A 3-Step Cartesian Genetic Programming for Designing Combinational Logic Circuits with Multiplexers

The design of digital circuits has been widely investigated in the literature but the evolution of complex combinational logic circuits is not an easy task for Cartesian Genetic Programming (CGP). We propose here a new approach in order to increase the capacity of CGP in finding feasible circuits (those with the same response of the truth table). The proposed procedure uses a 3-step evolution by coupling a 2-input multiplexer in each circuit's output. These multiplexers divide the truth table and the similarity between its inputs is maximized. Thus, don't-care situations are generated for the controls of the multiplexers, making the evolution of CGP easier. Also, a variant of the standard evolutionary strategy commonly adopted in CGP is proposed, where the following procedures are considered: (i) the Single Active Mutation (SAM), (ii) the Guided Active Mutation (GAM), and (iii) a crossover. The proposed methods are applied to combinational logic circuits with multiple outputs and the results obtained are compared to those found by a standard CGP with SAM. Benchmark problems with inputs from 9 to 12 are used in the computational experiments, and the objective is to find circuits that match the truth tables. The results show that (i) the combination of crossover, SAM, and GAM increases the performance of CGP, and (ii) the proposed 3-step method is the only technique tested here able to obtain feasible solutions in all independent runs.