This chapter introduces the basic concepts and notation of genetic algorithms (GA) and simulated annealing (SA), which are two basic search methodologies that can be used for modelling and simulation of complex non-linear dynamical systems. It presents the basic concepts and notation of Dynamical Systems and Fractal theory. Dynamical Systems theory gives the general framework for treating non-linear systems and enables the identification of the different dynamical behaviors that can occur for a particular dynamic system. Fractal theory gives the powerful concepts and techniques that can be used to measure the complexity of geometrical objects. GAs and SA have been used extensively for both continuous and discrete optimization problems. GAs are derivative-free optimization methods based on the concepts of natural selection and evolutionary processes. SA is another derivative-free optimization method that has drawn much attention for being as suitable for continuous as for discrete optimization problems.