# APPLICATION PARTICLE SWARM ALGORITHM TO MINIMIZE THE COST OF CONDUCTING MULTIVARIATE EXPERIMENT

## Authors

• N. D. Koshevoy National Aerospace University named after M. E. Zhukovskoho “HAI”, Kharkiv, Ukraine, Ukraine
• A. A. Beliaieva National Aerospace University named after M. E. Zhukovskoho “HAI”, Kharkiv, Ukraine, Ukraine

## Keywords:

method optimization, swarm particle, experimental design, cost, optimal plan

## Abstract

Context. The actual problem of obtaining a sequence of experiments in the conduct of a full factor experiment ensuring its minimum cost
has been solved.
Objective – is to create a method for optimizing multifactor experimental plans using an optimization algorithm for the particle swarm.
Method. A method is proposed for constructing an optimal experiment design matrix for the cost of implementation using the particle
swarm algorithm. The particle swarm method is based on modeling the behavior of the particle population in the parameter space of the
optimization problem. In the beginning, the number of factors and the cost of the transition for each level of factors are introduced. Then,
taking into account the input data, a composite matrix of experiment planning is formed. The particles are scattered randomly across the
entire composite experiment design matrix and each particle has a random velocity vector. After that, the particles begin to move along the
rows and columns of the matrix. At each point where the particle visited, the value of the experiment is calculated. In this case, each particle
remembers which (and where) the best value of the cost of the experiment, she personally found and where the point is located, which is the best among all the points that explored the particles. At each iteration, the particles correct their velocity (module and direction) in order to be closer to the best point on the one hand, which she found herself and, at the same time, to approach the point that is currently globally
better. After a certain number of iterations, the particles are collected near the best point. Then the current coordinate of each particle is
corrected. After this, the cost of the experiment is calculated at each new point, each particle checks whether the new coordinate has become
the best among all the points where it visited. Then, among all the new points, we check whether we have found a new globally better point,
and if found, remember its coordinates and the value of the cost of conducting the experiment in it. Then the gain is calculated in comparison
with the initial cost of the experiment.
Results. The software that implements the proposed method is developed, which was used in carrying out computational experiments to
study the properties of the method.
Conclusions. The conducted experiments confirmed the efficiency of the proposed method and the software that implements it, and also
allow them to be recommended for application in practice when constructing optimal experimental design matrices.

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