A Db-Scan Binarization Algorithm Applied to Matrix Covering Problems

Abstract

The integration of machine learning techniques and metaheuristic algorithms is an area of interest due to the great potential for applications. In particular, using these hybrid techniques to solve combinatorial optimization problems (COPs) to improve the quality of the solutions and convergence times is of great interest in operations research. In this article, the db-scan unsupervised learning technique is explored with the goal of using it in the binarization process of continuous swarm intelligence metaheuristic algorithms. The contribution of the db-scan operator to the binarization process is analyzed systematically through the design of random operators. Additionally, the behavior of this algorithm is studied and compared with other binarization methods based on clusters and transfer functions (TFs). To verify the results, the well-known set covering problem is addressed, and a real-world problem is solved. The results show that the integration of the db-scan technique produces consistently better results in terms of computation time and quality of the solutions when compared with TFs and random operators. Furthermore, when it is compared with other clustering techniques, we see that it achieves significantly improved convergence times.

A db-Scan Hybrid Algorithm: An Application to the Multidimensional Knapsack Problem

“…To carry out the different experiments, the PSO and CS algorithms were used. They were chosen mainly because they are simple to parameterize, both have successfully solved a large number of optimization problems [2,5,[80][81][82], and there are simplified convergence models for CS [83] and PSO [56].…”

“…Specific integrations explore machine learning applications in some of these operators. In the design of binary versions of algorithms that work naturally in continuous spaces, we find binarization operators in [2]. These binary operators use unsupervised learning techniques to perform the binarization process.…”

“…Each of these decisions can be modeled as an optimization problem or, in many cases, a combinatorial optimization problem (COP). Examples of COPs are found in different areas: machine learning [1], transportation [2], facility layout design [3], logistics [4], scheduling problems [2,5], resource allocation [6,7], routing problems [8], robotics applications [9], image analysis [10], engineering design problems [11], fault diagnosis of machinery [12], and manufacturing problems [13], among others. If the problem is large, metaheuristics have been a good approximation to obtain adequate solutions.…”

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

“…Specific integrations explore the machine-learning application in some of these operators [26]. In the design of binary versions of algorithms that work naturally in continuous spaces, we find binarization operators in [2]. These binary operators use unsupervised learning techniques to perform the binarization process.…”

“…From the research point of view, these problems present interesting challenges in the areas of operations research, computational complexity, and algorithm theory. Examples of combinatorial problems are found in, scheduling problems [1,2], transport [2], machine learning [3], facility layout design [4], logistics [5], allocation resources [6,7], routing problems [8,9], robotics applications [10], civil engineering problem [11][12][13], engineering design problem [14], fault diagnosis of machinery [15], and social sustainability of infrastructure projects [16], among others. Combinatorial optimization algorithms should explore the solutions space to find optimal solutions.…”