### HVAC Energy Consumption Optimization through Genetic Algorithms

One of the main problems in the AEC industry is the HVAC consumption in buildings. The reasons varies why it is necessary reduce the energy consumption. There are clear economic reasons, because a good energy consumption strategy could drive in reduce energy costs and impact in financial cost saving to consumers. Reducing energy use is also a solution to reduce greenhouse gas emissions. This work implement a Micro-Genetic Algorithm (MGA), to reduce heating and air-conditioning consumptions modifying a simple building geometry (a house) and the position and size of 2 windows.

The results showed that after few iterations the MGA was able to reduce the HVAC consumption in around 17%.

##### DESCRIPTION
###### A big window

The sun going through a big window in summer, will heat furniture and air, increasing the temperature in the room. Therefore, the air conditioning system will have to work to keep the room at 20ºC. The positive side, is that we can take advantage of the natural light for long time. We can also refresh the house, opening the window and releasing the heat trapped on walls and furniture by radiation during the day.

In winter, the same window will capture the heat, but unfortunately all the heat will be lost very quickly because escapes through the same window where it come. Therefore, we will have to turn on the heating quickly. The mistake is that all the heating produced will continue escaping trough the window, increasing heating consumptions.

###### A small window

A small window in summer, will not help to release the heat trapped on walls. The air conditioning will run for more hours to keep the temperature at 20ºC. And it will not possible to take advantage from the natural light compared to the big window.

In winter, the same small window will helps to keep the temperature in the room.

A big window performs well in summer but a lower performance in winter. On the contrary, the small window will be is not as useful in summer, but perform better in winter compared to the big window. The solution does not consist in to make a big or small window, but to find the optimum that balances both windows in dimension and position.

The objective is answer the following question:

Which is the building’s geometry and windows’ dimension and position to keep the temperature at 20º during the hottest and coldest day of the year with the lowest energy consumption?

##### MICRO GENETIC ALGORITHM

An MGA is similar in architecture to a Genetic Algorithm. The MGA use small populations and few generations (15 in ths work) in comparison to normal GAs where the population size and number of generations could easy reach the thousands. The MGA implements different strategies to avoid the fast convergence and yet poor solutions. The strategy consist in "locate" the highest ranked individual in the population in a promising area of the search space (elitism). And use a pool of individuals to control the diversity during the generations. This technique also involves the generation of random individuals. The idea behind, consist in explore further the search space and avoid to find only local minimum.

Micro Genetic Algorithms show few benefits. For example, since the algorithm is not evolving large populations, convergence can be achieved quickly and less memory is required to store populations. In some cases, the fitness function evaluation could take minutes or hours, which makes not practical to work with large populations. This point is very interesting for AEC industry, because the energy consumption calculation in large buildings is time-consuming. Another reason to implement a MGA is in high dimensional problems. The individuals in the population recall in large sizes which implies a large number of cost-function evaluation.

The MGA was implemented in laga and generative components was used as parametric software. Energy plus software was used for energy modelling and yet for the fitness evaluation. The connection between generative components and energy plus was implemented in C# and GC script.

The MGA in action.

##### PARAMETRIC MODEL

The parametric model is composed by 6 flat surfaces and 2 windows, facing East and West. The box (house) is 12m length (X direction), 10m width (Y direction) and 4 m height. The box-house geometry is controlled by 4 parameters. The windows are hosted by planes hosted in the East and West walls. Several vectors are used to define dimensions and positions of the windows. Once the model was built a test of many iterations was conducted to detect any inconsistency in the parametric definition.

##### ENERGY MODEL

The energy model is essential because sets the physical characteristics for the box-house, like where the building is located, weather conditions, walls insulation and thermal properties, windows properties, house geometry, windows dimension and position, etc. This information is defined in a energy plus file.

Energy model parameters:

• Building location: Country terrain, Chicago IL.
• Windows: Double Panel window with an interior camera of 3 mm.
• Walls: Wood siding outside, fiberglass quilt in the middle, and plasterboard in the interior.
• Roof: Roof deck outside, fiberglass quilt, in the middle and plasterboard in the interior.
• Floor: Thickness(m): 0.10, Conductivity(W/m-K): 1.7296, Density(kg/m3): 2243.0, Thermal Absorptance: 0.9, Solar Absorptance: 0.65, Visible Absorptance: 0.65
• HVAC system: Heating Supply Air Temperature(C): 50, Cooling Supply Air Temperature(C): 13, Heating Supply Air Humidity Ratio(kg-H2O/kg-air): 0.015, Cooling Supply Air Humidity Ratio(kg-H2O/kg-air): 0.01

The analysis correspond to the consumption of heating and cooling during the hottest and coldest day of a year.

