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Open AccessArticle

Black Hole Algorithm for Sustainable Design of Counterfort Retaining Walls

by Víctor Yepes 1,*,†, José V. Martí 1,† and José García 2,†
Institute of Concrete Science and Technology (ICITECH), Universitat Politècnica de València, 46022 València, Spain
Pontificia Universidad Católica de Valparaíso, 2362807 Valparaíso, Chile
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Sustainability 2020, 12(7), 2767;
Received: 25 February 2020 / Revised: 24 March 2020 / Accepted: 27 March 2020 / Published: 1 April 2020
(This article belongs to the Special Issue Sustainable Construction II)
The optimization of the cost and CO 2 emissions in earth-retaining walls is of relevance, since these structures are often used in civil engineering. The optimization of costs is essential for the competitiveness of the construction company, and the optimization of emissions is relevant in the environmental impact of construction. To address the optimization, black hole metaheuristics were used, along with a discretization mechanism based on min–max normalization. The stability of the algorithm was evaluated with respect to the solutions obtained; the steel and concrete values obtained in both optimizations were analyzed. Additionally, the geometric variables of the structure were compared. Finally, the results obtained were compared with another algorithm that solved the problem. The results show that there is a trade-off between the use of steel and concrete. The solutions that minimize CO 2 emissions prefer the use of concrete instead of those that optimize the cost. On the other hand, when comparing the geometric variables, it is seen that most remain similar in both optimizations except for the distance between buttresses. When comparing with another algorithm, the results show a good performance in optimization using the black hole algorithm. View Full-Text
Keywords: CO2 emission; earth-retaining walls; optimization; black hole; min–max discretization CO2 emission; earth-retaining walls; optimization; black hole; min–max discretization
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Yepes, V.; Martí, J.V.; García, J. Black Hole Algorithm for Sustainable Design of Counterfort Retaining Walls. Sustainability 2020, 12, 2767.

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