  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.
