evolution [18], harmony search [19]) or uncertainty quantification (statistical analysis [20], robust design [21]) require significantly larger amounts of objective function evaluations.…”

Section: Introductionmentioning

confidence: 99%

Expedited Design Closure of Antenna Input Characteristics by Trust Region Gradient Search and Principal Component Analysis

2020

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Optimization-based parameter tuning has become an inherent part of contemporary antenna design process. For the sake of reliability, it is typically conducted at the level of full-wave electromagnetic (EM) simulation models. This may incur considerable computational expenses depending on the cost of an individual EM analysis, the number of adjustable variables, the type of task (local, global, single-/ multi-objective optimization), and the constraints involved. For these reasons, utilization of conventional algorithms is often impractical. This paper proposes a novel gradient-based algorithm with numerical derivatives for expedited antenna optimization. The improvement of computational efficiency is obtained by employing a rank-one Broyden formula and restricting finite differentiation sensitivity updates to the principal directions of the Jacobian matrix, i.e., those corresponding to the most significant changes of the antenna responses. Comprehensive numerical validation carried out using three wideband antennas indicates that the presented methodology offers considerable savings of sixty percent with respect to the reference trust-region algorithm. At the same time, virtually no degradation of the design quality is observed. Furthermore, algorithm reliability is greatly improved (while offering comparable computational efficiency) over the recent state-of-the-art accelerated gradient-based procedures. INDEX TERMS Antenna design, design closure, gradient-based optimization, principal component analysis, electromagnetic (EM) simulation.

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A derivative-free level-set method for topology optimization

Cited by 32 publications

References 42 publications

Topology Optimisation Using MPBILs and Multi-Grid Ground Element

Topology Optimisation Using MPBILs and Multi-Grid Ground Element

A Non-Gradient Approach for Three Dimensional Topology Optimization

Expedited Design Closure of Antenna Input Characteristics by Trust Region Gradient Search and Principal Component Analysis

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