A Methodology for Optimizing the Objective Function in a High-dimensional Space Using the Swarm Intelligence Algorithm

A formal definition of the particle swarm method and the software algorithm based on it is given. The influence of the algorithm parameters on the global minimum search efficiency is studied using the example of a multiparameter function. The best parameters that allow achieving an average error from 0.05 % for a two-parameter function to 0.13 % for a function with 5 parameters are determined. It is found that increasing the swarm size and applying an increased number of iterations in a single numerical calculation are not the most effective means of increasing accuracy. It is shown that several sequential independent calculations, from the results of which the best one is selected, make the most sense. In this case, the required error of up to 1 % was guaranteed to be achieved by using 3 sequential calculations with a swarm size of 15 particles and 500 iterations on each calculation. High-precision calculations with an error of no more than 0.1 % required 10 sequential calculations with a swarm size of 30 particles and 1000 iterations in the calculation, the total amount of computational work was 0.3 million conditional iterations. When using a single calculation, an error of 0.13 % was achieved when performing at least 1.25 million conditional iterations.