The weighted independent domination problem: Integer linear programming models and metaheuristic approaches

Pinacho-Davidson, Pedro; Blum, Christian; Lozano, José A.

doi:10.1016/j.ejor.2017.08.044

Cited by 12 publications

(5 citation statements)

References 20 publications

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“…• New-1 and New-2 obtain higher quality results on the vast majority of random instances, in comparison to the other three ILP models. Additionally, both models successfully solve all instances with 100 nodes to optimality, in contrast to models from [15] that achieve optimality in only 4 or 5 groups out of the total 9 instance groups of that size. It is worth noting that the average execution time of New-1 and New-2 for instances with 100 nodes is relatively short, with around half completing in less than 1 second.…”

Section: Resultsmentioning

confidence: 97%

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Integer Linear Programming Models and Greedy Heuristic for the Minimum Weighted Independent Dominating Set Problem

Kapunac

2024

SJC

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This paper explores the Minimum Weighted Independent Dominating Set Problem and proposes novel approaches to tackle it. Namely, two integer linear programming formulations and a fast greedy heuristic as an alternative approach are proposed. Extensive computational experiments are conducted to evaluate the performance of these approaches on the established set of benchmark instances for the problem. The obtained results demonstrate that the introduced integer linear programming models are able to achieve optimal solutions on all instances with 100 nodes and significantly outperform existing exact methods on numerous other instances. Additionally, the greedy heuristic exhibits superior performance compared to competing greedy heuristics, particularly on random graphs. These findings suggest promising directions for future research, including the integration of these methods into hybrid algorithms or metaheuristic frameworks.

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Section: Resultsmentioning

confidence: 97%

“…There are two papers that handle the general graphs. In [15] multiple approaches have been proposed:…”

Section: Related Workmentioning

confidence: 99%

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Integer Linear Programming Models and Greedy Heuristic for the Minimum Weighted Independent Dominating Set Problem

Kapunac

2024

SJC

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“…Subsequently, Wang et al introduced a tabu search-based memetic MIDS algorithm [11], in which tabu method was used to prevent cycling problems and a repairing-based crossover strategy was added to compensate for infeasible solutions. For MWIDS, Davidson et al [12] built three different integer linear programming (ILP) models. At the same time, they put forward two different greedy heuristics, where one does not consider the weight of the edge and the other considers the weight of the edge.…”

Section: D E B Amentioning

confidence: 99%

Improved Memetic Algorithm for Solving the Minimum Weight Vertex Independent Dominating Set

Zhou

Liu

et al. 2020

Mathematics

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The minimum weight vertex independent dominating set (MWVIDS) problem is an important version of the minimum independent dominating set. The MWVIDS problem has a number of applications in many fields. However, the MWVIDS problem is known to be NP-hard and thus computationally challenging. In this work, we present the improved memetic algorithm called MSSAS for solving the MWVIDS problem. The proposed MSSAS algorithm combines probability-based dynamic optimization (PDO) (to generate good and diverse offspring solutions by assembling elements of existing good solutions) as well as a local search phase named C_LS (to seek high-quality local optima by combining the idea of constrained-based two-level configuration checking strategy and tabu mechanism). The extensive results on popular DIMACS and BHOLIB benchmarks demonstrate that MSSAS competes favorably with the state-of-the-art algorithms. In addition, we analyze the benefits of the newly raised components including two above proposed ideas with our memetic framework. It is worth mentioning that the combination of both components has excellent effects for the MWVIDS problem.

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“…However, these problems present some challenges to optimization, since most of these home visiting services still operate manually and without resorting to computational methods to support the scheduling and routing. Thus, these optimization problems have become increasingly complex and the search for improvements has been gaining impact in recent years [3].…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Approach to Operational Planning in Home Health Care

Alves

Duarte²,

Rocha³

et al. 2022

Communications in Computer and Information Science

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Home health care (HHC) management needs to plan their operations to synchronize professionals and allocate resources to perform several HHC services needed by patients. The growing demand for this type of service dictates the interest of all the stakeholders (professionals and patients) in finding high-quality daily solutions and logistics. Routing and scheduling are problems of combinatorial nature, extremely complex, and require sophisticated optimization approaches. This work aims to contribute to cost-efficient decision-making in the general improvement of the service quality. Thus, a mixed integer linear programming model, a genetic algorithm, and a hybrid approach were used to solve the operational planning through test instances of different sizes for public home care providers. Computational results are presented, followed by a discussion on the advantages and shortcomings, highlighting the strength of each approach.

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The weighted independent domination problem: Integer linear programming models and metaheuristic approaches

Cited by 12 publications

References 20 publications

Integer Linear Programming Models and Greedy Heuristic for the Minimum Weighted Independent Dominating Set Problem

Integer Linear Programming Models and Greedy Heuristic for the Minimum Weighted Independent Dominating Set Problem

Improved Memetic Algorithm for Solving the Minimum Weight Vertex Independent Dominating Set

A Hybrid Approach to Operational Planning in Home Health Care

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