Reducing Epistasis in Combinatorial Problems by Expansive Coding

This paper describes a new technique for tackling highly epistatic combinatorial optimization problems. Rather than having a simple representation, simple operators, a simple fitness function, but a highly epistatic search space, this technique is intended to spread the problem’s complexity more evenly. Using our new technique, known as expansive coding, the representation, operators and fitness function become more complicated, but the search space becomes less epistatic, and therefore easier for a GA to tackle. In effect, the combinatorial task is changed to a function optimization one. We demonstrate how this technique can be applied in the field of arithmetic algorithm design/electronic circuit simplification. In the design of a multiplier for quaternion numbers, consistently good results are obtained.