Optimization Algorithms, Distributed Computing and Intelligence

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 10 July 2025 | Viewed by 367

Special Issue Editor


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Guest Editor
Academy of Mathematics and Systems Science of the Chinese Academy of Sciences (CAS), Beijing, China
Interests: machine learning; AI4Science; optimization; statistical learning

Special Issue Information

Dear Colleagues,

The study of optimization algorithms such as gradient descent has a long history. Nowadays, they are widely applied in machine learning, especially in deep learning, where their analysis encounters new challenges. Theoretically, new research topics include understanding the optimization algorithms’ performance on non-linear models such as deep neural networks and the implicit bias of different optimizers, related to generalization and intelligence. In practice, issues facing deep learning, especially large models, that are worth studying include how to scale hyperparameters efficiently and design robust model optimizers.

We seek papers on insightful approaches to analyzing optimization algorithms, distributed computing intelligence in deep learning and large language models, and any other novel method for advancing these models.

Dr. Qi Meng
Guest Editor

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Keywords

  • non-convex optimization
  • optimization algorithms in deep learning
  • implicit bias
  • large-scale optimization
  • stochastic methods in optimization

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Published Papers (1 paper)

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Research

35 pages, 6933 KiB  
Article
Matrix-Based ACO for Solving Parametric Problems Using Heterogeneous Reconfigurable Computers and SIMD Accelerators
by Vladimir Sudakov and Yuri Titov
Mathematics 2025, 13(8), 1284; https://doi.org/10.3390/math13081284 - 14 Apr 2025
Viewed by 259
Abstract
This paper presents a new matrix representation of ant colony optimization (ACO) for solving parametric problems. This representation allows us to perform calculations using matrix processors and single-instruction multiple-data (SIMD) calculators. To solve the problem of stagnation of the method without a priori [...] Read more.
This paper presents a new matrix representation of ant colony optimization (ACO) for solving parametric problems. This representation allows us to perform calculations using matrix processors and single-instruction multiple-data (SIMD) calculators. To solve the problem of stagnation of the method without a priori information about the system, a new probabilistic formula for choosing the parameter value is proposed, based on the additive convolution of the number of pheromone weights and the number of visits to the vertex. The method can be performed as parallel calculations, which accelerates the process of determining the solution. However, the high speed of determining the solution should be correlated with the high speed of calculating the objective function, which can be difficult when using complex analytical and simulation models. Software has been developed in Python 3.12 and C/C++ 20 to study the proposed changes to the method. With parallel calculations, it is possible to separate the matrix modification of the method into SIMD and multiple-instruction multiple-data (MIMD) components and perform calculations on the appropriate equipment. According to the results of this research, when solving the problem of optimizing benchmark functions of various dimensions, it was possible to accelerate the method by more than 12 times on matrix SIMD central processing unit (CPU) accelerators. When calculating on the graphics processing unit (GPU), the acceleration was about six times due to the difficulties of implementing a pseudo-random number stream. The developed modifications were used to determine the optimal values of the SARIMA parameters when forecasting the volume of transportation by airlines of the Russian Federation. Mathematical dependencies of the acceleration factors on the algorithm parameters and the number of components were also determined, which allows us to estimate the possibilities of accelerating the algorithm by using a reconfigurable heterogeneous computer. Full article
(This article belongs to the Special Issue Optimization Algorithms, Distributed Computing and Intelligence)
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