The paper presents the method of optimal design of the building envelope. The influence of four types of windows, their size, building orientation, insulation of external walls, ceiling to unheated attic and ground floor on the life cycle costs in a single-family building in Polish climate conditions is analyzed. The optimization procedure is developed by means of the coupling between MATLAB and EnergyPlus. The results using three metaheuristic methods: genetic algorithms, particle swarm optimization, and algorithm based on teaching and learning are compared. The analyses have shown the possibility of reducing the life cycle costs through the optimal selection of the building structure. The high initial investment (above the required standard) pays off in the long run when using a building.

In the early stages of design the building designer faces different questions in relation to: building location (which is usually not really a decision of the building designer but of the owner of the building), building orientation, building shape, structural system to be adopted, building envelope and interior finishes. Naturally, this is a challenging procedure as each question has a wide range of different alternatives that globally will lead to an even wider range of different solutions. In addition, from the point of view of the environmental assessment, the problem is more complex as one solution may be beneficial in some environmental categories and simultaneously harmful in others [

Several design features can affect the energy efficiency of buildings, including the shape of the building, wall and roof construction, foundation type, insulation levels, window type and area, thermal mass, and shading. For a given floor area, determining the envelope configuration that results in minimum annual energy consumption can be a challenging task, but ultimately not very useful, since economic considerations must play a role in the construction of any real building. Indeed, the problem of building energy efficiency becomes more complex as economic factors are introduced. A building that consumes the absolute minimum amount of energy for its size is most likely not very cost-effective, since additional construction costs would overwhelm any savings from reduced energy use. Therefore, a balance must be found between increases in investment cost and recurring annual savings [

Each combination of design variables leads to a certain annual energy demand, under standard building use conditions. It therefore is of interest to characterize the full spectrum of possible combinations of variables, in order to identify those that have expected lower initial costs and those that have lower lifecycle costs, but also how distant from “the best” some other solution (e.g. one preferred due to architectural/non-energy criteria) may be. Therefore, it is important to develop methodologies that allow building designers to identify the combinations of design variables that, while insuring the achievement of the energy and environmental targets established, also have near-optimal lowest life cycle costs, or lowest investment costs, or a good compromise between investment costs and life cycle costs [

The designers often adopt building performance simulation (BPS) tools for analyzing the energy behaviours of buildings [

This paper presents the multi-variable optimization of chosen design parameters in a single-family building. The aim is to determine optimum solutions that will enable maximum energy and economic benefits during the lifetime of the building. The optimization procedure is developed by means of the coupling between MATLAB and EnergyPlus and implementing the optimization tools. Many works in this field used grand simplifications: thermal zones included several rooms or the analyses only one zone, the same casual gains assumed in the whole building, window size defined by the window-to-wall ratio. In this study a detailed analysis of the selected building has been performed. The rooms are modeled as separate zones with scheduled casual gains. The constructed algorithm individually selects optimum values from discreet sets for each design variable as well as automatically selects an external wall for a window in each room. Only such an algorithm enables to determine optimum design solutions for the optimized building. This paper also aims to present the comparison of three metaheuristic methods for the evaluation of the cost-optimality. Optimizations using one selected method (genetic algorithms) have already been carried out in earlier authors’ research [

Normally, in building performance optimization, an analytical formulation of the objective functions is not available [

More recently, optimization-based selection approaches have been proposed to select building shapes [

To perform the optimization analysis the simulation-optimization environment can consider a various objective functions, most often it is an annual energy demand, annual energy costs or life cycle costs of building. Gasparella et al. [

Some researches apply multi-objective optimization models. In the study conducted by Ascione et al. [

The optimization of the insulation thickness of a house considering both economic and environmental concerns is presented by Carreras et al. [

Multi-variable optimizations by coupling the building performance simulation program with optimization environment using genetic algorithms (GA) or particle swarm optimizer (PSO) or teaching-learning-based optimization (TLBO) were performed to determine the best path to minimize life cycle costs while reducing the energy use of a typical single-family house in Poland.

The energy modeling tool EnergyPlus [

The optimization algorithm methods and all procedures to exchange data between the simulation and the optimization tools were implemented in MATLAB R2017a language. Figure

Flowchart diagram for the developed simulation/optimization

The simulations were performed using reference weather data for Katowice. The simulations were run with a fifteen-minute time step. Internal heat gains were introduced into the model: occupants, equipment and lighting. An hourly schedule for heat gains was adopted in each room [

The single-family detached house without a cellar and with unused attic was chosen for the research. The ground floor of the building is shown in Figure

Ground floor view (dimensions in cm), adopted from Ferdyn-Grygierek and Grygierek [

