Genetic Algorithms Applied to Nonlinear and Complex Domains Genetic Algorithms Applied to Nonlinear and Complex Domains

The dissertation, titled \Genetic Algorithms Applied to Nonlinear and Complex Do-mains", describes and then applies a new class of powerful search algorithms (GAs) to certain domains. GAs are capable of solving complex and nonlinear problems where many parameters interact to produce a ``nal' result such as the optimization of the laser pulse in the interaction of an atom with an intense laser eld. GAs can very ef-ciently locate the global maximum by searching parameter space in problems which are unsuitable for a search using traditional methods. In particular, the dissertation contains new scientiic ndings in two areas. First, the dissertation examines the interaction of an ultra-intense short laser pulse with atoms. GAs are used to nd the optimal frequency for stabilizing atoms in the ionization process. This leads to a new theoretical formulation, to explain what is happening during the ionization process and how the electron is responding to nite (real-life) laser pulse shapes. It is shown that the dynamics of the process can be very sensitive to the ramp of the pulse at high frequencies. The new theory which is iii formulated, also uses a novel concept (known as the (t,t') method) to numerically solve the time-dependent Schrr odinger equation. Second, the dissertation also examines the use of GAs in modeling decision making problems. It compares GAs with traditional techniques to solve a class of problems known as Markov Decision Processes. The conclusion of the dissertation should give a clear idea of where GAs are applicable, especially in the physical sciences, in problems which are nonlinear and complex, i.e. diicult to analyze by other means.