J-MEANS: A new local search heuristic for minimum sum of squares clustering. A new local search heuristic, called J-Means, is proposed for solving the minimum sum of squares clustering problem. The neighborhood of the current solution is defined by all possible centroid-to-entity relocations followed by corresponding changes of assignments. Moves are made in such neighborhoods until a local optimum is reached. The new heuristic is compared with two other well-known local search heuristics, K- and H-Means as well as with H-Means+, an improved version of the latter in which degeneracy is removed. Moreover, another heuristic, which fits into the variable neighborhood search metaheuristic framework and uses J-Means in its local search step, is proposed too. Results on standard test problems from the literature are reported. It appears that J-Means outperforms the other local search methods, quite substantially when many entities and clusters are considered.

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  1. Aloise, Daniel; Castelo Damasceno, Nielsen; Mladenović, Nenad; Nobre Pinheiro, Daniel: On strategies to fix degenerate $k$-means solutions (2017)
  2. Chen, Binhui; Qu, Rong; Bai, Ruibin; Ishibuchi, Hisao: An investigation on compound neighborhoods for VRPTW (2017)
  3. Đorić, Danijela; Ait El Cadi, Abdessamad; Hanafi, Saïd; Mladenović, Nenad; Artiba, Abdelhakim: Clustering approach in maintenance of capillary railway network (2017)
  4. Nikolaev, Alexey; Mladenović, Nenad; Todosijević, Raca: J-means and I-means for minimum sum-of-squares clustering on networks (2017)
  5. Rusetskaya, Olga: Grouping cities based of their socio-economic indicators (2017)
  6. Todosijević, Raca; Urošević, Dragan; Mladenović, Nenad; Hanafi, Saïd: A general variable neighborhood search for solving the uncapacitated $r$-allocation $p$-hub Median problem (2017)
  7. Aloise, Daniel; Araújo, Arthur: A derivative-free algorithm for refining numerical microaggregation solutions (2015)
  8. Carrizosa, Emilio; Alguwaizani, Abdulrahman; Hansen, Pierre; Mladenović, Nenad: New heuristic for harmonic means clustering (2015)
  9. Zhikharevich, B. S.; Rusetskay, O. V.; Mladenović, N.: Clustering cities based on their development dynamics and variable neigborhood search (2015)
  10. Carrizosa, Emilio; Mladenović, Nenad; Todosijević, Raca: Variable neighborhood search for minimum sum-of-squares clustering on networks (2013)
  11. Alguwaizani, Abdulrahman: Degeneracy on $K$-means clustering (2012)
  12. Aloise, Daniel; Hansen, Pierre; Liberti, Leo: An improved column generation algorithm for minimum sum-of-squares clustering (2012)
  13. de Carvalho, Francisco de A. T.; Lechevallier, Yves; De Melo, Filipe M.: Partitioning hard clustering algorithms based on multiple dissimilarity matrices (2012)
  14. Hansen, Pierre; Ruiz, Manuel; Aloise, Daniel: A VNS heuristic for escaping local extrema entrapment in normalized cut clustering (2012) ioport
  15. Alguwaizani, Abdulrahman; Hansen, Pierre; Mladenović, Nenad; Ngai, Eric: Variable neighborhood search for harmonic means clustering (2011)
  16. Aloise, Daniel; Hansen, Pierre: Evaluating a branch-and-bound RLT-based algorithm for minimum sum-of-squares clustering (2011)
  17. Deng, Yumin; Bard, Jonathan F.: A reactive GRASP with path relinking for capacitated clustering (2011)
  18. Amiri, M.; Zandieh, M.; Yazdani, M.; Bagheri, A.: A variable neighbourhood search algorithm for the flexible job-shop scheduling problem (2010)
  19. Chiang, Mark Ming-Tso; Mirkin, Boris: Intelligent choice of the number of clusters in $K$-means clustering: an experimental study with different cluster spreads (2010)
  20. Galiev, Sh. I.; Karpova, M. A.: Optimization of multiple covering of a bounded set with circles (2010)

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