Matrix Domination: Convergence of a Genetic Algorithm Metaheuristic with the Wisdom of Crowds to Solve the NP-Complete Problem

This research explores the application of a genetic algorithm metaheuristic enriched by the wisdom of crowds in order to address the NP-Complete matrix domination problem (henceforth: TMDP) which is itself a constraint on related problems applied in graphs. Matrix domination involves accurately placing a subset of cells, referred to as dominators, within a matrix with the goal of their dominating the remainder of the cells. This research integrates the exploratory nature of a genetic algorithm with the wisdom of crowds to find more optimal solutions with user-defined parameters to work within computational complexity considerations and gauge performance mainly with a fitness evaluation function and a constraining function to combat the stochastic nature of genetic algorithms. With this, I propose a novel approach to MDP with a genetic algorithm that incorporates the wisdom of crowds, emphasizing collective decision-making in the selection process, and by exploring concepts of matrix permutations and their relevance in finding optimal solutions. Results demonstrate the potential of this convergence to generate efficient solutions, optimizing the trade-off between the number of dominators and their strategic placements within the matrices while efficiently ensuring consistent and complete matrix domination.