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In the Artificial Bee Colony (ABC) algorithm, the employed bee and the onlooker bee phase involve updating the candidate solutions by changing a value in one dimension, dubbed one-dimension update process. For some problems which the number of dimensions is very high, the one-dimension update process can cause the solution quality and convergence speed drop. This paper proposes a new algorithm, using reinforcement learning for solution updating in ABC algorithm, called R-ABC. After updating a solution by an employed bee, the new solution results in positive or negative reinforcement applied to the solution dimensions in the onlooker bee phase. Positive reinforcement is given when the candidate solution from the employed bee phase provides a better fitness value. The more often a dimension provides a better fitness value when changed, the higher the value of update becomes in the onlooker bee phase. Conversely, negative reinforcement is given when the candidate solution does not provide a better fitness value. The performance of the proposed algorithm is assessed on eight basic numerical benchmark functions in four categories with 100, 500, 700, and 900 dimensions, seven CEC2005’s shifted functions with 100, 500, 700, and 900 dimensions, and six CEC2014’s hybrid functions with 100 dimensions. The results show that the proposed algorithm provides solutions which are significantly better than all other algorithms for all tested dimensions on basic benchmark functions. The number of solutions provided by the R-ABC algorithm which are significantly better than those of other algorithms increases when the number of dimensions increases on the CEC2005’s shifted functions. The R-ABC algorithm is at least comparable to the state-of-the-art ABC variants on the CEC2014’s hybrid functions. [ABSTRACT FROM AUTHOR]

In this paper, the Hager and Zhang (HZ) conjugate gradient (CG) method and the modified HZ (MHZ) CG method are presented for large-scale nonsmooth convex minimization. Under some mild conditions, convergent results of the proposed methods are established. Numerical results show that the presented methods can be better efficiency for large-scale nonsmooth problems, and several problems are tested (with the maximum dimensions to 100,000 variables). [ABSTRACT FROM AUTHOR]