Genetic Optimization in Building Lifecycle Analysis by Grasshopper Jingyi Liu 2020-12-13 Introduction 1.1. Building Lifecycle Analysis (LCA)

The lifespan of a building is long, including both the embodied stage like material manufacturing as well as construction and the operational use-phase. In building lifecycle analysis, one common goal is to minimize both lifecycle cost and carbon impact. Lifecycle cost in dollars includes the cost of construction material, labor, and use-phase energy (natural gas and electricity). Lifecycle carbon impact in kgCO2eq includes carbon emissions due to material manufacturing and energy production. My project aims to conduct LCA in Grasshopper, a code-friendly platform in the design software Rhino, to recommend optimal design solutions with minimized cost and carbon impact during the early design stage. There are various design possibilities for an early-stage conceptual model. So, design uncertainty will be carefully considered in the case study part. Another innovative idea involved in this project is design diversity. Designers usually pursue high flexibility when choosing the design schemes. So, apart from lifecycle cost and carbon impact, design diversity will be added as the third objective to optimize at the end of the case study. 1.2. Genetic Optimization in the Field of Building Design

When it comes to optimization methods, they can generally be classified into two types: gradient-based and gradient-free. A detailed comparison between them is listed in Table.1. In the field of building design, gradient-free or sampling-based algorithms are preferred because of several reasons. Firstly, a building design always involves complex inputs, for example, both discrete categorical attributes like Wall Type & Insulation Material and continuous numerical attributes such as WWR & R-value. Gradient-free optimizations accept various types of inputs, unlike the gradient-based method, which only accepts continuous numerical inputs. Secondly, gradient-free algorithms lead to multiple optimal results when doing multi-objective optimization, unlike the gradient-based method that only reports a single optimal solution. For designers, they pursue design flexibility, especially during the early design stage. Thus, the gradient-free method is more popular in building design because it adapts to complex problem settings and provides designers with multiple optimal solutions.

Gradient-based Optimization Gradient-free Optimization (Sampling-based)

Theory

Gradient-based algorithms calculate derivatives to find the optimal values of a mathematical function. It reaches the minimum value by choosing the gradient direction, step size, and then checking convergence.

Gradient-free algorithms find optimal solutions by sampling the design space.

Common Algorithms

• Gradient Descent • Stochastic Gradient Descent • Coordinate Descent • Frank–Wolfe Algorithm • etc.

• Exhaustive Search • Genetic Algorithms (Evolutionary) • Particle Swarm • Simulated Annealing • Nelder-Mead

Advantages • Convergence time is guaranteed • Higher accuracy • Relatively high speed

• Can lead to multiple optimal solutions when doing multi-objective optimization

• Accept discrete, continuous, and noisy inputs, suitable for wider types of problems

Disadvantages • Only lead to one optimal solution • Require continuous numerical inputs, only

solving limited problems • Not easy for multi-objective optimizations

• Convergence time is not guaranteed; more time leads to more accurate results

• Relatively low speed • Users must adjust hyperparameters

Suitable Problems

• Engineering problems when one best solution is needed, and the problem can be stated mathematically

• Numbers have real meanings, cannot represent categorical inputs as integers

• Design problems when multiple solutions are needed to ensure flexibility and the problem is hard to be defined mathematically

• Numbers have no mathematical meanings, can assign integers to categorical inputs

Table.1. Comparison Between Gradient-based & Gradient-free Methods: Pros & Cons Among various gradient-free algorithms, the genetic algorithm is selected in this project because there are extensive literature resources about its applications in design. Many existing tools conduct building optimization by using a genetic algorithm as well. It is inspired by Darwin's theory of natural selection. It selects best-performance designs from the previous generation as parents to create child designs in the next generation. Detailed explanations of this algorithm will be given in the literature review section 3.3. 1.3. Structure of This Paper

This paper will begin with project motivation and originality, followed by the literature review part, mentioning some previous examples where genetic optimization is applied in design. By imitating some previous examples, the Methodology section will explain how to choose the proper optimization plug-in, calibrate hyperparameters, and measure diversity. These methods will be used in the case study to analyze a simple office model. The paper will conclude with the case study’s result visualization, a 3D Pareto Front diagram with three objectives: cost, impact, and diversity, followed by an optimization performance summary. In the end, the Future Work section will summarize the improvements needed in this project. Motivation & Background 2.1. Drawbacks of Existing LCA Tools This project's motivation comes from the designer's demand to receive sustainable suggestions during the early design stage. There are many existing LCA tools on the market, but they all have some drawbacks. For example, most tools, like RevitTally and OneClickLCA, require a detailed building model or construction assignment to conduct analysis, which takes time to build and modify. Since they are created to analyze one detailed design, they report fixed values without considering early-stage design uncertainty or diversity. 2.2. Originality: A New LCA Workflow in Grasshopper

