Justification of the combination of standard values of material characteristics of layers in the building envelope on the basis of quadratic optimization

Introduction. The relevance of the research is determined by the features of the design and organizational-and-technological solutions formed in the process of developing modern construction projects, consisting in the use of a limited composition of technological resources (building materials, machines and equipment), which determines the discreteness of the values of the characteristics of the above-mentioned solutions. The purpose of the study is to develop tools to justify the combination of standard values of the characteristics of materials used for the device of layers of the enclosing structure, using quadratic optimization tools.

Materials and methods. Mathematical models for optimization of the thickness for the materials used as layers of the enclosing structure in a residential building are developed, based on discrete and binary unknown variables, as well as on the criteria of the weighted average (by the thickness of layers) temperature, total thickness and thermal resistance of the structure. The mathematical models have a quadratic structure of the objective function and a linear structure of indirect constraints, but the presence of constraints related to the discreteness (binarity) of unknown variables significantly complicates the process of the models’ implementation due to the lack of suitable standard (available in modern software environments for mathematical modelling) computational algorithms. In this regard, it was decided to develop a user computational algorithm that includes the advantages of the branch and bound method used to determine the optimal values of unknown variables for which discreteness or binary requirements are specified, as well as the interior point method used to determine the optimal solution of the quadratic optimization model without taking into account the above requirements.

Results. To practically verify the developed mathematical models, the proposed computational algorithm was applied to justify the selection of standard material characteristics for the given enclosure structure. The resulting data enabled the establishment of dependencies between the thermal performance indicators of the structure and the required thickness of its layers.

Conclusions. Based on the analysis of the results obtained from using the developed mathematical models and computational algorithm, the significant practical value of the proposed tools was confirmed.

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