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Swarm intelligence optimization algorithm has been proved to perform well in the field of parameter optimization. In order to further improve the performance of intelligent optimization algorithm, this paper proposes an improved and adaptive tunicate swarm algorithm (IMATSA) based on tunicate swarm algorithm (TSA). IMATSA improves TSA in the following four aspects: population diversity, local search convergence speed, jumping out of local optimal position, and balancing global and local search. Firstly, IMATSA adopts Tent map and quadratic interpolation to initialize population and enhance the diversity. Secondly, IMATSA uses Golden-Sine algorithm to accelerate the convergence of local search. Thirdly, in the process of global development, IMATSA adopts Levy flight and the improved Gauss disturbance method to adaptively improves and coordinates the ability of global development and local search. Then, this paper verifies the performance of IMATSA based on 14 benchmark functions experiment, ablation experiment, parameter optimization experiments of Support Vector Machine (SVM) and Gradient Boosting Decision Tree (GBDT), Wilcoxon signed rank test and image multi-threshold segmentation experiment with the performance metrics are convergence speed, convergence value, significance level P-value, Peak Signal-to-Noise Ratio (PSNR) and Standard Deviation (STD). Experimental results show that IMATSA performs better in three kinds of benchmark functions; each component of IMATSA has a positive effect on the performance; IMATSA performs better in parameter optimization experiments of SVM experiment and GBDT; there is significant difference between IMATSA and other algorithms by Wilcoxon signed rank test; in image segmentation, the performance is directly proportional to the number of thresholds, and compared with other algorithms, IMATSA has better comprehensive performance. [ABSTRACT FROM AUTHOR]

Abstract: Leonard and Pellikaan developed the qth power algorithm to compute module bases for the integral closure of the polynomial ring in a class of function fields. In this paper, their algorithm is adapted to efficiently obtain an -basis for a class of Riemann–Roch spaces without having to compute the entire integral closure. This reformulation allows one to determine the complexity of the algorithm. Further, we obtain a simple characterization of the integral closure. [Copyright &y& Elsevier]

In order to improve the accuracy and performance of traditional image threshold segmentation algorithm, this paper proposes a multithreshold segmentation method named improved Harris hawk optimization (IMHHO). Firstly, IMHHO adopts Tent map and elite opposition-based learning to initialize population and enhance the diversity. Secondly, IMHHO uses quadratic interpolation to generate new individuals and enhance the local search ability. Finally, IMHHO adopts improved Gaussian disturbance method to disturb optimal solution, which coordinates the local and global search ability. Then, the performance of IMHHO is tested based on 14 benchmark functions. In image segmentation, different algorithms are tested to compare the comprehensive performance based on Otsu and Renyi entropy. Experiments show that IMHHO performs better in the three kinds of benchmark functions; the segmentation effect is directly proportional to the number of thresholds; compared with other algorithms, IMHHO has better comprehensive performance. [ABSTRACT FROM AUTHOR]