By knowing these drawbacks, I decided to create a new workflow that achieves the following goals: 1. Be able to analyze conceptual geometries by developing the workflow in Grasshopper, a code-friendly

platform in Rhino, a popular conceptual design software. 2. Consider early-stage design uncertainties by randomly sampling the design space for a conceptual

geometry, with variables selected from their uniform distributions. 3. Report diverse optimal solutions, ensuring users’ flexibility to choose from multiple design solutions. 4. Meanwhile, apply lifecycle thinking, considering cost and emissions from both embodied material and

operational energy usage. Literature Review 3.1. Pareto Front Optimal & Quasi-optimal Designs A previous phD student at MIT Material Systems Laboratory wrote a paper which introduces two important ideas: Pareto front plotting & Quasi-optimal. The genetic algorithm is selected in his project because “it is well-suited for problems where it is difficult or time-consuming to use exact optimization methods” (Joshua, 2018, p.38). Two objectives optimized in this project are cost and global warming potential (GWP). By running a set of optimizations, “it is possible to decide the Pareto frontier showing trade-offs between optimum impacts and costs if different weights are given to each” (Joshua, 2018, p.38). Design solutions closing to the left bottom corner are considered optimal, as shown on the left below.

Figure.2. Optimal Solutions on the Pareto front & Quasi-optimal Solutions Above the 75th Percentile

Moreover, Joshua not only cares about optimal designs on the Pareto front, but also those close to it, so that he could “extract design guidance on critical v.s. flexible design attributes to achieve near-optimum impact and cost” (Joshua, 2018, p.38). Designs above the 75th percentile of rankings are considered quasi-optimal. 0.75 is chosen to “represent a balance between proximity to the optimum region and a gain in flexibility” (Joshua, 2018, p.39). 3.2. Existing Optimization Tools in Grasshopper Traditionally, the optimization problem is done by coding. However, in the field of design, most designers have limited coding skills. Thus, “both evolutionary and gradient-based solvers exist in parametric software including Galapagos, Goat, and DSE for Grasshopper. The Core Studio at Thornton Tomasetti has developed TT Toolbox and Design Explorer” (Brown, 2016, p.2). And another tool called Octopus, used in our project, “was designed to

apply evolutionary principles to parametric design problems with multiple objectives. It includes features such as searching for trade-offs, forcing diversity of solutions, changing objectives during a search, and visualizing and exporting results” (Brown, 2016, p.2). A detailed comparison between their advantages and disadvantage will be given in section 4.1. Take DSE as an example, a design tool developed by MIT Digital Structure Team, “it read in design variables and their ranges and generates a list of design vectors that represent the design space. Geometry generation and objective functions are design specific and must be set up individually by the designer” (Brown, 2016, p.5). Most tools, including Octopus, apply similar approaches to conduct optimization. 3.3. Hyperparameters in Genetic Optimization The genetic algorithm can be implemented in five steps: generation of designs, quantitative evaluation, satisfaction check, user selection, and breeding of designs. In each new generation, “the entire population is replaced by designs generated from selected parents. Through the breeding of high-performing solutions over multiple generations, high quality and often optimal solutions can be found” (Brown, 2015, p.72). There are various tools designed with genetic optimization. One example is called structureFIT, as shown in Figure 3. This tool “allows users to explore geometric variations of structural trusses with a volume minimization quantitative goal in a graphical, web-based environment” (Brown, 2015, p.77). The tool visualizes the logic of genetic optimization well. Under the exploration mode, “the designer generates and reviews populations of designs in a graphical user interface. For each generation, the mutation rate and population size can be adjusted using sliders, and parents can be selected by clicking on designs” (Brown, 2015, p.78). The score shown under each truss image represents the volume of steel used. A lower score is better.

Figure.3. structureFIT User Interface structureFIT is considered a successful tool because of its user interactions, enabling users to explore different hyperparameters, including Generation Size, # Generations, and Mutation Rate. The paper also summarized some findings of the impact of different parameter values on the optimization performance. These parameters will appear again in my project, and one task is to find the best combination of them.

• When increasing Generation Size: Computation time is increasing, but the score is better

Allow the user to find more quasi-optimal design solutions in the last generation • When increasing # Generations:

Computation time is increasing, but the score is better Designs converge to the best solution but may lose diversity

• When increasing Mutation Rate: Move around the design space more quickly, meanwhile avoiding local minimums However, a high mutation rate may disrupt the evolutionary process, eliminating the positive

traits passed on by parents, leading to a less-satisfying score

Figure.4. Hyperparameters in Genetic Optimization 3.4. Design Diversity Measurement In section 3.3, the mutation rate is one parameter that influences design diversity. In a paper talking about quantifying diversity, distance is measured as the other way to control it. “Since the question of diversity in parametric design is not necessarily how many different types are present, or how well distributed they are, but rather involves characterizing how far apart different designs are in relation to all other designs, distance measurement (such as Euclidean) can be especially useful for design settings” (Brown, 2018, p.42).

