Evsutin O.O.  

Cellular automaton with objective function

This work introduces a modification of the classical model of cellular automata [1, 2], which dynamics designed to solve the continuous optimization problem. To do this in the cellular automaton model added objective function of n variables and alphabet internal states is modified as follows: the cells states adopted an n-dimensional vector with integer label.
This model named cellular automata with objective function. It is no longer a discrete, but retains properties locality and uniformity inherent in of a cellular automaton.
In the work studied the dynamics of cellular automata with the objective function in the choosing different local transition rules with deterministic and stochastic nature.
Based on introduced model obtained continuous optimization algorithms. They are in class of stochastic algorithms because utilize random variables in the cellular automaton with the objective function growing process.
Experiments indicate proposed algorithms is comparable by the efficiency with other continuous optimization algorithms, based on cellular automaton approach [3].
The project has been supported by the Ministry of Education and Science of the Russian Federation in the framework of the base part of state order TUSUR 2015 (project № 3657).

1. Kudrjavtzev V.B., Podkolzin A.S., Bolotov A.S. The foundations of the theory of homogeneous structures. Moscow: Nauka, 1990. P. 296. (In Russian. Osnovy teorii odnorodnyh struktur).
2. Bandman O.L. Discrete models of physical-chemical processes // Applied discrete mathematics. 2009. Iss. 3. P. 33–49. (In Russian. Diskretnoe modelirovanie fiziko-himicheskih processov).
3. Vafashoar R., Meybodi M.R., Momeni Azandaryani A.H. CLA-DE: a hybrid model based on cellular learning automata for numerical optimization // Applied Intelligence. 2012. V. 36, iss. 3. P. 735–748.

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