The use of constrained and unconstrained optimization models in gradation design of hot mix asphalt mixture

The paper describes the essential differences in determining optimal gradation of hot mix asphalt (HMA) mixture used in road building at the stages of its selection, initial design and production, and presents the respective algorithms. The models of constrained and unconstrained non-linear optimization are developed, allowing us to choose the best HMA mixture gradation based on mineral materials, whose gradation is known, when the total percent passing of HMA mixture aggregates is considered to be equally important for all sieves, or when preference is given to some of the sieves. A new linear optimization problem best suited for practical use due to its simplicity is offered. By introducing weight coefficients for the dimensions of the objective function of the model, zero deviations of the percent passing of HMA mixture aggregates from their standard values may be easily obtained, based on the preferences set. All mineral materials (aggregates) obtained at batch-type asphalt mixing plants should be used for HMA production. Their total mass is equal to unity, while the mass of each material is a positive quantity, and a predetermined relationship between the masses of imported filler and the reclaimed dust is used. In the experimental part of the work, the problems were solved using the SAS system.