Abstract
The linear binary model for finding set partitioning of the points in the plane is studied. We present heuristic which generates partitioning of points to clusters for a given number of seeds with searched seeds of clusters in a plane. For this cluster the convex hulls are constructed via Graham's scan algorithm. This approach is demonstrated on the real instance of Florida area with 235 points for 10 and 13 clusters.
Highlights
The set-partitioning problem is a well known NP-hard combinatorial problem
A real-world problem of this class for the vehicle routing problem in Florida area was formulated by Juricek [5]
We present two problems: G Convex set partitioning problem: A set of points in a plane have to be partitioned to a given number of clusters so that every two convex hulls of cluster members have empty intersection and the total area of cluster’s convex hulls is minimal
Summary
A real-world problem of this class for the vehicle routing problem in Florida area was formulated by Juricek [5]. He requires partitioning of customers to clusters. An intuitive criterion for the well-formed area of the cluster for one vehicle is the smallest convex polygon that encloses all points of cluster – convex hull. We present two problems: G Convex set partitioning problem: A set of points in a plane have to be partitioned to a given number of clusters so that every two convex hulls of cluster members have empty intersection and the total area of cluster’s convex hulls is minimal. G Convex location problem: A set of q seeds of clusters are searched with a bounded capacity of cluster and convex constraint for a pair of assigned points
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