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Open AccessArticle

The Buttressed Walls Problem: An Application of a Hybrid Clustering Particle Swarm Optimization Algorithm

by 1,†, 2,† and 2,*,†
1
Escuela de Ingeniería en Construcción, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, Chile
2
Institute of Concrete Science and Technology (ICITECH), Universitat Politècnica de València, 46022 València, Spain
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(6), 862; https://doi.org/10.3390/math8060862
Received: 12 May 2020 / Revised: 20 May 2020 / Accepted: 22 May 2020 / Published: 26 May 2020
(This article belongs to the Special Issue Optimization for Decision Making II)
The design of reinforced earth retaining walls is a combinatorial optimization problem of interest due to practical applications regarding the cost savings involved in the design and the optimization in the amount of CO 2 emissions generated in its construction. On the other hand, this problem presents important challenges in computational complexity since it involves 32 design variables; therefore we have in the order of 10 20 possible combinations. In this article, we propose a hybrid algorithm in which the particle swarm optimization method is integrated that solves optimization problems in continuous spaces with the db-scan clustering technique, with the aim of addressing the combinatorial problem of the design of reinforced earth retaining walls. This algorithm optimizes two objective functions: the carbon emissions embedded and the economic cost of reinforced concrete walls. To assess the contribution of the db-scan operator in the optimization process, a random operator was designed. The best solutions, the averages, and the interquartile ranges of the obtained distributions are compared. The db-scan algorithm was then compared with a hybrid version that uses k-means as the discretization method and with a discrete implementation of the harmony search algorithm. The results indicate that the db-scan operator significantly improves the quality of the solutions and that the proposed metaheuristic shows competitive results with respect to the harmony search algorithm. View Full-Text
Keywords: CO2 emission; earth-retaining walls; optimization; db-scan; particle swarm optimization CO2 emission; earth-retaining walls; optimization; db-scan; particle swarm optimization
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MDPI and ACS Style

García, J.; Martí, J.V.; Yepes, V. The Buttressed Walls Problem: An Application of a Hybrid Clustering Particle Swarm Optimization Algorithm. Mathematics 2020, 8, 862. https://doi.org/10.3390/math8060862

AMA Style

García J, Martí JV, Yepes V. The Buttressed Walls Problem: An Application of a Hybrid Clustering Particle Swarm Optimization Algorithm. Mathematics. 2020; 8(6):862. https://doi.org/10.3390/math8060862

Chicago/Turabian Style

García, José; Martí, José V.; Yepes, Víctor. 2020. "The Buttressed Walls Problem: An Application of a Hybrid Clustering Particle Swarm Optimization Algorithm" Mathematics 8, no. 6: 862. https://doi.org/10.3390/math8060862

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