A Hybrid k-Means Cuckoo Search Algorithm Applied to the Counterfort Retaining Walls Problem

Abstract

The counterfort retaining wall is one of the most frequent structures used in civil engineering. In this structure, optimization of cost and CO2 emissions are important. The first is relevant in the competitiveness and efficiency of the company, the second in environmental impact. From the point of view of computational complexity, the problem is challenging due to the large number of possible combinations in the solution space. In this article, a k-means cuckoo search hybrid algorithm is proposed where the cuckoo search metaheuristic is used as an optimization mechanism in continuous spaces and the unsupervised k-means learning technique to discretize the solutions. A random operator is designed to determine the contribution of the k-means operator in the optimization process. The best values, the averages, and the interquartile ranges of the obtained distributions are compared. The hybrid algorithm was later compared to a version of harmony search that also solved the problem. The results show that the k-mean operator contributes significantly to the quality of the solutions and that our algorithm is highly competitive, surpassing the results obtained by harmony search.

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

“…This hybrid algorithm was used to obtain a sustainable design buttressed walls. Recently, the db-scan binarization algorithm obtained versions of continuous metaheuristics that have been used to solve the set covering problem [6] and the multidimensional knapsack problem [10] which are NP-hard problems.…”

“…In practical structural optimization problems, the variables used must be discrete, so they are combinatorial optimization problems. However, combinatorial problems are found in a large number of real problems such as allocation resources [3,4], logistics [5], transport [6], routing problems [7,8], scheduling problems [6,9], and engineering design projects [10,11], among others. These problems present a space of solutions that grows exponentially with the variables used, so the metaheuristics, which were inspired by natural phenomena for continuous spaces, are a good approach to obtain optimum solutions to engineering problems.…”

“…In particular, a hybrid multistart optimization strategic method based on a variable neighborhood search threshold acceptance strategy [16] was used to reduce the cost and carbon-emissions in cantilever retaining walls. A hybrid harmony search together with a threshold acceptance strategy [17,18], the black hole algorithm [17] and a hybrid k-means cuckoo search algorithms [10] were applied to minimize both the economic cost and the CO 2 emissions in counterfort retaining walls. A CO 2 and cost analysis in precast-prestressed concrete road bridges was developed in [15].…”

“…The db-scan is very effective in binary combinatorial problems [6,10]. PSO is often used to solve continuous optimization problems and its tuning is very simple.…”

An Analysis of a KNN Perturbation Operator: An Application to the Binarization of Continuous Metaheuristics

“…In the case of the offline parameters, the following ML methodologies can be used: unsupervised learning, supervised learning, and surrogate-based optimization. For the case of sustainable wall design, the k-means unsupervised learning technique was used in [34] to allow algorithms that work naturally in continuous spaces to solve a combinatorial wall design problem. In the allocation of resources, the db-scan technique was used in [35], to solve the multidimensional knapsack problem.…”