The buttressed walls problem: An application of a hybrid clustering particle swarm optimization algorithm

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 CO₂ 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 10²⁰ 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.