  The k-means algorithm is one of the well-known and most popular clustering
algorithms. K-means seeks an optimal partition of the data by minimizing the
sum of squared error with an iterative optimization procedure, which belongs to
the category of hill climbing algorithms. As we know hill climbing searches are
famous for converging to local optimums. Since k-means can converge to a local
optimum, different initial points generally lead to different convergence
cancroids, which makes it important to start with a reasonable initial
partition in order to achieve high quality clustering solutions. However, in
theory, there exist no efficient and universal methods for determining such
initial partitions. In this paper we tried to find an optimum initial
partitioning for k-means algorithm. To achieve this goal we proposed a new
improved version of downhill simplex search, and then we used it in order to
find an optimal result for clustering approach and then compare this algorithm
with Genetic Algorithm base (GA), Genetic K-Means (GKM), Improved Genetic
K-Means (IGKM) and k-means algorithms.
