## 1 Introduction
In this study, the single-objective MINLP approach was used to perform the separate optimizations of the addressed structural system under the same design constraints but by considering different objectives: the minimization of mass, minimization of direct costs, and minimization of energy life-cycle costs. Thus, the optimization presented in this study is performed according to a single criterion that is most commonly used in structural  
Figure 1: Steel–concrete composite I-beam floor system. optimization (see, for example, references [24; 25]). Such a technique does not represent a multi-objective method, which are methods where all of the criteria are considered simultaneously in a single search process (see, e.g., references [15; 16; 26]). The optimization process in this paper rather falls into the domain of parametric optimization. The multi-parametric mass optimization of composite structures was thus conducted for the above-mentioned different parameters and is presented in the paper. Since we were also interested in how energy consumption in buildings affects the cost increases and changes in the mass/material consumption of composite structures, the so-called multi-parametric energy life-cycle cost (ELCC) optimization was performed and is presented in this study as well. The performed ELCC optimizations include the costs of space heating, ventilation, and air conditioning (HVAC). In terms of ELCC analysis, see, e.g., [27], other life-cycle costs such as the costs of maintenance, inspection, repair, demolition, removal, and the transportation and deposition/recycling of the dilapidated structures are not included in the current study. The efficiency classes derived from the standards for the energy consumption of buildings vary considerably from country to country. For this reason, a direct comparison of the energy efficiency classes and energy indicators between different countries is difficult. In most countries, buildings are considered energy efficient when energy consumption is 50 kWh/m\({}^{2}\) or below, they are deemed energy inefficient when energy consumption is around 100 kWh/m\({}^{2}\), and they are seen as highly energy inefficient when consumption is around 200 kWh/m\({}^{2}\). For more information on energy efficiency classes, see the references by [PERSON] and [PERSON] [28] and [PERSON] et al. [29]. As mentioned above, an annual energy consumption of less than 50 kWh per m\({}^{2}\) for space heating, ventilation, and air conditioning generally represents an energy efficient case (EEC) and good practise in the design of new houses/buildings. Although energy efficiency has increased in the last two decades due to improvements in the industrial sector and in households [30], energy consumption is still very high in existing, non-renovated buildings and is sometimes also in new buildings. For this reason, two additional cases are proposed for ELCC optimization, namely an energy inefficient case (EIC, 100 kWh/m\({}^{2}\)) and a high energy consumption case (HEC, 200 kWh/m\({}^{2}\)). Thus, when calculating the operating costs for the heating, ventilation, and air conditioning of buildings, three different energy consumption cases are considered altogether. The optimal results calculated with the above-mentioned different criteria are then compared in order to achieve competitive composite designs. These results are also compared with the direct cost optimization results calculated and presented by [PERSON] et al. [14]. Comparative diagrams are drawn. Diagrams such as the ones presented here can help researchers and engineers find a competitive composite floor structure (CFS) for a desired load and span. This study is a continuation of previous research [14], where only the multi-parametric direct cost optimization of CFSs was investigated.