回転不変性を考慮した超球交叉によるDifferential Evolutionの改良

抄録

Crossover is one of the most known nature inspired operations in heuristic optimization algorithms. It was traditionally inspired by the evolution of species, and it is well known for the capability of solving discrete optimization problems, which use integer valued vector. However, in recent years, algorithms such as Differential Evolution use it to solve continuous optimization problem, regardless of the fact that this usage is apart from the way species evolve using DNA sequence. This kind of crossover operation in continuous space creates new points in axis-wise directions, thus it is known that the performance of those algorithms using continuous crossover have different performance when we rotate the coordinate of an optimization problem. This is because uniform crossover is not a rotation invariant operation. In this paper, we consider of using rotationally invariant crossover called hypersphere crossover. However, since this crossover may not adopt to ill-conditioned problem with fixed radius, we propose scaling parameter and its tuning rule to change the radius of the hypersphere to compensate for the problem. We compare our proposal with traditional uniform crossover, and other rotation invariant crossover operations using many benchmarks. We use pair-wises ranked t-test to statistically verify the advantage of our proposal.