BINARY BAO FOR COMPUTING NON-ISOLATED METRIC DIMENSION PROBLEM

The NP-hard problem of determining the minimum non-isolated resolving set of graphs is examined in this study. If a connected graph G has a vertex set X that resolves G, then every vertex in G may be uniquely identified by its vector of distances to the vertices in X. In addition, the resolving set X of G is referred to as the non-isolated resolving set if the non-isolated vertex causes v ∈ X to not exist for all v. The smallest cardinality of a non-isolated resolving set in G is known as a non-isolated resolving number, or ni (G). Recently, a proposed heuristic technique called Aquila Optimizer (AO). It is an innovative optimization technique based on population size. The Aquila’s natural behavior was imitated in its creation. Its creation was modeled after the way aquilas in the wild pursue and capture their prey. In order to address continuous optimization problems in its original form, the AO algorithm was created. The non-isolated metric dimension is computed by a binary version of the Aquila optimizer (BAO) algorithm. The objects of BAO are binary encoded and used to represent which one of the vertices of the graph belongs to the non-isolated resolving set. The feasibility is enforced by repairing solutions such that an additional vertex generated from vertices of G is added to X and this repairing process is iterated until X becomes the non-isolated resolving set. This is the first attempt to determine the non-isolated metric dimension problem (MDP) heuristically. The proposed BAO is compared to binary smell agent optimization (BSAO), binary dragonfly algorithm (BDA) and binary sand cat swarm optimization (BSCSO) algorithms. Computational results confirm the superiority of the BAO for computing the non-isolated metric dimension.