A memetic algorithm for the weighted feedback vertex set problem

Carrabs, Francesco; Cerrone, Carmine; Cerulli, Raffaele

doi:10.1002/net.21577

Cited by 11 publications

(3 citation statements)

References 27 publications

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“…(2011) for the maximum weighted feedback vertex set problem, where more details can be encountered. The instances are available in Carrabs (2015). They consist of random, grid, toroidal, and hypercube graphs, and are classified as small, with

16 \le |V| \le 81

, or large, with

91 \le |V| \le 529

.…”

Section: Computational Experimentsmentioning

confidence: 99%

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Maximum weighted induced forests and trees: new formulations and a computational comparative review

Melo

Ribeiro

2021

Int Trans Operational Res

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Given a graph G=false(V,Efalse)$G=(V,E)$ with a weight wv$w_v$ associated with each vertex v∈V$v\in V$, the maximum weighted induced forest problem (MWIF) consists of encountering a maximum weighted subset V′⊆V$V^{\prime }\subseteq V$ of the vertices such that V′$V^{\prime }$ induces a forest. This NP‐hard problem is known to be equivalent to the minimum weighted feedback vertex set problem, which has applicability in a variety of domains. The closely related maximum weighted induced tree problem (MWIT), on the other hand, requires that the subset V′⊆V$V^{\prime }\subseteq V$ induces a tree. We propose two new integer programming formulations with an exponential number of constraints and branch‐and‐cut procedures for MWIF. Computational experiments using benchmark instances are performed comparing several formulations, including the newly proposed approaches and those available in the literature, when solved by a standard commercial mixed integer programming solver. More specifically, five formulations are compared, two compact ones (i.e., with a polynomial number of variables and constraints) and the three others with an exponential number of constraints. The experiments show that a new formulation for the problem based on directed cutset inequalities for eliminating cycles (DCUT) offers stronger linear relaxation bounds earlier in the search process. The results also indicate that the other new formulation, denoted tree with cycle elimination (TCYC), outperforms those available in the literature when it comes to the average times for proving optimality for the benchmark instances with up to 81 vertices. Additionally, this formulation can achieve much lower average times for solving the larger random instances that can be optimally solved. Furthermore, we show how the formulations for MWIF can be easily extended for MWIT. Such extension allowed us to analyze the difference between the optimal solution values of the two problems when considering different classes of graphs.

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16 \le |V| \le 81

, or large, with

91 \le |V| \le 529

.…”

Section: Computational Experimentsmentioning

confidence: 99%

“…Carrabs et al. (2014) proposed a memetic algorithm for MWFVS. Shi and Xu (2017) demonstrated graph theoretical results regarding the existence of induced forests with a certain number of vertices.…”

Section: Introductionmentioning

confidence: 99%

Maximum weighted induced forests and trees: new formulations and a computational comparative review

Melo

Ribeiro

2021

Int Trans Operational Res

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“…Carrabs, Cerulli, Gentili, and Parlato (2011) implemented a tabu search metaheuristic for the MWFVS which makes use of the algorithms described in Carrabs et al (2005) in the local search procedure. Carrabs, Cerrone, and Cerulli (2014) proposed a memetic algorithm for the MWFVS. Shi and Xu (2017) demonstrated graph theoretical results regarding the existence of induced forests with a certain number of vertices.…”

Section: Introductionmentioning

confidence: 99%

Maximum weighted induced forests and trees: New formulations and a computational comparative review

Melo,

Ribeiro

2021

Preprint

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Given a graph G = (V, E) with a weight wv associated with each vertex v ∈ V , the maximum weighted induced forest problem consists of encountering a maximum weighted subset V ⊆ V of the vertices such that V induces a forest. This NP-hard problem is known to be equivalent to the minimum weighted feedback vertex set problem, which has applicability in a variety of domains. The closely related maximum weighted induced tree problem, on the other hand, requires that the subset V ⊆ V induces a tree. We propose two new integer programming formulations with an exponential number of constraints and branch-and-cut procedures for the maximum weighted induced forest problem. Furthermore, we show how formulations for the problem can be very easily adapted to obtain maximum weighted induced trees. Computational experiments using benchmark instances are performed comparing several formulations, including the newly proposed approaches and those available in the literature, when implemented in a standard commercial MIP (mixed integer programming) solver. More specifically, five formulations are compared, two compact (i.e., with a polynomial number of variables and constraints) ones and the three others with an exponential number of constraints. The results indicate that one of the newly proposed formulations, denoted tree with cycle elimination (TCYC), outperforms those available in the literature when it comes to the average times for proving optimality for the small instances, especially the more challenging ones. Additionally, this formulation can achieve much lower average times for solving the larger random instances that can be optimally solved. The results also illustrate the impact of offering high quality initial feasible solutions in the performance of the formulations.

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Memetic Algorithms for Business Analytics and Data Science: A Brief Survey

Moscato

Mathieson

2019

Business and Consumer Analytics: New Ideas

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A memetic algorithm for the weighted feedback vertex set problem

Cited by 11 publications

References 27 publications

Maximum weighted induced forests and trees: new formulations and a computational comparative review

Maximum weighted induced forests and trees: new formulations and a computational comparative review

Maximum weighted induced forests and trees: New formulations and a computational comparative review

Memetic Algorithms for Business Analytics and Data Science: A Brief Survey

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