The life of each person, as well as society, is determined by the decisions made. Each such decision is aimed at optimizing social, economic, technological or technical processes. The use of computer science and computer technology to solve optimization problems is the basis of modern digital transformations. A lot of practical problems are optimization problems with or without constraints. The objective functions in such problems are in most cases complex, non-differentiable and polyextreme. Application of classical methods of continuous and discrete optimization in this case is impossible. In such cases, evolutionary algorithms, which do not require restrictions on the objective function and guarantee only probabilistic convergence to the global optimum, are used. Usually, such algorithms converge slowly, because a significant number of steps in them are performed in the wrong direction. A feature of the known evolutionary algorithms is that one or two parent solutions are used to generate potential offspring solutions. We propose methods in which a larger number of offsprings are used for the generation of offsprings, which allows considering more information about the features of the optimum search area and speeds up the search process. The advantages of the proposed methods are a deeper study of the area in the neighborhood of promising solutions and a reduction in the number of algorithm steps in unpromising directions. There are the Method of Deformed Stars and the Method of Fractal Structuring. These methods are parametric and allow for improvement. They can be used to solve placement and packaging problems, traveling salesman problem, and any objective function optimization problems.

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New Evolutionary Methods for Solving Optimization Problems in the Digital Transformation Processes

  • Vitaliy Snytyuk,
  • Nataliia Tmienova

摘要

The life of each person, as well as society, is determined by the decisions made. Each such decision is aimed at optimizing social, economic, technological or technical processes. The use of computer science and computer technology to solve optimization problems is the basis of modern digital transformations. A lot of practical problems are optimization problems with or without constraints. The objective functions in such problems are in most cases complex, non-differentiable and polyextreme. Application of classical methods of continuous and discrete optimization in this case is impossible. In such cases, evolutionary algorithms, which do not require restrictions on the objective function and guarantee only probabilistic convergence to the global optimum, are used. Usually, such algorithms converge slowly, because a significant number of steps in them are performed in the wrong direction. A feature of the known evolutionary algorithms is that one or two parent solutions are used to generate potential offspring solutions. We propose methods in which a larger number of offsprings are used for the generation of offsprings, which allows considering more information about the features of the optimum search area and speeds up the search process. The advantages of the proposed methods are a deeper study of the area in the neighborhood of promising solutions and a reduction in the number of algorithm steps in unpromising directions. There are the Method of Deformed Stars and the Method of Fractal Structuring. These methods are parametric and allow for improvement. They can be used to solve placement and packaging problems, traveling salesman problem, and any objective function optimization problems.