Potential- $K$- Means for Load Balancing and Cost Minimization in Mobile Recycling Network

Cyber-physical systems usually consist of large numbers of spatially distributed autonomous sensors that monitor physical conditions and communicate with a main location. We consider the problem of positioning mobile storage facilities in a recycling network consisting of two types of nodes: collection points (neighborhood recycling bins) and mobile storage centers, and of finding the optimal number of storage centers. Sensors at the collection points monitor and communicate fill levels to a main location, where the collection points are clustered. We present a variation of K-means, potential-K-means, that assigns each cluster to a storage center while balancing the storage center loads. It minimizes the total network cost, for a fixed number of storage centers. The algorithm is based on an analogy with the gravitational force exerted by masses. The “mass” of a cluster is inversely proportional to its current “size.” An instance is assigned to the cluster whose “mass” minimizes the “gravitational potential” on the instance's position. This decision is a reasonable compromise between instance-cluster distance and cluster "size.” The proposed algorithm produces smaller total costs than K-means. We show that storage center locations affect the total cost, and thus, very significant savings are achieved through this wireless monitoring of the collection points and dynamical positioning of the storage centers.