On gray-coded binary representation for supporting a (repair-by-interpolation) genetic operator for constrained Optimization Problems

A new genetic operator is proposed in the context of genetic algorithms that are applied to constrained optimization problems with binary decision variables. A solution is said to be feasible if it satisfies the constraints, and infeasible otherwise. Provided the two inputs of the operator are of differing feasibility, the operator outputs a infeasible/feasible pair that differ by only a single bit. This is valuable because any optimal solution is within a single bit of transitioning between infeasibility and feasibility, unless the constraints are irrelevant. The operator is implemented by binary search along a path connecting the two inputs. The path is a portion of a randomly selected Gray code (an ordered list of all binary strings having the property that adjacent strings differ by a single bit).