Presented in this paper is a derivation of a 2D catalytic reaction-based model to solve combinatorial optimization problems (COPs). The simulated catalytic reactions, a computational metaphor, occurs in an artificial chemical reactor that finds near-optimal solutions to COPs. The artificial environment is governed by catalytic reactions that can alter the structure of artificial molecular elements. Altering the molecular structure means finding new solutions to the COP. The molecular mass of the elements was considered as a measure of goodness of fit of the solutions. Several data structures and matrices were used to record the directions and locations of the molecules. These provided the model the 2D topology. The Traveling Salesperson Problem (TSP) was used as a working example. The performance of the model in finding a solution for the TSP was compared to the performance of a topology-less model. Experimental results show that the 2D model performs better than the topology-less one.