10.14489/vkit.2021.02.pp.003-012

DOI: 10.14489/vkit.2021.02.pp.003-012

Матренин П. В.
МЕТОД РАЗДЕЛЕНИЯ ОБЛАСТИ ДОПУСТИМЫХ ЗНАЧЕНИЙ ДЛЯ УВЕЛИЧЕНИЯ ВАРИАТИВНОСТИ ТЕСТОВЫХ ЗАДАЧ НЕПРЕРЫВНОЙ ОПТИМИЗАЦИИ
(c. 3-12)

Аннотация. Рассмотрены вопросы создания тестовых задач непрерывной оптимизации с нелинейными ограничениями и разбиением области допустимых решений. Предложен метод разбиения области допустимых решений с помощью многомерной сетки запрещенных решений. Метод прост в реализации и практически не влияет на вычислительную сложность задач. Проведено исследование на ряде широко используемых тестовых задач непрерывной оптимизации и популяционных алгоритмов.

Ключевые слова: непрерывная оптимизация; условная оптимизация; популяционные алгоритмы; генетический алгоритм; алгоритм роя частиц.

Matrenin P. V.
METHOD FOR SPLITTING THE FEASIBLE REGION TO INCREASE THE VARIABILITY OF CONTINUOUS OPTIMIZATION TEST PROBLEMS
(pp. 3-12)

Abstract. The solution of optimization problems is essential for the design and control of technical systems. The optimization problem arising in practice has a high dimension, nonlinear criteria, and constraints. There are a lot of continuous optimization tasks for testing and research of optimization algorithms performance. These tasks have a convex range of acceptable values limited to a specified range for each parameter. The problem of generating test multidimensional continuous optimization tasks with nonlinear constraints and splitting the feasible region is considered. A method was proposed for splitting the feasible region by separate domains using the multidimensional grid of forbidden solutions. As a result, the problem acquires properties closer to optimizing technical systems with complex constraints. The method allows creating an unlimited number of test optimization problems, which can be used to research and develop optimization algorithms. The method is simple to implement, and the impact on the computational complexity of tasks is insignificant. Research has been carried out on four widely used continuous single-objective optimization test functions, with the Genetic algorithm and the Particle Swarm Optimization algorithm. It is shown that the proposed method has an influence on the process of solving multidimensional continuous optimization problems by population algorithms and on the dependence of the accuracy of the algorithm on its heuristic coefficients.

Keywords: Continuous optimization; Constrained optimization; Population algorithms; Genetic algorithm; Particle swarm optimization.

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П. В. Матренин (Новосибирский государственный технический университет, Новосибирск, Россия; Научно-технический университет «Сириус», Сочи, Россия) E-mail: Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript

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P. V. Matrenin (Novosibirsk State Technical University, Novosibirsk, Russia; Sirius University of Science and Technology, Sochi, Russia) E-mail: Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript

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Eng

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12. Grosan C., Abraham A. A. (2009). Novel Global Optimization Technique for High Dimensional Functions. International Journal of Intelligent Systems, Vol. 24, (4), pp. 421 – 440.
13. Abiyev R. H., Tunay M. (2015). Optimization of High-Dimensional Functions through Hypercube Evaluation. Computational Intelligence and Neuroscience, Article ID 967320.
14. Cho H., Olivera F., Guikema S. D. (2014). A Derivation of the Number of Minima of the Griewank Function. Applied Mathematics and Computation, Vol. 204, (2), pp. 694 – 701.
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