Comparative analysis of self-organizing maps and genetic algorithms for distance-minimizing representation of 2D and 3D point distributions

The problem addressed in this work is how to position a small set of receivers among a much larger set of transmitters while optimizing some distance metrics which would lead to optimal communications especially in underwater exploration where signals degrade rapidly with distance. The set of transmitters are assumed to be in relatively slow motion, therefore the receivers must be constantly positioned while they follow the transmitters' changing distribution in space. As transmitters move, they are not statically allocated to receivers; they may change allocations. Thus, this problem entails dynamic clustering of the transmitters into clusters associated with the receivers and thus there is a need for determining the optimal placement of receivers. The problem is complex since the placement determines the clustering and the clustering determines the geometric medians which would be the optimal positions within each cluster. To address this complexity, this work compares a heuristic approach of Self Organizing Maps (SOMs) which maps the distribution density of the transmitters and a Genetic Algorithms (GAs) approach to optimize a distance based metric. The method was deployed on data points distributed within a 2D plane, then the search space was expanded to 3D cases and the clustering was carried out using SOM and GA. Overall, simulation results showed that GA outperformed SOM in optimizing the cost function, especially in 3D space.