Figure.5. Four Methods to Measure Design Diversity

The paper introduces four types of distance measurement methods, as shown in Figure 5. One-Point Method “measures the maximum distance between the centroid and each of the individual designs, effectively measuring

the furthest outlier in the set” (Brown, 2018, p.44). Std.Deviation Method “measures the sparseness at the center of the design set, which is the average distance between a given point and each of the surrounding points” (Brown, 2018, p.44). All-Points Distance “measures the average distance between each point and every other point in the design set while ignoring the centroid or median” (Brown, 2018, p.45). This is the default method used in Octopus. And a comparison between different methods will be illustrated in section 5.4. Finally, the Pareto Front Distance only looks at the distance between points on the Pareto front. This can be used to evaluate the performance of all three previous methods. Methodology 4.1. Optimization Tools in Grasshopper As mentioned in section 3.2., there are many optimization plug-ins in Grasshopper. A detailed comparison between them is listed in Table.6. A score is assigned by using (0.5*Cost+0.5*Impact)/10^6 to compare accuracy. A lower score means higher accuracy because it corresponds to a pair of minimized cost and carbon impact.

Time (1000)

Accuracy (average)

Support Multi-Objective Optimization (MOO)?

Support Multiple Optimal Choices?

Algorithms Accept Discrete?

Goat 2 mins 67.64 NO NO Local Linear Local Quadratic LocalSubplex Global Deterministic Global Evolutionary

NO

Galapagos 20 mins 64.46 NO YES Evolutionary YES DSE Radical

1 min 68 NO NO Gradient Descent NO

DSE Pareto-Front

90 mins 63.95 YES YES Genetic Algorithm (NSGA-II multi-objective algorithm)

NO

Octopus 30 mins 60.7 YES YES Genetic Algorithm (SPEA-2 multi-objective algorithm)

YES

Table.6. Optimization Tool Selection Within Grasshopper Among these tools, Octopus is selected for my project. Firstly, Goat and DSE Radical are deselected because they only generate one optimal solution; however, designers want multiple choices. Also, these two plug-ins are gradient-based, not suitable for discrete inputs such as GlazingType and EquipmentType. Secondly, Galapagos is deselected. Although it applies a gradient-free algorithm, it does not support multi-objective optimization. However, in my case, there are three objectives: cost, impact, and diversity. Lastly, the DSE Pareto-Front is deselected. It is very time-consuming. And the worse thing is that it doesn’t support integer optimization. So, there is no way to optimize discrete categorical inputs. In contrast, Octopus is the most suitable choice because it:

• Only takes 30 mins to finish 1000 runs, not too slow • Features the lowest score, which means the optimized cost and carbon impact • Supports multi-objective optimization • Generates multiple optimal solutions, ensuring design flexibility • Applies gradient-free genetic algorithm, able to optimize both discrete categorical attributes and continuous

numerical attributes

4.2. Optimization Tool Selection: Octopus As shown in Figure.7, this is the user interface of Octopus. The 2D Pareto front plotted includes two objectives: lifecycle cost (red axis) and lifecycle carbon impact (green axis). At the top-right corner, users can adjust key hyperparameters, including:

• Population Size / Generation Size • # Generations / Max Generations • Mutation Rate

Then, at the left-bottom corner, the parallel coordinate diagram shows different combinations of variable values. As the # Generations increases, the paths will change from diverse to more concentrated to the optimal solutions. At the right-bottom corner, the minimum objective values from each generation are recorded. They will tend to be lower as the # Generations increases.

Figure.7. Octopus User Interface 4.3. Hyperparameter Calibration To save users’ time, I will calibrate three key hyperparameters in section 5.3 and make recommendations to users in advance. Recommendations will be made by running multiple times for certain parameter values and then exploring the performance. Recommendations will be given for:

• Ratio = GenerationSize / #Generations • #Data = GenerationSize * #Generations • Mutation Rate

Two evaluation metrics are: • the time (mins) needed to finish 200 runs • the accuracy score (0.5*Cost+0.5*Impact) / 10^6.

Pareto Front Visualization

Hyper-Parameter Adjusting

Parallel Coordinates Objective Value Evolution

3 Optimal Solutions On the Pareto Front

4.4. Diversity Measurement Method Selection As mentioned in section 3.4, there are multiple methods to measure diversity. In the case study section 5.4, they will be modified to adapt to my project needs. Several metrics will be applied to measure their performance, and the best one will be selected as the third objective to optimize. Evaluation metrics include:

• Score (to Ensure Accuracy) • # Points on the Pareto front (to Check Flexibility) • Distance for Points on the Pareto front (to Check Flexibility)

4.5. Weight Adjusting for Better Performance Usually, there is a trade-off between design diversity and accuracy. This trade-off could be controlled by assigning larger or smaller weight on diversity. Moreover, different weights on cost and impact represent different emphasis as well. For example, when cost saving is more important than impact, and high accuracy is needed, 6/10*cost+4/10*impact+1/10*diversity will be a better choice compared to 1/3*cost+1/3*impact+1/3*diversity. The effect of different weights will be explored in the section 5.5. Case Study 5.1. LCA Analysis Workflow in Grasshopper To better illustrate how to use Octopus, a case study will be conducted for a 30m*30m*35m conceptual office tower in Rhino. Detailed processes are listed below:

Figure.8. Grasshopper LCA Workflow

1. Python Environment Set-up: Enable to use Python packages, for example, numpy, pandas, matplotlib, and sklearn etc. in Grasshopper

2. LCA Pre-setting: Set the climate, analysis period, and geometry style

3. Geometry Information Extraction:

Extract key geometry information such as floor perimeter, floor area, façade area

4. Generate the Design Space: There are various design possibilities for a conceptual geometry. When doing genetic optimization, different design solutions need to be sampled, and then the genetic algorithm will locate the optimal ones. Design solutions are sampled by randomly generating combinations of building attribute variables. Variable values are selected from two types of distributions: discrete and continuous.

