BIO-INSPIRED SCALABLE ALGORITHM IN PROBLEMS OF MULTIDIMENSIONAL OPTIMIZATION
Abstract
Bioinspired algorithms are mathematical transformations that allow to transform the input flow
of information into the output according to the rules based on the simulation of the mechanisms of evolution,
as well as on the statistical approach to the study of situations and iterative approximation to the
desired solution. Bioinspired algorithms have certain advantages over traditional deterministic optimization
methods, better exploring the space of finding solutions. However, in the era of big data, the suitability
of bioinspired algorithms for processing them, like most other methods, is questionable. Big data
poses new computational challenges, including due to its very high dimensionality and sparsity. Multidimensional
problems bring additional complexity to the study of the solution search space. An urgent
task is to develop a scalable bioinspired algorithm that can support the diversity of the population ofsolutions and find a balance between the rate of convergence of the algorithm and the diversification of
the search in the space of solutions. The paper presents a scalable bioinspired algorithm capable of
solving multidimensional optimization problems of high dimension using a hierarchical multipopulation
approach. The scalability of the algorithm assumes that its computational cost increases in direct proportion
to the increase in the amount of data processed, as well as the ability to give the best solution for
its current capabilities at any time of calculation, even if the calculation process is not completed by a
natural stop. Scalability also includes the ability to perform calculations within the limited memory of
the computer being used. The algorithm uses a special mutation operator to support the diversity of the
solution population, expanding the search for solutions at the expense of less promising solutions. Evaluation
of the effectiveness of the proposed algorithm is performed on the set of multidimensional optimization
functions benchmarks: Griewangk, Rastrigin, Rosenbrock, Schwefel. The indicators of the developed
algorithm are compared with the indicators of competing algorithms. The experiments show in
favor of a scalable algorithm, and the differences in the values of optimized functions for the developed
algorithm are statistically significant compared to competing algorithms, especially with increasing
dimension of the problem.
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