Review of Basic Local Searches for Solving the Minimum Sum-of-Squares Clustering Problem

Pereira, Thiago; Aloise, Daniel; Brimberg, Jack; Mladenović, Nenad

doi:10.1007/978-3-319-99142-9_13

Cited by 3 publications

(1 citation statement)

References 35 publications

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“…The p-median problem with equal weights and squared Euclidean distances is used in many papers to model clustering problems (e.g., Aloise, 2009;Hartigan and Wong, 1979;Lloyd, 1982;MacQueen, 1967). For recent reviews see Bagirov et al (2015); Pereira et al (2018).…”

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confidence: 99%

Partitioning Items Into Mutually Exclusive Groups

Kalczyński¹,

Goldstein²,

Drezner³

2020

Preprint

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We investigate a new model for partitioning a set of items into groups (clusters). The number of groups is given and the distances between items are well defined. These distances may include weights. The sum of the distances between all members of the same group is calculated for each group, and the objective is to find the partition of the set of items that minimizes the sum of these individual sums. Two problems are formulated and solved. In the first problem the number of items in each group are given. For example, all groups must have the same number of items. In the second problem there is no restriction on the number of items in each group.We propose an optimal algorithm for each of the two problems as well as a heuristic algorithm. Problems with up to 100 items and 50 groups are tested. In the majority of instances the optimal solution was found using IBM's CPLEX. The heuristic approach, which is very fast, found all confirmed optimal solutions and equal or better solutions when CPLEX was stopped after five hours. The problem with given group sizes can also be formulated and solved as a quadratic assignment problem.

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confidence: 99%

Partitioning Items Into Mutually Exclusive Groups

Kalczyński¹,

Goldstein²,

Drezner³

2020

Preprint

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An Efficient Heuristic for the k-Partitioning Problem

Kalczynski,

Goldstein,

Drezner

2023

Oper. Res. Forum

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Less is more: simple algorithms for the minimum sum of squares clustering problem

Kalczyński

Brimberg

Drezner

2021

IMA Journal of Management Mathematics

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The clustering problem has many applications in machine learning, operations research and statistics. We propose three algorithms to create starting solutions for improvement algorithms for the minimum sum of squares clustering problem. We test the algorithms on 72 instances that were investigated in the literature. We found five new best known solutions and matched the best known solution for 66 of the remaining 67 instances. Thus, we are able to demonstrate that good starting solutions combined with a simple local search get results comparable with, and sometimes even better than, more sophisticated algorithms used in the literature.

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Review of Basic Local Searches for Solving the Minimum Sum-of-Squares Clustering Problem

Cited by 3 publications

References 35 publications

Partitioning Items Into Mutually Exclusive Groups

Partitioning Items Into Mutually Exclusive Groups

An Efficient Heuristic for the k-Partitioning Problem

Less is more: simple algorithms for the minimum sum of squares clustering problem

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