Evolutionary optimization methods for high-dimensional complex systems: Theory, algorithm, and application to rainfall-runoff models

With the growth of computer capability, direct search methods for global optimization have been implemented to address a wide range of problems in science and engineering owing to their outstanding features: (1) require no mathematic modeling of the objective systems or their derivatives, (2) cope with practical difficulties such as non-convexity, discontinuity, multimodality, and (3) perform high efficiency and efficacy in practice. In particular, the last two decades have witnessed a boom of evolutionary computation, an active branch of direct search which produces a population of particles to probe the search space. Many evolutionary algorithms have been developed, catalyzed by the rapid expansion of their applications in real-world problems. On the other hand, evolutionary algorithms have been frequently unsuccessful in solving high-dimensional problems in practical applications. The solution for high-dimensional optimization remains a major challenge in research community of evolutionary computation. This dissertation is dedicated to the investigation of theoretical obstacles for evolutionary search strategy in high-dimensional spaces and the development of algorithms to break through these barriers. We have identified three major causes that are responsible for the inefficiency and/or ineffectiveness of evolution search in high-dimensional spaces: (1) the volume of the search space increases exponentially with the increase of dimensionality, which fatigues strategies relying too much on stochastic process and favors schemes making good use of information from the response surface of the objective function; (2) failure to keep the search proceeding in the full space spanned by all parameters to be optimized is not a trivial issue in high-dimensional problems and special procedures are needed to assure it; and (3) Bound violation is prevailing in high-dimensional search and therefore proper bound handling strategy is of great importance. A new strategy, SCPCA (Shuffled Complex evolution with Principal Component Analysis), is designed to deal with these difficulties. Examinations of this strategy on six sophisticated composition benchmark functions demonstrate that SCPCA surpasses the two most popular algorithms, PSO and DE, on high-dimensional problems. Applying the SCPCA strategy to parameter calibration of the National Weather Service Sacramento-Soil Moisture Account (SAC-SMA) model produces parameter values and parameter uncertainty distributions compared with the previous studies.