An Efficient Heuristic for the k-Partitioning Problem

We investigate the k-partitioning problem, in which a set of items is divided into mutually exclusive and collectively exhaustive non-empty groups (clusters). The number of groups is given, and the distances between items, which may include weights, are defined. 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 formulations of the problem are proposed and solved. In the first problem, the number of items in each group is given. In the second problem, there is no restriction on the number of items in each group. We propose an optimal algorithm for each of these two problems and an efficient heuristic algorithm that found all confirmed optimal solutions and improved several best-known solutions. © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.