Comparing the efficiency of some modifications of the evolutionary strategy algorithm

The article introduces the results of comparing the efficiency of the stochastic global optimization searching methods and considers some well-known modifications of the evolutionary strategy algorithm. We describe a basic algorithm and its modifications: (α + β)-algorithm, (α+ β)-algorithm with the mutation width parameter self-adapting, αβ-algorithm, αβ-algorithm with the mutation width parameter self-adapting, coevolutionary algorithm. The article examines the efficiency of the mentioned modifications on the Rosenbrock one-extremum ravine function and Rastrigin multiextremal function. Efficiency comparison has been conducted according to such parameters as the achieved value of the objective function, the probability of the global extremum localization and the number of the required tests. The results of the investigation can be used when choosing the most efficient optimization algorithm.

References

[1] Karpenko A.P. Sovremennye algoritmy poiskovoy optimizatsii [Modern search optimization algorithms]. Moscow, Bauman Press, 2014, 446 p.

[2] Karpenko A.P. Hybrid population algorithms for parametrical optimization of design decisions. Informatsionnye tekhnologii [Information Technologies], 2013, no. S12, pp. 6–15.

[3] Andrusenko A.S., Karpenko A.P., Sokolyanskiy V.V., Yamchenko Yu.V. Sovremennye metody poiskovoy optimizatsii v zadache opredeleniya parametrov intellektual’nogo kapitala [Modern search optimization algorithms in problem of intellectual capital characterization]. Moscow, Sputnik+, 2017, 101 p.

[4] Bäck T. Evolutionary algorithms in theory and practice: evolution strategies, evolutionary programming, genetic algorithms. Oxford university press, 1996, 314 p.

[5] Rechenberg I. Cybernetic solution path of an experimental problem. Royal Aircraft Establishment Transl., Farnborough, 1965, no. 1122, 24 p.

[6] Rechenberg I. Evolutionsstrategie Optimierung technischer Systeme nach Prinzipien der biologishen Evolution. Holzmann-Froboog, 1973, 170 p.

[7] Eiben Á.E., Hinterding R., Michalewicz Z. Parameter control in evolutionary algorithms. IEEE Transactions on evolutionary computation, 1999, vol. 3, no. 2, pp. 124–141.

[8] Bäck T. Self-adaptation in genetic algorithms. Proc. 1st European conf. on Artificial Life, MIT Press, 1992, pp. 263–271.

[9] Rosenbrock H. An automatic method for finding the greatest or least value of a function. The Computer Journal, 1960, vol. 3, no. 1, pp. 175–184.

[10] Rastrigin L.A. Sistemy ekstremal’nogo upravleniya [Extremal control systems]. Moscow, Nauka publ., 1974, 630 p.