• Discrete Distribution: For categorical attributes such as Wall Type, if there are five types of wall, they will be represented as integers from 1 to 5. Integer can be assigned to represent categorical attributes because numbers don’t have mathematical meanings in gradient-free sampling-based genetic optimization. For example, we can track the corresponding type of wall by knowing the optimal integer reported for Wall Type. Other discrete variables include:

Categorical Building Attributes Discrete Variables Assigned Integers Equipment Types 3PackagedSingleZoneAC

4PackagedSingleZoneHP 5VAVAirCooled+HydronicHeat 6VAVAirCooled+ElectricHeat 7VAVWaterCooled+HydronicHeat 8VAVWaterCooled_ElectricHeat 11FanCoilUnitDOAS 12ActiveChillBeamsDOAS

0 1 2 3 4 5 6 7

Equipment Efficiency medium high

0 1

Wall Type SolidSteelFrame SolidWood SolidMetal SolidMass Glazing

0 1 2 3 4

Insulation Material (Between Studs)

FiberGlass MineralWool Cellulose PolyurethaneFoam PolystyreneEPS PolystyreneXPS

0 1 2 3 4 5

Insulation Material (Continuous Layer)

PolystyreneEPS PolystyreneXPS

0 1

Glazing Type Double6halfAir Double12halfAir Double6halfArgon Double12halfArgon Double6halfAirLowE Double12halfAirLowE Double6halfArgonLowE Double12halfArgonLowE Triple6halfAir Triple12halfAir Triple6halfArgon Triple12halfArgon Triple6halfAirLowE Triple12halfAirLowE Triple6halfArgonLowE Triple12halfArgonLowE

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Table.9.(1) Categorical Building Attributes These variables are generated by creating a dictionary between “categories” and “integers,” and then iterate different “categories” by creating a number slider with only integers.

• Uniform Distribution: For numerical attributes such as WWR (window to wall ratio 0.1-0.9) and Orientation (0-360), they are uniformly distributed, and the minimum and maximum boundaries are determined based on common sense and categorical attribute selections. Other uniformly distributed variables include:

Numerical Building Attributes Numerical Ranges Conditions WWR Window-to-wall Ratio

0.1-0.6 WallType: nonGlazing 0.8-0.9 WallType: Glazing

Heating Gas Efficiency When Using Natural Gas: 3PackagedSingleZoneAC 5VAVAirCooled+HydronicHeat 7VAVWaterCooled+HydronicHeat 11FanCoilUnitDOAS 12ActiveChillBeamsDOAS

0.77-0.84 EquipEfficiency: Medium 0.84-0.9 EquipEfficiency: High

Heating Electricity Efficiency When Using Electricity: 4PackagedSingleZoneHP 6VAVAirCooled+ElectricHeat 8VAVWaterCooled_ElectricHeat

3-4 EquipEfficiency: Medium 4-5 EquipEfficiency: High

Cooling Efficiency 3.17-4.33 EquipEfficiency: Medium 4.33-5.5 EquipEfficiency: High

Fan Efficiency 0.63-0.67 EquipEfficiency: Medium 0.67-0.7 EquipEfficiency: High

Sensible Rate When DOAS is Needed: 11FanCoilUnitDOAS 12ActiveChillBeamsDOAS

0.57-0.69 EquipEfficiency: Medium 0.69-0.81 EquipEfficiency: High

Latent Rate When DOAS is Needed: 11FanCoilUnitDOAS 12ActiveChillBeamsDOAS

0.69-0.77 EquipEfficiency: Medium 0.77-0.86 EquipEfficiency: High

Orientation 0-360 degrees

Insul.Thickness Between Studs 1-6” R-value Needs to Meet ASHRAE Standards Insuk.Thickness Continuous 0-2”

Roof Thickness 2-9” Floor Thickness 2-9”

Table.9.(2) Numerical Building Attributes These variables are generated by creating number sliders with discrete integers (for categorical attributes) or continuous floats (for numerical attributes). Categorical attributes determine the boundaries of many numerical attributes.

5. Calculate the Embodied Cost & Impact: For each combination of building attribute values, embodied cost (U.S. dollars) and environmental impact (kgCO2eq) will be calculated using the RSMean cost database and the openLCA ecoinvent carbon database.

6. Energy Usage Prediction: Surrogate Modelling Traditionally, Honeybee Energy-Plus and Open-Studio functions are used in Grasshopper to calculate annual energy usage for a building model. However, it takes 2-10 mins to finish energy simulation for one building model. It is fine for one simulation, but it is too time-consuming to sample a design space with thousands of simulations.

