Matrix-Based ACO for Solving Parametric Problems Using Heterogeneous Reconfigurable Computers and SIMD Accelerators

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 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.