Chaotic Binarization Schemes for Solving Combinatorial Optimization Problems Using Continuous Metaheuristics
Chaotic maps are sources of randomness formed by a set of rules and chaotic variables. They have been incorporated into metaheuristics because they improve the balance of exploration and exploitation, and with this, they allow one to obtain better results. In the present work, chaotic maps are used...
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MDPI AG
2024-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/2/262 |
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| author | Felipe Cisternas-Caneo Broderick Crawford Ricardo Soto Giovanni Giachetti Álex Paz Alvaro Peña Fritz |
| author_facet | Felipe Cisternas-Caneo Broderick Crawford Ricardo Soto Giovanni Giachetti Álex Paz Alvaro Peña Fritz |
| author_sort | Felipe Cisternas-Caneo |
| collection | DOAJ |
| description | Chaotic maps are sources of randomness formed by a set of rules and chaotic variables. They have been incorporated into metaheuristics because they improve the balance of exploration and exploitation, and with this, they allow one to obtain better results. In the present work, chaotic maps are used to modify the behavior of the binarization rules that allow continuous metaheuristics to solve binary combinatorial optimization problems. In particular, seven different chaotic maps, three different binarization rules, and three continuous metaheuristics are used, which are the Sine Cosine Algorithm, Grey Wolf Optimizer, and Whale Optimization Algorithm. A classic combinatorial optimization problem is solved: the 0-1 Knapsack Problem. Experimental results indicate that chaotic maps have an impact on the binarization rule, leading to better results. Specifically, experiments incorporating the standard binarization rule and the complement binarization rule performed better than experiments incorporating the elitist binarization rule. The experiment with the best results was STD_TENT, which uses the standard binarization rule and the tent chaotic map. |
| first_indexed | 2024-03-08T10:42:47Z |
| format | Article |
| id | doaj.art-ea5809d780db41008aab2a9142b7a7a5 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-08T10:42:47Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-ea5809d780db41008aab2a9142b7a7a52024-01-26T17:32:25ZengMDPI AGMathematics2227-73902024-01-0112226210.3390/math12020262Chaotic Binarization Schemes for Solving Combinatorial Optimization Problems Using Continuous MetaheuristicsFelipe Cisternas-Caneo0Broderick Crawford1Ricardo Soto2Giovanni Giachetti3Álex Paz4Alvaro Peña Fritz5Escuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso 2362807, ChileEscuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso 2362807, ChileEscuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso 2362807, ChileFacultad de Ingeniería, Universidad Andres Bello, Antonio Varas 880, Providencia, Santiago 7591538, ChileEscuela de Ingeniería de Construcción y Transporte, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2147, Valparaíso 2362804, ChileEscuela de Ingeniería de Construcción y Transporte, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2147, Valparaíso 2362804, ChileChaotic maps are sources of randomness formed by a set of rules and chaotic variables. They have been incorporated into metaheuristics because they improve the balance of exploration and exploitation, and with this, they allow one to obtain better results. In the present work, chaotic maps are used to modify the behavior of the binarization rules that allow continuous metaheuristics to solve binary combinatorial optimization problems. In particular, seven different chaotic maps, three different binarization rules, and three continuous metaheuristics are used, which are the Sine Cosine Algorithm, Grey Wolf Optimizer, and Whale Optimization Algorithm. A classic combinatorial optimization problem is solved: the 0-1 Knapsack Problem. Experimental results indicate that chaotic maps have an impact on the binarization rule, leading to better results. Specifically, experiments incorporating the standard binarization rule and the complement binarization rule performed better than experiments incorporating the elitist binarization rule. The experiment with the best results was STD_TENT, which uses the standard binarization rule and the tent chaotic map.https://www.mdpi.com/2227-7390/12/2/262chaotic mapsbinarization schemesknapsack problemSine Cosine AlgorithmGrey Wolf OptimizerWhale Optimization Algorithm |
| spellingShingle | Felipe Cisternas-Caneo Broderick Crawford Ricardo Soto Giovanni Giachetti Álex Paz Alvaro Peña Fritz Chaotic Binarization Schemes for Solving Combinatorial Optimization Problems Using Continuous Metaheuristics Mathematics chaotic maps binarization schemes knapsack problem Sine Cosine Algorithm Grey Wolf Optimizer Whale Optimization Algorithm |
| title | Chaotic Binarization Schemes for Solving Combinatorial Optimization Problems Using Continuous Metaheuristics |
| title_full | Chaotic Binarization Schemes for Solving Combinatorial Optimization Problems Using Continuous Metaheuristics |
| title_fullStr | Chaotic Binarization Schemes for Solving Combinatorial Optimization Problems Using Continuous Metaheuristics |
| title_full_unstemmed | Chaotic Binarization Schemes for Solving Combinatorial Optimization Problems Using Continuous Metaheuristics |
| title_short | Chaotic Binarization Schemes for Solving Combinatorial Optimization Problems Using Continuous Metaheuristics |
| title_sort | chaotic binarization schemes for solving combinatorial optimization problems using continuous metaheuristics |
| topic | chaotic maps binarization schemes knapsack problem Sine Cosine Algorithm Grey Wolf Optimizer Whale Optimization Algorithm |
| url | https://www.mdpi.com/2227-7390/12/2/262 |
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