Thus, a surrogate model is developed to replace the Honeybee Open-Studio function. This model is trained with big data generated by Open-Studio in advance. The dataset includes feature inputs like Wall R-value and Glazing U-value, and objective outputs of annual energy usages, including natural gas for heating and electricity for heating, cooling, lighting, and equipment.

7. Calculate the Operational Cost & Impact: After knowing the energy usage, operational energy costs (U.S. dollars) will be calculated based on price information on the EIA (Energy Information Administration) official website. The environmental impact will be calculated based on a series of Handshake Excels.

8. Connect Variables & Objectives to Octopus: The purpose of Octopus in our project is to find the optimal combinations of building attribute variables that minimize three objective values:

• Lifecycle Cost (U.S. dollars): • Lifecycle Environmental Impact (kgCO2eq): • Design Diversity

5.2. LCA Analysis by Using Octopus: Preliminary Results The first run is tried without the 3rd objective Design Diversity, because we will discuss it in more detail later. After connecting variables (building attributes) and objectives (cost & impact) to Octopus, the first run is conducted with the following settings: Generation Size=30, #Generations=30, & Mutation Rate=0.5

Figure.10. Octopus Preliminary Result with 1000 Data It takes around 30 mins to finish the optimization. The optimal design solution is colored in purple in the top-right corner, with detailed construction information on the yellow panel back on the Grasshopper canvas. Also, looking

at the parallel coordinate diagrams, they change from diverse to more concentrated on a few optimal solutions as the # Generations increases, as shown in Figure 10 above. 5.3. Octopus: Parameter Calibration Now that we can do genetic optimization in Grasshopper, it’s time to think about doing it more efficiently since 30 mins (1000 runs) is not fast. It will be great to save some time with the same accuracy by exploring different combinations of hyperparameters and the number of runs. Firstly, different Ratio = GenerationSize / #Generations is explored for 200 runs to test its impact on results. The Mutation Rate = 0.5 is fixed. When measuring accuracy, Score = (0.5*cost+0.5*impact)/10^6, and a lower score represents higher accuracy. There are several criteria to measure optimization performance:

• The time needed to finish the optimization • The average score of the optimal designs (on the Pareto front) • The average score of the quasi-optimal designs (in the last generation)

After explorations, a Ratio between 0.5 and 2 leads to less time needed and higher accuracy, as shown in Figure 11. Later, when we test the amount of data needed, we will apply a Ratio = 1. The amount of data #Data equals GenerationSize * #Generations. Based on findings from Table.11, 200~400 data generated within 5~15 minutes is enough for satisfying accuracy. It is not worth running more data since the trade-off between time and the amount of data is significant. The last parameter tested is Mutation Rate. A Rate around 0.5 leads to less time needed, higher accuracy, and better diversity. A high Mutation Rate results in diverse design paths on the parallel coordinate diagram.

Figure.11 Hyperparameter Adjusting: Generation Size, # Generations, & #Data

5.4. Design Diversity Measurement

In the previous section, Design Diversity is the first time mentioned. Higher Mutation Rate leads to better diversity. However, increasing the Mutation Rate alone still cannot guarantee spread-out results; for example, by looking at the optimal solutions reported when Generation Size=14, #Generations=14, & Mutation Rate=0.5, almost all solutions feature equipment type 5 and a WWR close to 0.1. This is correct since type 5 VAVAirCooled+HydronicHeating is very energy-efficient, and a small WWR helps with saving heating energy. However, designers do not always want such a small WWR. They may still want to look at solutions with higher WWR, like 0.3 or 0.5, when they need a large glazing area and better transparency. Thus, there is a need to think about an alternative way to enhance design diversity by using distance.

As mentioned in section 3.4 and 4.4. Different distance methods are modified to adjust to my project needs, and their performances are evaluated by a set of criteria, as shown in Table 12. One-Point Distance is measured between each newly generated design and the centroid. The centroid is taken as the combination of average attribute values for all previously generated designs. Assuming there are n attributes, One-Point Distance is calculated as ∑ �(𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑎𝑎𝑎𝑎𝑎𝑎𝑁𝑁. i − 𝐴𝐴𝐴𝐴𝑁𝑁𝐴𝐴𝑎𝑎𝐴𝐴𝑁𝑁. i)2𝑛𝑛i=0 . The centroid will update as more designs are generated. Std.Deviation

Method measures the sum of normalized standard deviations of each attribute ∑ 𝑠𝑠𝑠𝑠𝑠𝑠(𝐴𝐴𝑠𝑠𝑠𝑠𝐴𝐴𝐴𝐴𝐴𝐴𝑎𝑎𝑠𝑠𝑁𝑁𝑁𝑁𝑎𝑎𝑎𝑎𝑎𝑎𝑁𝑁𝑠𝑠. 𝐴𝐴)𝑛𝑛𝑖𝑖=0 .

