To improve the convergence speed of distributed online optimization algorithms, a fast first-order Online Distributed Dual Average optimization (FODD) algorithm was proposed by sequentially adding edges to the underlying network topology. Firstly, aiming at solving the problem of the online distributed optimization to make the selected edge and network model mix quickly by using the method of edge addition, a mathematical model was established and solved by FODD. Secondly, the relationship between network topology designed and the convergence rate of the online distributed dual average algorithm was revealed, which clearly showed that, by improving the algebraic connectivity of the underlying topology network, the Regret bound could also be greatly improved. The Online Distributed Dual Average (ODDA) algorithm was extended from static networks to time-varying networks. Meanwhile, the proposed FODD algorithm was proved to be convergent and the convergence rate was specified. Finally, the results of numerical simulations show that, compared with existing algorithms such as ODDA, the proposed FODD algorithm has better convergence performance.

Some problems of the current load balancing algorithms for distributed systems include:1) The role of each node in the system is fixed, and the system has no adaptability. 2) The load balancing algorithm is not universal. 3) The migration task is too large, and the load balance cycle is too long. To solve these problems, a hybrid load balancing algorithm was proposed. Firstly, a distributed receiving system model was designed, by which the system tasks were divided into three parts:receiving level, handling level and storing level. In receiving level, a home-made transmission protocol was used to improve the reception capability of the system. And then, in the load balancing algorithm, random load migration strategy was used. According to the status of the nodes, the tasks of load were randomly migrated. The problems of long load balance cycle and load moving back were solved by this strategy. Finally, the distributed control node selecting strategy was adopted to make the nodes adaptable. The experimental results show that the average delay in each layer of the system is in milliseconds, and the system load balancing takes less than 3 minutes, which proves that the load balancing mechanism has short load balance cycle and fast response, and can improve the reception capability of the distributed system.

In the traditional Fuzzy C-Means (FCM) clustering algorithm, the initial clustering center is uncertain and the number of clusters should be preset in advance which may lead to inaccurate results. The fuzzy clustering algorithm based on midpoint density function was put forward. Firstly, the stepwise regression thought was integrated as the initial clustering center selection method to avoid convergence from local circulation, and then the number of clusters was determined, finally according to the results, the validity index of fuzzy clustering including overlap degree and resolution was judged to determin the optimal number of clusters. The results prove that, compared with the traditional improved FCM, the proposed algorithm reduces the number of iterations and increases the average accuracy by 12%. The experimental results show that the proposed algorithm can reduce the processing time of clustering, and it is better than the comparison algorithm on the average accuracy and the clustering performance index.