Exploring Further Advantages in an Alternative Formulation for the Set Covering Problem

Lanza-Gutiérrez, José M.; Caballé, Nuria C.; Crawford, Broderick; Soto, Ricardo; Gómez–Pulido, Juan A.; Paredes, Fernando

doi:10.1155/2020/5473501

Cited by 7 publications

(3 citation statements)

References 73 publications

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“…Finally, x corresponds to the area to be covered. The mathematical model of the set covering problem is explained in more detail in [67]. This problem formulation has inspired the modeling of different real-world problems such as airline and bus crew scheduling [68], the location of gas detectors for industrial plants [69], plant location selection [70], the location of emergency services [71], dynamic vehicle routing problems [72], the location of electric vehicle charging points in California [73], disaster management systems [74], emergency humanitarian logistics [75], the optimal UAV locations for the purpose of generating wireless communication networks in disaster areas [76], among others.…”

Section: Set Covering Problemmentioning

confidence: 99%

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: Set Covering Problemmentioning

confidence: 99%

Binarization of Metaheuristics: Is the Transfer Function Really Important?

Lemus-Romani,

Crawford,

Cisternas-Caneo

et al. 2023

Biomimetics

Self Cite

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“…To solve a combinatorial problem such as the SCP with WOA, we need to translate the continuous solutions generated by WOA to the binary domain [7]. One of the most widely used techniques in the literature is the two-step technique [36]. As the name implies, it transfers the continuous solutions to the binary domain in two steps.…”

Section: Whale Optimization Algorithm: Q-binary Versionmentioning

confidence: 99%

Embedded Learning Approaches in the Whale Optimizer to Solve Coverage Combinatorial Problems

et al. 2022

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When we face real problems using computational resources, we understand that it is common to find combinatorial problems in binary domains. Moreover, we have to take into account a large number of possible candidate solutions, since these can be numerous and make it complicated for classical algorithmic techniques to address them. When this happens, in most cases, it becomes a problem due to the high resource cost they generate, so it is of utmost importance to solve these problems efficiently. To cope with this problem, we can apply other methods, such as metaheuristics. There are some metaheuristics that allow operation in discrete search spaces; however, in the case of continuous swarm intelligence metaheuristics, it is necessary to adapt them to operate in discrete domains. To perform this adaptation, it is necessary to use a binary scheme to take advantage of the original moves of the metaheuristics designed for continuous problems. In this work, we propose to hybridize the whale optimization algorithm metaheuristic with the Q-learning reinforcement learning technique, which we call (the QBWOA). By using this technique, we are able to realize an smart and fully online binarization scheme selector, the results have been statistically promising thanks to the respective tables and graphs.

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“…The set covering problem is a well-known optimization problem in the heuristics and mathematical programming literature [18,19]. In this background, most studies in SCP considered the earlier SCP formulation presented by Lanza-Gutierrez et al [20] and defined it as follows. If K is a set of n objects and L is a set of m subsets of k where subsets take non-negative cost, then the purpose of SCP is to minimize the cost group of subsets X ( L, in a way that each agent of K belongs to at least one subset of the group X.…”

Section: Literaturementioning

confidence: 99%

A New Direct Coefficient-Based Heuristic Algorithm for Set Covering Problems

Hashemi¹,

Gholami²,

Venkatadri³

et al. 2021

Int. J. Fuzzy Syst.

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The set covering problem is a fundamental model which comprises a wide range of important applications such as crew scheduling problems that need to cover a set of trips. It is one of the most common issues in the facility location problem, which requires further investigations, particularly in emergency and service facilities. As such, the objective of this study is to propose a new coefficient-based heuristic algorithm for the set covering problems. This paper has accordingly presented the algorithm that evaluates the qualification of subsets by directly applying a fitness function. This fitness function is formulated based on sets and subsets coefficients in a way that the subsets of selected sets have the lowest probability to be selected in the next iteration. The algorithm is not only capable of constructing an answer within polynomial time, but can solve complex set covering problems without conventional restrictions. The performance of this algorithm is evaluated on benchmark instances including a set of reproduced and selected OR-library problems within different sizes. Computational results indicate that the proposed heuristic algorithm produces better solutions, especially in large-scale problems comparing simulated annealing in terms of quality and time.

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Exploring Further Advantages in an Alternative Formulation for the Set Covering Problem

Cited by 7 publications

References 73 publications

Binarization of Metaheuristics: Is the Transfer Function Really Important?

Binarization of Metaheuristics: Is the Transfer Function Really Important?

Embedded Learning Approaches in the Whale Optimizer to Solve Coverage Combinatorial Problems

A New Direct Coefficient-Based Heuristic Algorithm for Set Covering Problems

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