Geometric approach to finding the best possible solutions based on composition optimization of the mixed aggregate of fine-grained concrete

Abstract

The work proposes a geometric approach to the search for optimal solutions, based on the hypothesis that the optimal solution is one in which geometric objects, which characterize mutually opposite properties of the investigated process, approach each other most closely. Then the search for the optimal solution is reduced to minimizing the metric characteristics between the simulated geometric entities. In order to bring the initial data into compliance with each other, it is proposed to use their normalization at the stage of preliminary preparation before building a geometric model of the process. There is presented a computational experiment to find an optimal composition of a combined aggregate from industrial wastes to achieve the best physical and mechanical properties of fine-grained concrete, involving construction of corresponding geometric models in the form of response surfaces belonging to 4-dimensional space.