Binary rat swarm optimizer algorithm for computing independent domination metric dimension problem

Abstract

In this article, we look at the NP-hard problem of determining the minimum independent domination metric dimension of graphs. A vertex set B of a connected graph G(V,E) resolves G if every vertex of G is uniquely recognized by its vector of distances to the vertices in B. If there are no neighboring vertices in a resolving set B of G, then B is independent. Every vertex of G that does not belong to B must be a neighbor of at least one vertex in B for a resolving set to be dominant. The metric dimension of G, independent metric dimension of G, and independent dominant metric dimension of G are, respectively, the cardinality of the smallest resolving set of G, the minimal independent resolving set, and the minimal independent domination resolving set. We propose the first attempt to use a binary version of the Rat Swarm Optimizer Algorithm (BRSOA) to heuristically calculate the smallest independent dominant resolving set of graphs. The search agent of BRSOA are binary-encoded and used to identify which one of the vertices of the graph belongs to the independent domination resolving set. The feasibility is enforced by repairing search agent such that an additional vertex created from vertices of G is added to B, and this repairing process is repeated until B becomes the independent domination resolving set. Using theoretically computed graph findings and comparisons to competing methods, the proposed BRSOA is put to the test. BRSOA surpasses the binary Grey Wolf Optimizer (BGWO), the binary Particle Swarm Optimizer (BPSO), the binary Whale Optimizer (BWOA), the binary Gravitational Search Algorithm (BGSA), and the binary Moth-Flame Optimization (BMFO), according to computational results and their analysis.