Investigating Gate-Level Evolutionary Development of Combinational Multipliers Using Enhanced Cellular Automata-Based Model

Cellular automata represent a computational model that is based on updating the states of the cells, that are arranged in a regular structure, by means of local interactions between the cells. Cellular automata have often been utilized as a developmental model in engineering areas to solve many complex problems. In the area of the evolutionary algorithms, cellular automata can be applied as an indirect mapping between genotypes and phenotypes. In the recent years, this approach has successfully been applied on the
evolutionary development of digital circuits at the gate level. Combinational multipliers represent a class of circuits that is usually considered as hard task for the design using the evolutionary techniques. In our previous research regarding
the cellular automata-based development, 2x2-bit multipliers were successfully evolved using this approach. Combinational multipliers have been chosen in this paper to demonstrate capabilities of an advanced developmental system that allows to apply cellular automata of different sizes in order to design larger instances of this kind of circuits. In the experiments presented herein, the 2x3-bit and 3x3-bit multipliers will be considered which represent the first case when such instances of multipliers have been successfully developed at the gate level using cellular automata. The proposed developmental model is investigated in detail with respect to the success rate of the evolutionary experiments for different experimental setups (such as the cellular automata size, the number of cell states and developmental steps). Moreover, it will be demonstrated that different ways of connections of the circuit outputs can be utilized without a significant influence on the successfulness of the evolutionary process.