##### WORKFLOW

The code transform the polygon vertices in the parametric model to a list of strings. After that, analyse the energy plus file (IDF file format) in order to create a new IDF with the recent modified vertices (new hose-box geometry) and windows (size and position). Once the new IDF file is created, the code calls energy plus to execute the energy analysis and the code wait until the energy report is finished. The code reads the report and extract heating, cooling and room temperature. This data is used as a fitness to classify the different individuals in the population.

The individuals are composed by a list of 31 doubles. The first 30 values represent the X,Y,Z coordinates of the parametric model and the last value is the fitness function. Once the individual is created is saved into the array population. After the population is created the elitism selection is executed.

The next step in the MGA is the crossover, in which the highest ranked individuals exchange part of their chromosome to constitute a new candidate solution (offspring), inheriting the properties from their parents. The crossover is performed only in certain parts of the chromosome, the rest is set randomly in order to avoid local minimum. Since the population is small and the algorithm is only tested in 5 generations, it's necessary to explore all possible solutions during the small period of time in which the MGA runs.

The offspring genes are mutated randomly by a factor. In this work, the best tested results set this value around 0.5. The mutation is calculated by a random value between 0 and 1, then is added or subtracted to one of the values in the gene:

`offspringMutate[i] = low + r * (low – high) (2`

The offspring mutated and the highest ranked solution from the previous generation are used in the new population and 3 new individuals are generated randomly in order to load the new population.

##### RESULTS

The MGA was tested 14 times, with no variation in data environment, energy properties and with the same number of generations. results were that in

• In 6 test, the MGA was able to optimize in each 5 generation
• In 6 test, the MGA was able to optimize in 4 generations
• In 1 test, the MGA only optimize in 1 generation
• In 1 test, the MGA was unable to optimize.

The energy consumption average at the beginning of the 12 successful optimization was: 4,100,503 Jules means: 1139.029 W/h. The energy consumption average after the optimization was: 3,494,576 Jules means: 970.715 W/h. This represents a reduction of 17.21% in energy consumption during the hottest and coldest day of the year. The best individual in all successfully tests reduced the energy consumption to: 3,023,091.22 Jules means: 840.412 W/h.

The above images, shows the 12 successful test with the energy consumptions before and after the optimization process.

##### CONCLUSION

The result show the MGA performed in most cases very good results decreasing the HVAC consumption around 17.00%. The MGA "bend" the box-house to reduce the area exposed to the East and West and also reduced the total volume of the interior space which has a direct impact in HVAC consumption.

The windows size and position were set randomly to avoid local minimum. Nevertheless, it is possible to observe similarities in windows size and position in the successful tests. For example, the MGA preferred small windows located near the top wall edges. The East and West windows were always located on the top right side of the wall. The MGA also proposed bigger and vertical shape East windows. In the other hand West windows where smaller and horizontal shape.

The MGA locate 10 times the West horizontal window near the top edge of the wall. In contrast, the East window was generated near the bottom wall edge 6 times and 4 times near the top edge wall. The MGA in all cases tried to reduce the total volume of the building and bend the box-house geometry,East and West surfaces to the South (10 times) and to the North, 2 times.

The MGA was able to generate out of 14 test 13 possible solutions with low energy consumption levels. This make the box-house more sustainable, which is an issue that concerns AEC industry and also is reflected in the building budget monthly.

The minimum windows size was not constrained which can represent an uncomfortable spatial relationship between the interior and the exterior of the building. Therefore, this parameter should be revised in the following steps. This box-house energy analysis takes about 3.7 seconds per evaluation, including the necessary report to read the solutions and inform the MGA the HVAC consumption.

One of the main problems with small populations is not explore the space search efficiently and only find minimum locals. The high power of inheritance in a complete crossover stops the optimization in the second or third generation falling directly in minimum locals.

A much more complex geometry, optimized by a Micro Genetic Algorithm