OptiMap: Heuristic Clustering Algorithm for Minimum Cost Paths

Grouping algorithms refer to a procedure where certain entities within a community can form new sub-communities according to their characteristic features without disrupting the general order of the community. These sub-communities generally show division in a way that contributes to the order of the parent communities from which they are separated. The main purpose of grouping algorithms is to divide the elements in the data set into groups within a purpose according to their similarities or certain features. This purpose is often based on grouping similar entities within a group into a certain cluster according to their features. Unlike grouping certain entities within a group according to their similarities, in cases where certain problems cannot be solved holistically, there are also approaches that focus on solving the problem specifically for these sub-groups by creating sub-groups according to the scope of the problem. Such approaches enable large and complex problems to be solved by dividing them into more manageable parts. Each sub-group addresses a specific aspect of the problem, and in this way, a holistic solution is obtained by combining the sub-groups. Within the scope of the study, the problem of multiple resources navigating randomly distributed multiple targets in a way that follows minimum-cost paths is addressed. In this context, a new heuristic grouping algorithm is proposed that can group entities within a region where certain targets are located in a way to obtain minimum transit paths. This proposed algorithm is based on the fact that each target to be grouped knows its closest neighbor and uses this information to divide the group in a way to reveal minimum transit paths. Within the scope of the study, first of all, a matrix called the heuristic matrix, which contains the neighborhood information and costs of the targets, is created. This heuristic matrix is scanned with a specially designed search algorithm and the target that can create potential minimum transit paths is grouped in the same group. After the implementation of the originally created OptiMap grouping algorithm, the testing phase was started. In order to evaluate the ability of the OptiMap algorithm to group in a way to reveal minimum cost paths, test scenarios were created for regions with uniform and complex distributions. As a result of testing the OptiMap algorithm under different scenarios with different target distributions, it was seen that it can group in a way to create minimum transit paths.