This paper presents a new generalized cellular automata (GCA) approach to effectively solve a class of optimization problems subject to a binary constraint matrix. In contrast to the Hopfield-type neural network (HNN) and cellular neural network (CNN), the proposed GCA approach has the pyramid architecture and evolutionary dynamics related to multi-granularity macro-cells. This paper discusses the GCA?s dynamics, algorithm and properties. The simulations on the travelling salesman problems (TSP) and the fast packet switching problems (FPSP) show that the GCA approach has advantages over the HNN and CNN methods in terms of the solution quality, optimal ratio, convergence speed, real-time performance, interconnection complexity, and parameter selection.