# GHOST—Gate to Hybrid Optimization of Structural Topologies

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Problem

## 3. The Hybrid Algorithm

#### 3.1. Concept

#### 3.2. Performance

## 4. Generation of Optimal Topologies

## 5. The Engineering Example

## 6. Concluding Remarks

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The hybrid algorithm performance. Switching between the update rules depending on the current compliance values resulting from an application of both approaches.

**Figure 3.**The generation of an optimal topology using Algorithm (1). (

**a**) The final topology and (

**b**) the compliance history.

**Figure 4.**The generation of an optimal topology using Algorithm (2). (

**a**) The final topology and (

**b**) the compliance history.

**Figure 5.**The generation of an optimal topology using Algorithm (H). (

**a**) The final topology and (

**b**) the compliance history.

**Figure 6.**A comparison of the performance of the components Algorithms (1) and (2) running separately and the hybrid one: the iteration control (

**a**) and the time control (

**b**).

**Figure 7.**The hybrid algorithm performance. Switching between the update rules of Algorithms (1) and (2).

**Figure 8.**The overview of the topology generation process. The intermediate images for the selected iterations: 1 (

**a**), 10 (

**b**), 15 (

**c**), 20 (

**d**), 25 (

**e**) and 50 (

**f**).

**Figure 10.**The generation of minimal compliance topologies for test structure 1. (

**a**) The final topology using Algorithm (1). (

**b**) The final topology using Algorithm (2).

**Figure 11.**The performance of the hybrid algorithm applied to test structure 1. (

**a**) The final topology using hybrid Algorithm (H). (

**b**) A comparison of the performance of the component Algorithms (1) and (2) running separately and the hybrid one.

**Figure 12.**The overview of the topology generation process. The intermediate images for the selected iterations: 1 (

**a**), 4 (

**b**), 6 (

**c**), 8 (

**d**), 20 (

**e**) and 100 (

**f**).

**Figure 14.**The generation of minimal compliance topologies for test structure 2. (

**a**) The final topology using Algorithm (1). (

**b**) The final topology using Algorithm (2).

**Figure 15.**The performance of the hybrid algorithm applied to test structure 2. (

**a**) The final topology using hybrid Algorithm (H). (

**b**) A comparison of the performance of the component Algorithms (1) and (2) running separately and the hybrid one.

**Figure 16.**The overview of the topology generation process. The intermediate images for the selected iterations: 1 (

**a**), 4 (

**b**), 6 (

**c**), 8 (

**d**), 20 (

**e**) and 100 (

**f**).

**Figure 18.**The generation of minimal compliance topologies for test structure 3. (

**a**) The final topology using Algorithm (1). (

**b**) The final topology using Algorithm (2).

**Figure 19.**The performance of the hybrid algorithm applied to test structure 3. (

**a**) The final topology using hybrid Algorithm (H). (

**b**) A comparison of the performance of the component Algorithms (1) and (2) running separately and the hybrid one.

**Figure 20.**The overview of the topology generation process. The intermediate images for the selected iterations: 2 (

**a**), 4 (

**b**), 6 (

**c**), 8 (

**d**), 20 (

**e**) and 100 (

**f**), respectively.

**Figure 22.**The generation of minimal compliance topologies for test structure 4. (

**a**) The final topology using Algorithm (1). (

**b**) The final topology using Algorithm (2).

**Figure 23.**The performance of the hybrid algorithm applied to test structure 4. (

**a**) The final topology using hybrid Algorithm (H). (

**b**) A comparison of the performance of the component Algorithms (1) and (2) running separately and the hybrid one.

**Figure 24.**The overview of the topology generation process. The intermediate images for the selected iterations: 2 (

**a**), 4 (

**b**), 6 (

**c**), 8 (

**d**), 10 (

**e**) and 100 (

**f**).

**Figure 27.**The generation of minimal compliance topologies for the control arm structure. (

**a**) The final topology using Algorithm (1). (

**b**) The final topology using Algorithm (2).

**Figure 28.**The final topology using hybrid Algorithm (H) (

**a**). The hybrid algorithm performance: Switching between the update rules of Algorithms (1) and (2) (

**b**).

**Table 1.**A comparison of the results. The values of compliance (Nmm) obtained using the algorithms considered in the paper and select other ones are presented. The same number of iterations has been performed for all tests.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Bochenek, B.; Tajs-Zielińska, K.
GHOST—Gate to Hybrid Optimization of Structural Topologies. *Materials* **2019**, *12*, 1152.
https://doi.org/10.3390/ma12071152

**AMA Style**

Bochenek B, Tajs-Zielińska K.
GHOST—Gate to Hybrid Optimization of Structural Topologies. *Materials*. 2019; 12(7):1152.
https://doi.org/10.3390/ma12071152

**Chicago/Turabian Style**

Bochenek, Bogdan, and Katarzyna Tajs-Zielińska.
2019. "GHOST—Gate to Hybrid Optimization of Structural Topologies" *Materials* 12, no. 7: 1152.
https://doi.org/10.3390/ma12071152