New bounds and constraint propagation techniques for the clique partitioning problem

Jaehn, Florian; Pesch, Erwin

doi:10.1016/j.dam.2013.02.011

Cited by 27 publications

(35 citation statements)

References 18 publications

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“…We describe how to use obtained upper bounds to construct the exact solution of CPP. The proposed method is similar to the algorithm of Jaehn and Pesch [29] and its further development in [39]. But by significantly improving the upper bound's initial estimates and recalculation procedure, it achieves a decrease of a couple of orders of magnitude in computational complexity and execution time.…”

Section: Introductionmentioning

confidence: 98%

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Subnetwork Constraints for Tighter Upper Bounds and Exact Solution of the Clique Partitioning Problem

Belyi,

Sobolevsky,

Kurbatski

et al. 2021

Preprint

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We consider a variant of the clustering problem for a complete weighted graph. The aim is to partition the nodes into clusters maximizing the sum of the edge weights within the clusters. This problem is known as the clique partitioning problem, being NP-hard in the general case of having edge weights of different signs. We propose a new method of estimating an upper bound of the objective function that we combine with the classical branch-and-bound technique to find the exact solution. We evaluate our approach on a broad range of random graphs and real-world networks. The proposed approach provided tighter upper bounds and achieved significant convergence speed improvements compared to known alternative methods.

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Section: Introductionmentioning

confidence: 98%

“…Given the NP-hardness of CPP, exact solutions are rarely proposed. Most of the existing approaches utilize the branch-and-bound method [19,29] or cutting plane technique [3,9]. Many use both methods through the means of optimization software packages that internally implement them.…”

Section: Introductionmentioning

confidence: 99%

Subnetwork Constraints for Tighter Upper Bounds and Exact Solution of the Clique Partitioning Problem

Belyi,

Sobolevsky,

Kurbatski

et al. 2021

Preprint

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“…Xu Y [5] improved the classical clique partition algorithm to solve the imaging satellite task-clustering Task clustering has gained more and more attention for Earth observation satellites and has been a research focus on the preprocessing field for satellite missions. Jenhn.et al [3] proposed a branch and bound algorithm for clique partition, contributing to the development of graphic theory. In 2013, Wu G [2] proposed a two-phase scheduling method that considers task clustering of Earth observation satellites.…”

Section: Introductionmentioning

confidence: 99%

A GA-SA Hybrid Planning Algorithm Combined with Improved Clustering for LEO Observation Satellite Missions

Long

et al. 2019

Algorithms

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This paper presents a space mission planning tool, which was developed for LEO (Low Earth Orbit) observation satellites. The tool is focused on a two-phase planning strategy with clustering preprocessing and mission planning, where an improved clustering algorithm is applied, and a hybrid algorithm that combines the genetic algorithm with the simulated annealing algorithm (GA–SA) is given and discussed. Experimental simulation studies demonstrate that the GA–SA algorithm with the improved clique partition algorithm based on the graph theory model exhibits higher fitness value and better optimization performance and reliability than the GA or SA algorithms alone.

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“…Given the relevance of CPP, a number of solving procedures have been reported in the literature, including both exact and heuristic methods. Most of the exact methods follow the branch and bound framework [10,20,21]) and cutting plane method [17]. However, exact methods may become prohibitively expensive when they are used to solve large instances.…”

Section: Introductionmentioning

confidence: 99%

A three-phased local search approach for the clique partitioning problem

Zhou¹,

Hao²,

Goëffon³

2015

J Comb Optim

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This paper presents a three-phased local search heuristic CPP-P 3 for solving the Clique Partitioning Problem (CPP). CPP-P 3 iterates a descent search, an exploration search and a directed perturbation. We also define the Top Move of a vertex, in order to build a restricted and focused neighborhood. The exploration search is ensured by a tabu procedure, while the directed perturbation uses a GRASP-like method. To assess the performance of the proposed approach, we carry out extensive experiments on benchmark instances of the literature as well as newly generated instances. We demonstrate the effectiveness of our approach with respect to the current best performing algorithms both in terms of solution quality and computation efficiency. We present improved best solutions for a number of benchmark instances. Additional analyses are shown to highlight the critical role of the Top Move-based neighborhood for the performance of our algorithm and the relation between instance hardness and algorithm behavior.

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New bounds and constraint propagation techniques for the clique partitioning problem

Cited by 27 publications

References 18 publications

Subnetwork Constraints for Tighter Upper Bounds and Exact Solution of the Clique Partitioning Problem

Subnetwork Constraints for Tighter Upper Bounds and Exact Solution of the Clique Partitioning Problem

A GA-SA Hybrid Planning Algorithm Combined with Improved Clustering for LEO Observation Satellite Missions

A three-phased local search approach for the clique partitioning problem

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