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Differential evolution (DE) is an efficient and robust evolutionary algorithm (EA), that has been widely and successfully applied to solve global optimization problems in diverse real-world applications. As the population structure has a major influence on the behavior of an EA, effectively incorporating population topology into DE has recently attracted increasing attention. Previous works have shown the effectiveness of different topologies in improving the performance of DE and revealed that different topologies can have different effects on the population’s ability to solve optimization problems. However, the synergy of different topologies for the problems being solved has not been systematically investigated in most DE variants. Moreover, individuals with different fitness values play different roles in guiding the search during the evolutionary process. Nevertheless, the individual-dependent roles are not considered in most DE variants that consider the population topology. To overcome these drawbacks and utilize the information that is derived from the differences between the fitness values of individuals for topology adaption, we propose a multi-topology-based DE (MTDE) algorithm that includes an ensemble of multiple population topologies (MPT), an individual-dependent adaptive topology selection (ITS) scheme, and a topology-dependent mutation (TDM) strategy. In the ensemble of MPT, multiple population topologies with different degrees of connectivity are employed. In the ITS scheme, each individual adaptively selects the topology that is most compatible its role in guiding the search based on its fitness value. In the TDM strategy, the parents for mutation are chosen from the neighborhood of the current individual based on the corresponding topology to generate offspring. The effectiveness of the proposed algorithm is extensively evaluated on a suite of benchmark functions. Experimental results demonstrate the competitive performance of MTDE when compared with other state-of-the-art DE variants and EAs. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of recovering a tensor with missing data. We propose a new model combining the total variation regularization and low-rank matrix factorization. A block coordinate decent (BCD) algorithm is developed to efficiently solve the proposed optimization model. We theoretically show that under some mild conditions, the algorithm converges to the coordinate wise minimizers. Experimental results are reported to demonstrate the effectiveness of the proposed model and the efficiency of the numerical scheme. [ABSTRACT FROM AUTHOR]