Querying Beneficial Constraints Before Clustering Using Facility Location Analysis

This paper examines the problem of querying beneficial constraints before clustering. Existing methods in this area choose constraints heuristically based on some prior assumptions on the usefulness of constraints. However, the usefulness and propagation of constraints are two important issues in the constraints selection that are not investigated simultaneously in most existing works. This paper addresses the problem of querying beneficial constraints using facility location analysis that is one of the most well-studied areas of the operations research. To this end, the source problem of querying k beneficial constraints is transformed into an instance of target uncapacitated k-facility location problem (k-UFL) and then is benefited from existing algorithms in the target space to find a solution to the k-UFL problem. The solution to the k-UFL problem is then transformed into a solution of the source problem of querying k beneficial constraints. Both usefulness and propagation of constraints are achieved in this paper by respectively mapping them into the corresponding opening and service costs in target problem space and then minimizing the total cost in target space. The proposed method is based on an optimization framework and is entirely different from existing methods in the constraints selection that are limited to greedy approaches. A range of experiments is presented to compare the proposed method to alternatives and explore its behavior in the selection of clustering constraints.