Normalization is done by using (𝐴𝐴𝑠𝑠𝑠𝑠𝐴𝐴𝐴𝐴𝐴𝐴𝑎𝑎𝑠𝑠𝑁𝑁𝑁𝑁𝑎𝑎𝑎𝑎𝑎𝑎𝑁𝑁 - 𝐼𝐼𝑠𝑠𝑠𝑠 min.) / ( 𝐼𝐼𝑠𝑠𝑠𝑠 𝑚𝑚𝑎𝑎𝑚𝑚. - 𝐼𝐼𝑠𝑠𝑠𝑠 𝑚𝑚𝐴𝐴𝑚𝑚 .), which normalizes each attribute value to a number between 0 and 1, ensuring that all attributes are at the same magnitude. Std.Deviation Method is used for Pareto front diversity too. Lastly, All-Points Distance measures the average distances between the newly generated design and all previous designs, ignoring the centroid. This is the default method in Octopus by checking the “Diversify Parameter” function.

Looking at average performance recorded in Table 12, different measurements are compared by looking at both result accuracy and diversity. Results are created with Generation Size=30, #Generations=10, & Mutation Rate=0.5. After comparison, the One-Point Distance method is selected due to several reasons:

• Although All-Points Distance leads to the highest diversity; its score is larger than others, which means less satisfying accuracy.

• Although Std.Deviation Method features the lowest score, its solutions are less diverse. For example, when other methods recommend six types of equipment, it only recommends one. When other methods provide WWR options as large as 0.6, it only stops at 0.48.

• In contrast, One-Point Distance performs moderately for both result diversity and accuracy

Table 12. Performance Comparison Between Different Diversity / Distance Measurements

As shown in Figure 13, this is the 3D Pareto front diagram plotted with three objectives: lifecycle cost (red axis), lifecycle impact (green axis), and diversity (One-Point Distance). Notice that diversity is measured as “- One-Point Distance,” since Octopus only does minimization problem. Minimized “- One-Point Distance” corresponds to maximized distance and largest diversity, so points at lower positions feature larger distances to the average solution. A trade-off between accuracy and diversity is obvious since larger |One-Point Distance| features higher cost and impact.

Figure 13. A Trade-off Between Diversity & Accuracy 5.5. Weight Explorations & Optimization Performance Comparison Now that the sacrifice of a higher diversity is smaller accuracy, it is important to control the level of diversity. In my project, it is controlled by assigning weights on objectives. Instead of directly optimizing three objectives, I will optimize the weight*objective. For example, if 1/3*cost & 1/3*impact & 1/3*diversity does not perform well in terms of accuracy, we can modify the diversity weight to 2/5*cost & 2/5*impact & 1/5*diversity. Table 14 shows the performance difference between different weight settings. To emphasize the advantage of applying optimization in lifecycle analysis, the results obtained after optimization will be compared with those obtained from exhaustive sampling as well. Saving percentage is calculated by looking at the minimized cost or impact and the average value: (average-min.)/average.

Table 14. Optimization Performance Comparison with Different Weights According to Table 14, optimization dose help locate optimal designs more efficiently because, firstly, all optimization workflows reduce run time from 30 mins to 10 mins. Secondly, they all feature a lower optimal score compared to 68.65 recorded for the exhaustive sampling method. The best score, 60.87, is achieved when there is no diversity added as the third objective, saving 7.13% cost and 23.31% carbon impact. 1/3 weight on diversity seems too large since its score of 67.43 is higher than 60.87. However, after lowering diversity weight to 1/5, the score improves to be 63.26. Apart from adjusting the weight on diversity, weights for cost and impact are user-adjustable as well. For instance, if the user cares about cost more than impact, he could assign weight as large as 3/5 on cost. This will lead to 13.56% saving, which corresponds to around $ 8.5 million saved. Conclusion 6.1. Finalized Optimization Method in our LCA Workflow In conclusion, genetic optimization is selected to find optimal solutions more efficiently because:

• It supports multi-objective optimization • It leads to multiple/dis-dominant optimal solutions, ensuring design flexibility • Suitable for various problems

Among existing optimization tools inside Grasshopper, Octopus is selected because: • It supports various types of variables, both discrete and continuous numbers • Relatively high speed • User-friendly Interface

6.2. Hyperparameter Suggestions & Amount of Data Needed One step before running Octopus is hyperparameter adjusting. Based on conclusions drawn from section 5.3:

• Ratio of Generation Size / #Generations: A ratio between o.5 and 1 is preferred with less time needed, better performance, and acceptable diversity.

• Amount of Data: 200~400 runs within 5~15 mins will be enough for generating good results.

• Mutation Rate: A rate close to 0.5 is preferred with less time needed, better performance, and acceptable diversity.

