We believe that the physical world can be described mathematically by the interplay of geometry and dynamics. Here in this thesis we investigate the effect of geometry and dynamics in two areas: Damage Spreading in Complex Networks and the implement and performance of Quasi-Parallel Genetic Algorithms (QPGA) using different communication topologies. We can see that although the two topics seem unrelated, topology and dynamics play crucial roles in both systems. In simple damage spreading, we focus on the effect of complex network structures; for more complicated damage spreading models, the effect of different dynamics is discussed. In QPGA, we show that both the geometry of the communication network structure (topology) and the chromosome exchange rules (dynamics) greatly influence the...[ Read more ]

We believe that the physical world can be described mathematically by the interplay of geometry and dynamics. Here in this thesis we investigate the effect of geometry and dynamics in two areas: Damage Spreading in Complex Networks and the implement and performance of Quasi-Parallel Genetic Algorithms (QPGA) using different communication topologies. We can see that although the two topics seem unrelated, topology and dynamics play crucial roles in both systems. In simple damage spreading, we focus on the effect of complex network structures; for more complicated damage spreading models, the effect of different dynamics is discussed. In QPGA, we show that both the geometry of the communication network structure (topology) and the chromosome exchange rules (dynamics) greatly influence the performance of such parallel optimization algorithms.

My thesis is organized in the following way. In Part I, I wil first give an introduction on the topics. In Part II, I will cover my research in Damage Spreading in Complex Networks, and in Part III the research on Quasi-parallel Genetic Algorithms is introduced. Finally I will give some discussions and conclusions in Part IV.