Characteristics of the reference building

Number of occupants | 4 |

Number of heated floors | 1 |

Area of heated floor | 150 m^{2} |

Floor-to-floor height | 2.6 m |

External wall construction | Brick with polystyrene insulation, ^{2}K |

Ceiling construction | Ferroconcrete with mineral wool insulation, ^{2}K |

Roof construction | Covered with ceramic tiles and uninsulated |

Ground floor construction | Concrete with polystyrene insulation, ^{2}K |

Windows construction | Double glazed, PCV frame, _{glass} = 1.00 W/m^{2}K |

Opaque external wall | 102.15 m^{2} |

Window area | 23.25 m^{2} |

Ventilation | Natural |

Cooling System | Split system air conditioner (electricity) |

Heating System | Central heating with radiators (natural gas boiler) |

The house has four bedrooms and an open space kitchen and a living room. The building is air conditioned (split system) and equipped with a hot water central heating system. The cooling set point is kept at 24°C and heating set point at 20°C. The ventilation air flow was adopted in accordance with the Polish standard [^{3}/h (it is about 0.3 air change per hour).

In optimization analysis the most common design options available in Poland are chosen as design variables (Table

Glazing type characterized by two parameters of the glazing, i.e.: heat transfer coefficient (

Windows area (glazing + frame) defined by the sixteen discrete values of windows size. Depending on the size of the window the frame surface is automatically calculated for each window.

External walls, ground floor and ceiling to the unheated attic defined by the thickness of polystyrene and mineral wool. Six options for all kinds of partition are considered.

Orientation defined by the azimuth angle between the north and the front of the house. Sixteen options for the orientation are considered.

Cost data for design variables and options used for the optimization analysis

Design variable | Options | Cost^{*} |
---|---|---|

Glazing type for window | G10 (_{glass}=1.0 W/m^{2} K, _{glass}=0.7 W/m^{2} K, _{glass}=0.6 W/m^{2} K, _{glass}=0.5 W/m^{2} K, |
148 PLN/m^{2}^{2}^{2}^{2} |

Windows area | Height: 1.5 m^{2} |
0 PLN for all options |

Insulation | ||

Ground floor: polystyrene (λ = 0.031 W/mK) | 5, 6, 8, 10, 12, 15 cm (thickness) | 223 PLN/m^{3} |

External wall: polystyrene (λ = 0.031 W/mK) | 12, 15, 18, 20, 22, 25 cm (thickness) | 198 PLN/m^{3} |

Ceiling to unheated attic: mineral wool (λ = 0.038 W/mK) | 20, 22, 25, 28, 30, 35 cm (thickness) | 1.36 PLN/m^{2} for 1 cm of thickness |

Azimuth (orientation of the building relatively to the north) | 0–337.5 with step 22.5 | 0 PLN for all options |

Additionally included the costs of window frame and installation and cost of external wall construction |

1 PLN = ~0.23 EURO

The newly-constructed buildings in Poland must meet Technical Conditions [^{2}. In the reference building the glazing area amounts to 15.7 m^{2}. The overestimated value results from the adopted assumptions: there are all windows in each room (Figure

Objective functions are the selected simulation results which vary depending on the parametric input combinations, and are the values to be minimized by the optimization algorithm. In this study, the cost function is selected as the life cycle cost (LCC). The LCC is “the sum of the present value of investment and operating costs for the building and service systems, including those related to maintenance and replacement, over a specified lifespan” [

In the study life cycle cost was defined by Eq. (

Where:

_{H}

_{C}

η_{H}

η_{C}

_{H(gas)} – price of energy from natural gas, according to the applicable tariffs,

_{C(el.)} – price of electrical energy, according to the applicable tariffs.

The following data are assumed for the LCC calculations:

efficiency of heating system _{H}

efficiency of cooling system _{C}

price of energy from natural gas _{H(gas)} = 0.1694 PLN/kWh at 1^{st} June 2018,

price of electrical energy _{C(el.)} = 0.5565 PLN/kWh at 1^{st} June 2018,

investment costs (Table

nominal interest rate _{e} = 2.8%,

lifespan

The energy performance of a building depends on a great number of parameters and is further influenced by external conditions and internal gains. In order to improve the energy performance of a building the correct parameters should be determined, which requires the right optimization tool. Bearing in mind a great number of variables which can be combined we might end up facing a vast number of combinations while the building itself will not be so complex. It is of vital importance to choose the right tool to solve such a complex problem [

Metaheuristic search techniques are developed to make this search within computationally acceptable time period. They also are classified as population-based or nature-inspired optimization methods The main idea of all metaheuristic optimization methods is to follow some heuristics in order to obtain the best solution for an optimization problem. In this study, three optimum design algorithms are applied for the solution of the discrete programming problem: genetic algorithm (GA), particle swarm optimizer (PSO) and teaching-learning-based optimization (TLBO). The first two are most often used in building envelope optimization. TLBO is a relatively new method and requires a minimum number of parameters (population size and number of iteration steps). In this work, it was assumed that design variables are discrete, therefore the special version of these methods are used.