6.3. Design Diversity as the Third Objective Based on conclusions drawn from section 5.4, the best method to measure diversity is One-Point Distance, which maximizes the distance between a newly generated design and the average of all previously generated designs. There is a trade-off between diversity and accuracy, but the weight on diversity can be adjusted to control accuracy. 6.4. Performance Summary Based on section 5.5, compared to exhaustive sampling, genetic optimization helps save analysis time and improve accuracy. By playing with different weights on three objectives, users can control diversity, accuracy, and special emphasis on cost or impact. Contribution & Potential Impact 7.1. Optimization of Both Categorical & Numerical Variables One challenge solved in this project is the optimization of combinational categorical & numerical variables. Gradient-free genetic optimization is used to deal with this complex problem. Since genetic optimization accepts numerical and categorical variables, discrete integers can be assigned to represent categorical attributes. For example, when there are five wall types, they can be represented as 0, 1, 2, 3, 4, respectively. 7.2. Help with Early-Design-Stage LCA Suggestions Another unique point of this LCA workflow is analyzing conceptual geometries by randomly sampling the design space and then finding optimal solutions. By sampling different combinations of variables, the process fully considers early-design-stage uncertainties. By providing users with multiple optimal solutions, the process enables design flexibility. 7.3. Design Diversity & Weight Assignment The idea of design diversity is innovative in the field of parametric design. Distance is added as the third objective to quantify and maximize diversity, ensuring users’ flexibility to choose from various design solutions. Different weights assigned on three objectives help the designer with customizing the optimization goals.

Future Work 8.1 ASHRAE Limitations Among all the attributes, thicknesses of the wall, roof, and floor are crucial. Right now, they are selected from uniform distributions and the max. & min. boundaries are determined based on common sense. For example, the insulation thickness between studs varies between 1” and 6”. However, there should be more limitations added to these attributes. For example, ASHRAE standard lists min. R-values for different climate zones and the min.thickness should be calculated based on this. Thus, the min.thickness should be decided by different climate zones and insulation materials. 8.2. Diversity Measurement (Entropy) for Categorical Attributes In my project, diversity is measured as the distance for both categorical and numerical attributes. However, distance is not the proper metric for categorical attributes since the difference between 5 and 3 and the difference between 7 and 3 describe the same thing: two different categorical types. It doesn’t mean that 7-3=4 has a higher diversity compared to 5-3=2. In this case, entropy might be an alternative way to quantify diversity for categorical attributes, which requires further explorations. 8.3. User-Adjustable Attribute Boundaries In terms of user experience, it is a good idea to make attribute boundaries adjustable to customize their needs. Take WWR as an example; designers may prefer smaller WWR for a museum because lighting needs to be strictly controlled for a better exhibition environment; in this case, they could set the min.WWR as 0.1. In contrast, designers may prefer higher WWR for office towers since they want natural lighting and a modern appearance; in this case, they could set the min.WWR as 0.5. This could be done by giving instructions on how to adjust the slider min. & max. values. 8.4 Data Exportation for Attribute Feature Analysis Lastly, apart from recommending detailed design solutions as done in this project, I am also interested in analyzing attribute features of these recommended designs. To do this, a dataset with both attribute values and objective values is needed. These data could be exported from Octopus. However, Octopus automatically normalizes all the attribute values when doing optimization; so, they need to be decoded before the analysis. This is also one of the next steps to be explored.

References Ochsendorf, John A., Caitlin T. Mueller. “Combining Structural Performance and Designer Preferences in

Evolutionary Design Space Exploration.” Automation in Construction, 70-82. Amsterdam, Netherlands: February, 2015.

Brown, Nathan, Caitlin T. Mueller, and Stavros Tseranidis. “Multi-objective Optimization for Diversity and

Performance in Conceptual Structural Design.” In Proceedings of the 3rd International Association for Shell and Spatial Structures IASS, 17-20. Amsterdam, Netherlands: August, 2015.

Brown, Nathan, Caitlin T. Mueller, and Jonathas Felipe. “Early-stage Integration of Architectural and Structural

Performance in a Parametric Multi-objective Design Tool.” In Proceedings of the 3rd International Conference on Structures and Architecture ICSA, edited by Paulo J.S. Cruz, 1103-1111. CRC Press/Balkema: Jan 1, 2016.

Brown, Nathan, and Caitlin T. Mueller. “Quantifying Diversity in Parametric Design: A Comparison of Possible Metrics.” Artificial Intelligence for Engineering Design, Analysis and Manufacturing, 41-51. U.K., Cambridge University Press: January, 2018.

Hester, Joshua, et al. “Building Design-space Exploration Through Quasi-optimization of Life Cycle Impacts and

Costs.” Building and Environment. vol. 144 (2018): pp. 34-44. https://www.sciencedirect.com/science/article/abs/pii/S0360132318304712.

Hester, Joshua, Jeremy Gregory, and Randolph Kirchain. “Sequential Early-design Guidance for Residential Single-family Buildings Using a Probabilistic Metamodel of Energy Consumption.” Energy and Buildings. vol. 134 (2017): pp. 202-211. https://www.sciencedirect.com/science/article/abs/pii/S037877881631369X.

Brown, Nathan, Caitlin T. Mueller, and Stavros Tseranidis. “Data-Driven Approximation Algorithms for Rapid Performance Evaluation and Optimization of Civil Structures.” Automation in Construction 72 (2016) 279–293. Amsterdam, Netherlands: August, 2015.

