Finding minimum label spanning trees using cross‐entropy method

Vaisman, Radislav

doi:10.1002/net.22057

Cited by 5 publications

(3 citation statements)

References 29 publications

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“…Silva et al [9] proposed a compact binary integer programming model to solve GMLSTP, in [10] the authors introduced a mixed-integer linear program (MIP) formulation for MLSTP and applied the capacity of exploration of a new local search method based on MIP to find results. Other evolutionary algorithms included the Simulated Annealing and Reactive Tabu Search [11], the Ant Colony Optimization [12], firefly algorithm [13], multi-objective optimization [14], cross-entropy method [15], etc.…”

Section: Algorithms For the Sgmlstp And Its Variantsmentioning

confidence: 99%

A Novel Heuristics for the Strong Generalized Minimum Label Spanning Tree Problem

Long,

Li,

Long

et al. 2023

Frontiers in Artificial Intelligence and Applications

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The strong generalized minimum label spanning tree problem (SGMLSTP) is to search the minimum label spanning tree (MLST) from an Edge-labeled graph (ELG), in which each edge is associated with one or more labels. SGMLSTP is commonly existed in reality and proven NP-hard. In recent years, researchers have proposed some algorithms; however, high computational costs are still severe obstacle, especially for large size graphs. In this paper, we propose a novel heuristics to solve SGMLSTP. We decompose the problem into two sub-problems, one is to search a connected subgraph with minimum labels from the original graph, the other is to search a spanning tree from the subgraph. As the latter sub-problem is solved, we focus on the former sub-problem and propose a community-based zigzag piloting algorithm: Firstly a label graph is derived from the original edge-labeled graph; then the label graph is partitioned and some label community (or community combinations) is chosen to form an initial solution; finally, the zigzag piloting process is applied to refine the initial solution. Label partition finds the initial solution quickly, the zigzag piloting process improves solution refinement. Experimental results on typical benchmark datasets show better effectiveness and performance of our algorithm than that of the state-of-the-art algorithms.

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Section: Algorithms For the Sgmlstp And Its Variantsmentioning

confidence: 99%

A Novel Heuristics for the Strong Generalized Minimum Label Spanning Tree Problem

Long,

Li,

Long

et al. 2023

Frontiers in Artificial Intelligence and Applications

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“…Computational experiments show that the MSLB outperforms the state-of-the-art metaheuristics with respect to optimality and processing times. In [32], Vaisman proposes a new method to solve the MLSTP called the cross-entropy method, which relies on rigorous developments in the fields of information theory and stochastic simulation. Experimentations indicate that the proposed algorithm can obtain optimal or near-optimal solutions while using a reasonable computational time.…”

Section: Classical Labeled Problems In Graphsmentioning

confidence: 99%

The edge-labeled survivable network design problem: Formulations and branch-and-cut

2022

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Abstract. In this paper, we study a variant of the survivable network design problem, that is the survivable network design problem with labels (colors) on the edges. In particular, we address the Generalized Labeled Two Edge Connected Subgraph Problem (GLTECSP) that has many applications in telecommunication and transportation. Given a connected undirected graph G such that with each edge is associated a set of labels (colors), the GLTECSP consists in finding a two-edge connected spanning subgraph of G with a minimum number of distinct labels. We propose two Integer Programming (IP) formulations for the problem, a natural formulation using cuts on the edges, and a compact formulation using color-cuts. We devise Branch-and-Cut algorithms to solve both formulations and compare them on sets of randomly generated instances. Computational results show that the compact formulation outperforms the natural one regarding the linear relaxation and the computational time. Moreover, the compact formulation is able to solve to optimality several instances left unsolved within the time limit by the natural formulation.

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“…Silva et al [9] proposed a compact binary integer programming model to solve the GMLSTP, in [10] the authors introduced a mixed-integer linear program (MIP) formulation for the MLSTP and applied the capacity of exploration of a new local search method based on MIP to find results. Other evolutionary algorithms included the Simulated Annealing and Reactive Tabu Search [11], the Ant Colony Optimization [12], firefly algorithm [13], multi-objective optimization [14], cross-entropy method [15], etc. Heuristic algorithms show better performance in finding the MLST [1], Chwatal and Raidl [16] abstracted the MLSTP and the GMLSTP with the mixed integer programming, They have also proposed several cuts to strengthen the models and implemented branch-and-cut and branch-and-cut-and-price algorithms to search feasible MLST solutions; Cerrone et al [17] applied carousel greedy to solve the MLSTP problem; In [18] the authors introduced a single-commodity flow mathematical formulation that perfectly represents the MLST and the SGMLST, and proposed three greedy algorithms, namely MMVCA (multi-label MVCA), MMVCA extended with CG(Constructive Greedy), and CG with the Pilot Method, to search promising solutions.…”

Section: Related Work 21 Algorithms For the Sgmlstp And Its Variantsmentioning

confidence: 99%

Community-based Zigzag Piloting Algorithm for the Strong Generalized Minimum Label Spanning Tree Problem

Long

LONG

et al. 2022

Preprint

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Edge-labeled graph (ELG) is an important abstract model of many practical applications, in which each edge is associated with one or more labels. Searching the minimum label spanning tree (MLST) of ELG is an important issue and proved NP-hard. In the last decade, researchers have put forward some algorithms, however, high computational cost and lower searching effectiveness are still the main obstacles, especially for large-size graphs. In this paper, we propose a heuristic to solve the strong generalized MLST problem (SGMLSTP). We decompose the SGMLSTP into two sub-problems, one is to search a sub-graph containing one or more spanning trees with the minimum labels from the original graph, and another is to search a spanning tree from the acquired sub-graph. As the latter sub-problem is already solved effectively, we focus on the former sub-problem and propose a community-based zigzag piloting algorithm: Firstly a weighted label graph is derived from the edge-labeled graph; then the label graph is partitioned and label communities are chosen in combination to form the initial solutions; finally, the zigzag piloting process is applied to make the initial solutions feasible and refined, of which the optimum one has the least labels. Label partition largely reduces the computation cost of searching the initial solutions, the zigzag piloting process help increase searching effectiveness, and experimental results on typical benchmark datasets fully verify this point and show better effectiveness and performance than that of the state-of-the-art algorithms.

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Finding minimum label spanning trees using cross‐entropy method

Cited by 5 publications

References 29 publications

A Novel Heuristics for the Strong Generalized Minimum Label Spanning Tree Problem

A Novel Heuristics for the Strong Generalized Minimum Label Spanning Tree Problem

The edge-labeled survivable network design problem: Formulations and branch-and-cut

Community-based Zigzag Piloting Algorithm for the Strong Generalized Minimum Label Spanning Tree Problem

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