Synthesis of evolutionary mechanisms in the development of an adaptive optimization algorithm

Y.V. Ivanchuk, O.O. Borysuk

Abstract


The article develops an effective method for solving optimization problems based on the synthesis of evolution ary mechanisms of nature’s development, which are based on the principles of genetic search for the best solu tions. It analyzes evolutionary concepts of biological species development by such well-known scientists as Ch. Darwin, J. Lamarck, Hugo de Vries, K. Popper, and M. Kimura. The key mechanisms for the emergence of new individuals with better adaptation (the best solutions) are identified. Based on the known relevant concepts, the main provisions of the theory of evolution are developed. Corresponding models are constructed, which in turn become computational analogies for the development of evolutionary methods for solving optimization prob lems. An optimization method has been developed based on a genetic algorithm, which is based on the basic operators of evolution: reproduction (selection), crossover, and mutation. A distinctive feature of the proposed approach is the hybridization of the classical genetic algorithm with adaptive mechanisms for parameter tuning and local improvement of solutions. The genetic algorithm used reproduction operators (tournament and roulette wheel selection), single- and double-point crossover, and mutation. This allows for an increase in the efficiency of global search in terms of convergence (number of computational iterations) and solution accuracy (average absolute error of the solution at 100 runs), as well as avoiding the stopping of the computational process at local extrema. Based on the developed optimization method, a genetic algorithm has been created that incorporates all the mechanisms of evolutionary computation. A genetic algorithm has been developed that contains all the mech anisms of evolutionary computation. Based on the genetic algorithm, model problems of multi-criteria optimi sation were calculated in Python in binary coding of the optimal solution (OneMax, LeadingOnes) and in coding of the solution using real numbers (two-extreme function). In the corresponding test problems, the stable achieve ment of the global extremum of the objective function and the stability of the algorithm were recorded. This allows us to conclude that the proposed method of optimizing multi-criteria functions based on genetic algo rithms is effective.

Prombles in programming 2025; 3: 53-65


Keywords


objective function; genetic algorithm; mutation; recombination; fitness; chromosome; generation

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