Maximally diverse grouping: an iterated tabu search approach

Palubeckis, Gintaras; Ostreika, Armantas; Rubliauskas, Dalius

doi:10.1057/jors.2014.23

Cited by 22 publications

(10 citation statements)

References 28 publications

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“…The EVND method employs three complementary neighborhoods i.e., N 1 , N 2 and the 2-1 exchange neighborhood N 3 . While N 1 and N 2 are very popular and their effectiveness has been shown on a number of the clustering problems in the literature [5,6,9,28,29,31], N 3 is not well studied and thus less understood. In this section, we assess the influence of N 3 on the performance of the IVNS algorithm.…”

Section: Analysis and Discussionmentioning

confidence: 99%

“…The CCP is closely related to three other clustering problems: the graph partitioning problem (GPP) [2][3][4]15,30], the maximally diverse grouping problem (MDGP) [5,10,14,19,28,29,33], and the handover minimization problem (HMP) [23,26]. First, the GPP is a special case of the CCP when the lower and upper capacity limits of the clusters are respectively set to 0 and (1 +…”

Section: Introductionmentioning

confidence: 99%

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Iterated variable neighborhood search for the capacitated clustering problem

Lai

Hao

2016

Engineering Applications of Artificial Intelligence

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The NP-hard capacitated clustering problem (CCP) is a general model with a number of relevant applications. This paper proposes a highly effective iterated variable neighborhood search (IVNS) algorithm for solving the problem. IVNS combines an extended variable neighborhood descent method and a randomized shake procedure to explore effectively the search space. The computational results obtained on three sets of 133 benchmarks reveal that the proposed algorithm competes favorably with the state-of-the-art algorithms in the literature both in terms of solution quality and computational efficiency. In particular, IVNS discovers an improved best known result (new lower bounds) for 28 out of 83 most popular instances, while matching the current best known results for the remaining 55 instances. Several essential components of the proposed algorithm are investigated to understand their impacts on the performance of algorithm.

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Section: Analysis and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Iterated variable neighborhood search for the capacitated clustering problem

Lai

Hao

2016

Engineering Applications of Artificial Intelligence

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“…OneMove operator: Given a solution s = {C 1 , C 2 , ..., C p }, OneM ove transfers a node v from its original cluster i to another cluster j such that the capacity constraint is respected, i.e., |C i | − w v ≥ L i and |C j | + w v ≤ U j . To rapidly evaluate the gain value for each candidate move, our algorithm employs a fast incremental evaluation technique similar to that used in [6,24,34,37]. The main idea is to maintain an incremental matrix γ, where each element γ[v][g] represents the sum of the edge weights between v and other nodes located in cluster g of the current solution, i.e., γ[v][g] = u∈Cg c uv .…”

Section: Neighborhood Structuresmentioning

confidence: 99%

“…Note that CCP is closely related to the Graph Partitioning Problem (GPP) [4,5,16] where the lower and the upper capacity limits of the clusters are respectively set to 0 and a predetermined imbalance parameter. Moreover, the Maximally Diverse Grouping Problem (MDGP) [6,17,22,25,34,37,38] is a special case of CCP, when G is a complete graph with unit cost node weights. Consequently, CCP is an NP-hard problem as MDGP is known to be NPhard.…”

Section: Introductionmentioning

confidence: 99%

Heuristic search to the capacitated clustering problem

Zhou

Benlic²,

et al. 2019

European Journal of Operational Research

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Given a weighted graph, the capacitated clustering problem (CCP) is to partition a set of nodes into a given number of distinct clusters (or groups) with restricted capacities, while maximizing the sum of edge weights corresponding to two nodes from the same cluster. CCP is an NP-hard problem with many relevant applications. This paper proposes two effective algorithms for CCP: a Tabu Search (denoted as FITS) that alternates between exploration in feasible and infeasible search space regions, and a Memetic Algorithm (MA) that combines FITS with a dedicated cluster-based crossover. Extensive computational results on five sets of 183 benchmark instances from the literature indicate that the proposed FITS competes favorably with the state-of-the-art algorithms. Additionally, an experimental comparison between FITS and MA under an extended time limit demonstrates that further improvements in terms of the solution quality can be achieved with MA in most cases. We also analyze several essential components of the proposed algorithms to understand their importance to the success of these approaches.

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“…Furthermore, to find the best solutions of the other combinatorial optimization problems, several heuristic algorithms are employed, such as a variable neighborhood search algorithm [8,9], a tabu search algorithm [10][11][12][13], a simulated annealing algorithm [14][15][16][17], and a greedy algorithm [18].…”

Section: Related Workmentioning

confidence: 99%

An Efficient Memetic Algorithm for the Minimum Load Coloring Problem

Zhang

Qiao

2019

Mathematics

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Given a graph G with n vertices and l edges, the load distribution of a coloring q: V → {red, blue} is defined as dq = (rq, bq), in which rq is the number of edges with at least one end-vertex colored red and bq is the number of edges with at least one end-vertex colored blue. The minimum load coloring problem (MLCP) is to find a coloring q such that the maximum load, lq = 1/l × max{rq, bq}, is minimized. This problem has been proved to be NP-complete. This paper proposes a memetic algorithm for MLCP based on an improved K-OPT local search and an evolutionary operation. Furthermore, a data splitting operation is executed to expand the data amount of global search, and a disturbance operation is employed to improve the search ability of the algorithm. Experiments are carried out on the benchmark DIMACS to compare the searching results from memetic algorithm and the proposed algorithms. The experimental results show that a greater number of best results for the graphs can be found by the memetic algorithm, which can improve the best known results of MLCP.

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Maximally diverse grouping: an iterated tabu search approach

Cited by 22 publications

References 28 publications

Iterated variable neighborhood search for the capacitated clustering problem

Iterated variable neighborhood search for the capacitated clustering problem

Heuristic search to the capacitated clustering problem

An Efficient Memetic Algorithm for the Minimum Load Coloring Problem

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