Continuous reformulations and heuristics for the euclidean travelling salesperson problem

Tuomo Valkonen; Tommi Kärkkäinen

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The paper gives a new interpretation and a possible optimization of the well-known $k$ -means algorithm for searching for a locally optimal partition of the set $𝒜 = {a_{i} \in ℝ^{n} : i = 1, \dots, m}$ which consists of $k$ disjoint nonempty subsets $π_{1}, \dots, π_{k}$ , $1 \leq k \leq m$ . For this purpose, a new divided $k$ -means algorithm was constructed as a limit case of the known smoothed $k$ -means algorithm. It is shown that the algorithm constructed in this way coincides with the $k$ -means algorithm if during the iterative procedure no data points appear in the...

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