The burden that has come upon the environment, combined with the ever-declining fossil fuel reserves, has led to the need of reducing the conventional energy consumption in building sector and to the promotion of systems based on Renewable Energy Sources (RES). This paper deals with the optimization of multi energy systems in order to cover the needs of hot water in domestic use. In particular, integer linear programming models are formulated and the optimal solutions regarding the degree of participation of the multi energy systems are explored; economic, energy, and environmental criteria are assumed. The respective mathematical programming approaches include linear objective functions, multiple objective functions that either do or do not use weights, as well as goal programming-based ones. The modeling and solution of the problems is done with the General Algebraic Modeling System (GAMS). The case study refers to residential use; both conventional and RES systems are selected for the respective energy demand coverage. The time step of the analysis is 1 hour, in the context of annual operation. According to the results, in the case of the energy criterion, biomass predominates, or heat pumps, when biomass is not included, with an increase in participation of solar thermal collectors when the environmental criterion is introduced. The participation of solar thermal factor is also reinforced in the case of goal programming, because of the relaxation of the initial targets. The analysis demonstrated that the existing integer linear programming methodological tools can be used for investigating problems of multiple energy systems or comparing subsystems.

The increase of energy utilization reinforced the need of reducing the primary energy consumption based on fossil fuels and the limitation of carbon dioxide (CO2) emissions to the atmosphere. Such goals aim at the provision of affordable and generally clean energy for the citizens. However, the final decision making is hard to be achieved, due not only to the multitude variety of such proposed technologies, but also to the consideration of different criteria and scenarios, that in many cases are conflicting with each other. This paper deals with the optimization of the building envelope design considering thermal insulation, economic, and environmental aspects. The Life Cycle Assessment perspective is implemented for the data of the environmental criterion, focusing on the CO2 emissions and the cumulative energy demand. The decision making refers not only to the selection of the appropriate thermal insulation material and its width, but also to the choice of the window frame material. In that way, Mathematical Programming (MP) models for the optimization of such criteria were developed. The General Algebraic Modeling System (GAMS) was used to model these problems and the BARON solver was used to solve them. The respective MP models include mixed integer nonlinear programming problems, multiple objective functions, as well as multi-criteria techniques such as goal programming. According to the results, the increase of the envelope thermal protection implies that the economic and environmental costs are higher, displaying the importance of criteria compensation. For smoothing the conflicting criteria, a weighting sensitivity analysis was conducted, showing that reference optimal values are formed for certain ranges of weights, elaborating the framework of decision-making without having to precisely prescribe them beforehand. All in all, the use of the optimization models can improve and facilitate the building design process by analyzing the advantages and drawbacks of the various materials/technologies and allowing the comparative evaluation of the considered alternatives.