A Variable-Length Chromosome Evolutionary Algorithm for Reversible Circuit Synthesis

A variable-length chromosome evolutionary algorithm for reversible circuit synthesis (VLEA RC) is presented to improve the quality of solutions in terms of quantum cost. The synthesis problem is formulated as a minimization problem with an equality constraint. To begin with, a modified stochastic ranking method for constraint handling is devised. This gives a better balance between decreasing the constraint violation and increasing the objective value through the use of parsimony pressure. Then, a periodic population update mechanism is applied when the evolution process stagnates. This mechanism employs heuristic information extracted from the positive polarity Reed-Muller expansion of the reversible specification. This can improve the feasible ratio and reduce the search space effectively. Our design is tested on several widely used benchmarks with circuit size varying from 4 to 30 inputs. The results show that the proposed method can find high quality solutions for the tested benchmarks as well as improve the circuit size that can be handled compared to previous evolutionary methods.