This first part of the work is devoted to development of high-performance cement composites (HPCCs) with aim to elaborate a mix design methodology for obtaining defined properties of HPCC with industrial by-products such as fly ash, silica fume, and colloidal silica. The research employs innovative methods of experimental design and response surface optimization to find a compromise between the set compressive strength and mix workability. Stage 1 consists in selecting appropriate raw materials and designing an initial mix. Stage 2 involves finding an optimal dosage of superplasticizer. Stage 3 is the response surface optimization, which includes experiment planning with variable parameters x1 (fly ash) and x2 (nanosilica), conducting practical experiments, results of analysis and approximation, using mathematical models of 1st, 2nd, and 3rd order polynomials. The final Stage 4 implies finding the optimal compromise solution between strength and mix flowability, as well as experimental validation of the results obtained. The approach developed can be used for the design of similar multi-component mixes.