An Evolution Strategy Using a Continuous Version of the Gray-Code Neighbourhood Distribution

We derive a continuous probability distribution which generates neig- hbours of a point in an interval in a similar way to the bitwise mutation of a Gray code binary string. This distribution has some interesting scale-free properties which are analogues of properties of the Gray code neighbourhood structure. A simple (1+1)-ES using the new distribution is proposed and evaluated on a set of benchmark problems, on which it performs remarkably well. The critical parame- ter is theprecision of the distribution, which corresponds to the string length in the discrete case. The algorithm is also tested on a difficult real-world problem from medical imaging, on which it also performs well. Some observations concerning the scale-free properties of the distribution are made, although further analysis is required to understand why this simple algorithm works so well.