The problem of finding optimal configuration of automated/smart power distribution systems topology is an NP-hard combinatorial optimization problem. It becomes more complex when the time varying nature of loads is taken into account. In this paper, a systematic approach is proposed to determine an optimal long-term reconfiguration schedule. To solve the optimization problem, a novel adaptive fuzzy-based parallel genetic algorithm (GA) is proposed that employs the concept of parallel computing in identifying the optimal configuration of the network. The integration of fuzzy logic into the proposed method enhances the efficiency of the parallel GA by adaptively modifying the migration rates among different processors during the optimization process. A computationally efficient graph encoding method based on Dandelion coding strategy is developed, which automatically generates radial topologies and prevents the construction of infeasible radial networks in the optimization process. In order to consider the dynamic behavior of the load and reduce the load condition scenarios over the year under study, fuzzy C-mean clustering method is utilized. Finally, the performance of the proposed method is demonstrated on a 119-bus distribution network, and is compared with that of conventional single GA and conventional parallel GA.