A Solution to the Crucial Problem of Population Degeneration in High-Dimensional Evolutionary Optimization

Three popular evolutionary optimization algorithms are tested on high-dimensional benchmark functions. An important phenomenon responsible for many failures - “population degeneration” - is discovered. That is, through evolution, the population of searching particles degenerates into a subspace of the search space, and the global optimum is exclusive from the subspace. Subsequently, the search will tend to be confined to this subspace and eventually miss the global optimum. Principal components analysis (PCA) is introduced to discover population degeneration and to remedy its adverse effects. The experiment results reveal that an algorithm's efficacy and efficiency are closely related to the population degeneration phenomenon. Guidelines for improving evolutionary algorithms for high-dimensional global optimization are addressed. An application to highly nonlinear hydrological models demonstrates the efficacy of improved evolutionary algorithms in solving complex practical problems.