Results of computational experiments carried out in the process of solving the problem related to determination of the layer materials’ optimal thicknesses for different variants of enclosing structure
Description
This report describes the results of computational experiments performed with respect to different variants of the enclosing structure in the process of solving the problem related to determination of the optimal thicknesses for the materials used as layers within the structure. Each individual computational experiment involved implementation of quadratic optimization model based on discrete or binary unknown variables that determine the values of the thicknesses for the materials in the layers of a certain variant of the structure, using the indicators of the weighted average (by layer thickness) temperature of the enclosing structure, as well as its thickness and thermal resistance. The source data used for implementation of an individual computational experiment with application of the above-mentioned model included the values of thermal resistance on the inner and outer surfaces of the structure, the values of the thermal conductivity coefficients of the materials in the layers, the values of the temperature of the indoor and outdoor air, and the required values of the thickness and thermal resistance of the structure. A series of computational experiments was performed with respect to each variant of the enclosing structure in accordance with variation of the structure’s thickness (with a minimum difference between alternative values of the thickness for the material used as the layer of the structure) with fixed values of the remaining elements of the initial data. More detailed information about the structure of the computational experiments and the results of their implementation is presented in the main sections of the report.
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The implementation of mathematical models was carried out with the use of algorithm created in the “Matlab” software environment based on the corresponding programming language, which involves the use of the interior point method for the implementation of derivative models without taking into account the limitations of discreteness or binarity, as well as the branch and bound method - to ensure that the limitations of discreteness or binarity are taken into account in the process of optimal solution search for the original model; the selection of an unknown variable for branching was made based on the minimum deviation of the current value of the variable from the nearest standard value; the selection of the highest-priority subproblem for branching was carried out on the basis of the objective function’s minimum value obtained from the results of implementation of the corresponding derivative mathematical model.