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.

中文翻译：

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支撑墙问题：混合聚类粒子群优化算法的应用

由于实际应用中加筋土挡土墙的设计是一个有意义的组合优化问题，涉及设计方面的成本节省和CO量的优化 ${}_2$ 施工中产生的废气。另一方面，该问题涉及32个设计变量，因此在计算复杂度方面提出了重要的挑战。因此我们的顺序是 ${10}^{20}$ 可能的组合。在本文中，我们提出了一种混合算法，其中集成了粒子群优化方法，使用db-scan聚类技术解决了连续空间中的优化问题，目的是解决加筋土挡土墙设计的组合问题。该算法优化了两个目标函数：埋入的碳排放量和钢筋混凝土墙的经济成本。为了评估优化过程中db-scan运算符的作用，设计了一个随机运算符。比较获得的分布的最佳解，平均值和四分位数范围。然后，将db-scan算法与使用k-means作为离散化方法的混合版本以及和声搜索算法的离散实现进行了比较。