APPLICATION PARTICLE SWARM ALGORITHM TO MINIMIZE THE COST OF CONDUCTING MULTIVARIATE EXPERIMENT
Keywords:method optimization, swarm particle, experimental design, cost, optimal plan
AbstractContext. 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.
Hoskins D. S. Combinatorics and Statistical Inferecing, Applied
Optimal Designs, 2007, Vol. 4, pp. 147–179.
Morgan J. P. Association Schemes: Designed Experiments, Algebra
and Combinatorics, Journal of the American Statistical
Association, Vol. 100, No. 471, 2005, pp. 1092–1093.
Bailey R. A., Cameron P. G. Combinatorics of optimal designs,
Surveys in Combinatorics, Vol. 365, 2009, pp. 19–73.
Koshevoj N. D., Kostenko E. M. Optimal’noe po stoimostnym
i vremennym zatratam planirovanie jeksperimenta. Poltava,
izdatel’ Shevchenko R. V., 2013, 317 p.
Koshevoy N. D., Beliaieva A. A. Primenenie algoritma tabupoiska
dlja minimizacii stoimosti provedenija mnogofaktornogo
jeksperimenta. Kiev, Zbіrnik naukovih prats VIyskovogo Institutu
KiYivskogo natsIonalnogo unIversitetu Im. T. G. Shevchenka,
, No. 53, pp. 85–91.
Poli R. An analysis of publications on particle swarm optimisation
applications. Technical Report CSM-469 (Department of
Computer Science, University of Essex, UK) – may 2007.
Poli R. Analysis of the publications on the applications of particle
swarm optimisation, Journal of Artificial Evolution and
Applications, 2008, pp. 1–10. DOI:10.1155/2008/685175
Min-Yuan Cheng, Kuo-Yu Huang and Hung-Ming Chen (2012),
K-means Particle Swarm Optimization with Embedded Chaotic
Search for Solving Multidimensional Problems, Applied
Mathematics and Computation, Vol. 219, No. 6, pp. 3091––
Shafiq Alam, Gillian Dobbie, Yun Sing Koh, Patricia Riddle and
Saeed Ur Rehman, Research on Particle Swarm Optimization
based clustering: a systematic review of literature and techniques,
Swarm and Evolutionary Computation, 2014, Vol. 17, No. 8,
Gal’chenko V. Ja, Jakimov A. N. Populjacionnye
metajevresticheskie algoritmy optimizacii roem chastic : Uchebnoe
posobie. Cherkassy, FLP Tretjakov A. N., 2015, 160 p.
How to Cite
Copyright (c) 2018 N. D. Koshevoy, A. A. Beliaieva
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Creative Commons Licensing Notifications in the Copyright Notices
The journal allows the authors to hold the copyright without restrictions and to retain publishing rights without restrictions.
The journal allows readers to read, download, copy, distribute, print, search, or link to the full texts of its articles.
The journal allows to reuse and remixing of its content, in accordance with a Creative Commons license СС BY -SA.
Authors who publish with this journal agree to the following terms:
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License CC BY-SA that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.