GAs are the most popular methods, which have found vast amount of applications in a wide spectrum of diverse engineering disciplines [

PSO was proposed by Kennedy and Eberhart in 1995 [

Rao et al. [

These methods have already been used in many optimization problems. The optimization algorithm used in this study, based on all-year building performance simulations, is time-consuming. Therefore, it is important to choose a method that gives good results in an acceptable time. This study is to demonstrate the method with the best compromise between the simulation duration and the quality of the obtained results. 48 individuals and 80 (40 for TLBO) simulation steps were assumed in the simulations. The duration of the simulation on the AMD Ryzen 5 1600X processor is 1.5 h (12 parallel simulations in EnergyPlus).

The results will be compared to the reference building. The aims of the simulations are: to determine whether higher investments costs that improve the thermal performance of a building are cost-effective for an investor and to check which optimization method gives better results.

It was assumed that there must be at least one window in each of the rooms and two windows in the living room. In the simulations it was assumed that the minimum glazing area is at least 1:8 of the floor area in the room (according to Technical Conditions [

Figure

Life cycle costs convergence history

Table

Optimal results

Case | Reference building | Building after optimization | |||
---|---|---|---|---|---|

GA | PSO | TLBO | |||

Type of glazing | G10 | G05 | G05 | G05 | |

Window area, m^{2} |
W1 | 3.375 | 5.250 | 3.000 | 3.000 |

W2 | 3.375 | 4.500 | 0 | 6.375 | |

W3 | 3.375 | 4.125 | 6.375 | 0 | |

W4 | 2.250 | 3.375 | 2.250 | 2.250 | |

W5 | 1.875 | 4.125 | 2.250 | 3.375 | |

W6 | 1.875 | 0 | 1.500 | 0 | |

W7 | 3.375 | 3.375 | 3.375 | 3.375 | |

W8 | 1.875 | 3.000 | 2.250 | 0 | |

W9 | 1.875 | 1.125 | 1.500 | 3.375 | |

Insulation, cm | external walls | 12 | 15 | 18 | 18 |

ground floor | 5 | 15 | 10 | 12 | |

ceiling | 20 | 22 | 28 | 28 | |

Building orientation, deg (clockwise) | 0 | 180 | 247.5 | 247.5 | |

Sum of windows area, m^{2} |
23.25 | 28.875 | 22.500 | 21.750 | |

Sum of glazing area, m^{2} |
15.711 | 19.592 | 15.396 | 14.941 | |

LCC, PLN | 38 408 | 32 611 | 31 760 | 31 299 | |

LCC savings, % | 0 | 15 | 17 | 19 | |

Heating demand, kWh/m^{2} |
52.6 | 32.1 | 30.9 | 29.1 | |

Cooling demand, kWh/m^{2} |
9.7 | 19.1 | 13.2 | 13.4 | |

Total energy savings, % | 0 | 18 | 29 | 32 |

After optimization, the thermal parameters of the external partitions have changed in comparison to the reference building. The insulation thicknesses increased by 6 cm (50%) for external walls, by 8 cm (40%) for ceiling to the unheated attic, and by 7 cm (140%) for floor on the ground. A window with the lowest

The total area of the glazing has changed slightly, decreased by 5%. However, the number of windows has decreased to the minimum value (one in rooms and two in the living room). As a result, the area of some windows increased significantly, for example W2 window (almost twice).

The building has been rotated so that the windows of rooms with small internal gains (rooms 2–4) face the south-east side. In turn the largest window of the living room (large internal gains) was directed to the north-west side. What makes it possible to balance the heat in the whole building both in winter and in summer.

Despite the choice of the most expensive window option and additional costs related to thicker isolation of external partitions, optimization has reduced life cycle costs by 19%.

The paper presents the methodology and the tool aimed at supporting the choice of economically effective building solutions. The detailed multi-zone model of a building and the gains that are attributed to the relevant zones contributed to maximize the obtained results (reduced LCC). In many works on this subject, the size of the windows is determined only by the ratio of their area to the façade area [

The analyses have shown the possibility of reducing the life cycle costs through the optimal selection of the building structure. The high initial investment (above the required standard) pays off in the long run when using a building.

The developed simulation environment can also be used to optimize other building parameters. The simulation environment can easily be extended to other types of buildings.

The work was performed within Statutory works BK234/RB-5/2019 and BK-220/RIE1/2019, funded by the Ministry of Science and Higher Education.