A Data-Driven Dynamic Discretization Framework to Solve Combinatorial Problems Using Continuous Metaheuristics

Cisternas-Caneo, Felipe; Crawford, Broderick; Soto, Ricardo; Fuente‐Mella, Hanns de la; Tapia, Diego; Lemus-Romani, José; Castillo, Mauricio; Becerra-Rozas, Marcelo; Paredes, Fernando; Misra, Sanjay

doi:10.1007/978-3-030-73603-3_7

Cited by 8 publications

(9 citation statements)

References 18 publications

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“…While some MHs operate on binary domains without a binary scheme, studies have demonstrated that continuous MHs supported by a binary scheme perform exceptionally well on multiple NP-hard combinatorial problems [ 1 ]. Examples of such MHs include the binary bat algorithm [ 28 , 29 ], particle swarm optimization [ 30 ], binary sine cosine algorithm [ 2 , 31 , 32 , 33 ], binary salp swarm algorithm [ 34 , 35 ], binary grey wolf optimizer [ 32 , 36 , 37 ], binary dragonfly algorithm [ 38 , 39 ], the binary whale optimization algorithm [ 2 , 32 , 40 ], and the binary magnetic optimization algorithm [ 41 ].…”

Section: Related Workmentioning

confidence: 99%

“…In the literature, various related works have proposed the hybridization of the sine cosine algorithm, grey wolf optimizer, whale optimization algorithm, and Q-learning [ 2 , 31 , 36 , 40 ]. Q-learning was used as a dynamic binarization scheme selector in each of the metaheuristics, allowing them to solve binary combinatorial problems.…”

Section: Related Workmentioning

confidence: 99%

“…As can be seen in Section 2.3 , metaheuristics perform the search process alternating between intensification (exploration) and diversification (exploitation). Previous proposals [ 2 , 31 , 40 , 60 , 61 ] used these phases as the states to use in Q-learning. In these papers, the authors determined the stage of the search process by calculating the population diversity.…”

Section: Related Workmentioning

confidence: 99%

“…Secondly, another five sets with 18 actions will be formed, where the S-shaped, V-shaped, X-shaped, and Z-shaped families will be used as transfer functions and the binarization function will be fixed in each set. Thirdly, a set with 40 actions will be formed, replicating the same work presented by the authors in [ 2 , 31 , 36 , 40 ]. Finally, a set with 80 actions will be formed, where the S-shaped, V-shaped, X-shaped, and Z-shaped families will be used as transfer functions and all the binarization functions will be used.…”

Section: The Proposal: Analysis Of Different Sets Of Actionsmentioning

confidence: 99%

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Binarization of Metaheuristics: Is the Transfer Function Really Important?

Lemus-Romani,

Crawford,

Cisternas-Caneo

et al. 2023

Biomimetics

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In this work, an approach is proposed to solve binary combinatorial problems using continuous metaheuristics. It focuses on the importance of binarization in the optimization process, as it can have a significant impact on the performance of the algorithm. Different binarization schemes are presented and a set of actions, which combine different transfer functions and binarization rules, under a selector based on reinforcement learning is proposed. The experimental results show that the binarization rules have a greater impact than transfer functions on the performance of the algorithms and that some sets of actions are statistically better than others. In particular, it was found that sets that incorporate the elite or elite roulette binarization rule are the best. Furthermore, exploration and exploitation were analyzed through percentage graphs and a statistical test was performed to determine the best set of actions. Overall, this work provides a practical approach for the selection of binarization schemes in binary combinatorial problems and offers guidance for future research in this field.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: The Proposal: Analysis Of Different Sets Of Actionsmentioning

confidence: 99%

See 2 more Smart Citations

Binarization of Metaheuristics: Is the Transfer Function Really Important?

Lemus-Romani,

Crawford,

Cisternas-Caneo

et al. 2023

Biomimetics

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show abstract

“…The study of metaheuristics has grown in recent years, with hybridizations emerging as the current trend. There exist hybridizations between metaheuristics such as those proposed in [2][3][4][5], hyperheuristic approaches where a high-level metaheuristic guides another low-level one [6][7][8], approaches where machine learning techniques enhance metaheuristics [9][10][11], and other approaches in which chaos theory is utilized to modify the stochastic behavior of metaheuristics [12][13][14][15].…”

mentioning

confidence: 99%

Chaotic Binarization Schemes for Solving Combinatorial Optimization Problems Using Continuous Metaheuristics

Cisternas-Caneo,

Crawford,

Soto

et al. 2024

Mathematics

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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.

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