Fuzzy zoning: a lagrangean relaxation approach

This research arises from the need of equality in real life problems. Clustering algorithms are being used in many applications where equality is an interest, such as districting (either zonal or political) and industry (distribution companies). One of the well known clustering algorithms is Fuzzy clustering. We add an equality constraint to the existing model. We call the new problem ”Zoning” problem. One of the application where equality can play a critical role is Wireless Sensor Network. A Lagrangean relaxation based approach is developed to solve Zonnig problem. The proposed algorithm is simulated and the results show robust performance regarding the equality of the clusters.