DEにおけるExponential Crossoverの再評価

抄録

Differential Evolution (DE) is an Evolutionary Algorithm (EA) that was primarily designed for real parameter optimization problems. Despite its relative simplicity, DE has been shown to be competitive with more complex optimization algorithms, and has been applied to many practical problems. The two most common type of crossover in DE are binomial crossover, analogous to uniform crossover in GA's, and exponential crossover, analogous to 1 or 2 point crossover in GA's. Although binomial crossover appears to be more frequently used in state-of-the-art DEs, a number of recent papers have reported successful usage of exponential crossover. In this paper, we demonstrate that exponential crossover exploits an unnatural feature of some widely used synthetic benchmarks such as the Rosenbrock function - dependencies between adjacent variables. However, there is no particular reason that adjacent variables should have such dependencies in real-world, black-box optimization problems, and such dependencies are an artifact of synthetic benchmarks. We show that this unnatural problem structure can be easily eliminated using the randomization procedure and exponential crossover performs quite poorly on benchmarks without this artificial feature for standard DE as well as state-of-the-art adaptive DE. We also show that shuffled exponential crossover, which removes this kind of search bias, significantly outperforms exponential crossover.