Using Surrogate Model to Speed Up Energy-Plus Simulation When doing Building Lifecyle Analysis

Introduction

1.1. Energy-Plus in Building Lifecycle Analysis

Energy-Plus is one of the most popular engines that simulate energy consumption, including heating, cooling, equipment, and lighting. When doing building lifecycle analysis, it can be used to simulate operational energy usage. The environmental impact and cost for the energy usage will be then added to the lifecycle environmental impact and cost. Early design stage life cycle analysis can be done in Grasshopper, a code-friendly plug-in for the architecture software Rhino. Grasshopper is a suitable choice for lifecycle analysis because it can extract geometry information; more importantly, one of its packages called Honeybee can do energy modeling and interact with energy-plus within Grasshopper.

1.2. Need for Computational Speed

During the early design stage, users want to receive a quick response so that they could test more design options. However, it takes around 30s to finish an energy-plus simulation, and the time becomes longer when the geometries and building zones get more complicated. According to Doherty Threshold, “computer response time for optimal productivity has been estimated at 400ms” (Brown, 2015, p.280). Thus, there is a need to speed up the energy plus simulation process. Moreover, since there are many design opportunities during the early design stage, to get the lifecycle impact and cost distributions, we need to run hundreds of energy-plus simulations. In this case, a faster process is needed, as well.

1.3. Surrogate Modelling

One approach to speed up the energy-plus simulation process is to replace it with a surrogate model; in other words, an approximation algorithm. The surrogate model functions as a black box, with features as inputs and targets as outputs. It is trained with existing data, and it is used to predict target values based on new inputs. There are many existing algorithms to use in Python. Hyperparameters of algorithms can be adjusted to find the model with the highest accuracy. In this paper, we will focus on using the available packages and applying them in Grasshopper instead of the algorithm's theory.

1.4. Surrogate Modelling in Honeybee

Surrogate models are built-in Jupyter notebook using Python. It is easy to use the model for predictions in Jupyter notebook. However, the model is not simply an equation, so an extra step is needed to apply the model in Grasshopper. The Pickle function with the model inserted will replace the energy plus function.

1.5. Organization of Paper

This paper will first introduce features and targets in the lifecycle analysis for the exterior facades, followed by a brief introduction of different surrogate models and performance comparison methods. Then, the paper will illustrate the data generation process in grasshopper, including numerical and categorical features, as well as targets. It will also introduce the evaluation criteria for model performances in the background section.

As for methodologies, the paper will illustrate processes including data generation in Grasshopper by using python, surrogate model building process in Jupyter notebook, and the model applying process by using Pickle. When describing the modeling building process, this paper will compare two approaches, training numerical features and categorical features.

Background

2.1. Life Cycle Analysis for Exterior Facades

Building lifecycle analysis includes aspects such as structure, façade, equipment, and so on. This paper focuses on the operational analysis for exterior wall options. Insulation is the key factor that influences a building’s thermal performance. Thicker insulation leads to less energy used for heating and cooling but requires more material. To find the best wall assembly options, we need to simulate the wall assembly's energy performance. We can do that by using energy-plus, and we want to build a surrogate model to speed up this process.

2.2. Features & Targets

The target for the analysis is annual electricity usage (GWh) for heating, cooling, lighting, and equipment. Different wall assemblies have different thermal performance. A wall assembly contains many layers, and they are the features. A breakdown example of features can be found in Fig.1 Features & Target for Exterior Wall Analysis. There are eight categorical features: Wall Type, Façade Material, Insulation Thickness, Insulation Material, Number of Panes, Pane Coating, Air Space, and Air Type. Options for Wall Type are chosen based on the DOA commercial reference buildings. There are four wall types included in the reference: Solid Concrete, Solid Metal, Solid Steel Frame, and Solid Wood Frame. Another two types added are ICF (Insulated Concrete Frame Wall) and Curtain Wall. Façade Material options include Stucco, Brick, Metal Siding, Wood Siding, Concrete Masonry, and Stone Masonry. Insulation Thickness ranges from 1” to 6”. Insulation material options are selected based on market search. Six most popular insulation material is selected: Cellulose, Mineral Wool, Fiber Glass, Polyurethane Foam, EPS, and XPS. As for window properties, the first feature is the number of panes, and it can be single, double, or triple glazed. The pane coating options are low E-coated or non-coated. Air Space means the distance between two window panes. It can be either 6.4” or 12.6”. Then Air Type can be either argon or normal air. Apart from these categorical features, there are also numerical ones. WWR% refers to the window ratio. Shading Ratio% refers to how much percentage of the glazing façade can be shaded with shading devices. Then, Ext.Wall R-value (m2·K/W) is determined by Wall Type, Façade Material, Insulation Thickness, and Insulation Material. The higher R-value is, the better the thermal performance is. U-value is the reverse of R-value. Window U-value is

determined by the number of Panes, Pane Coating, Air Space, and Air Type. A huge amount of these feature combinations, together with their corresponding target values, are the dataset prepared to train the surrogate model.

Fig 1. Features & Target for Exterior Wall Analysis

2.3. Model Types & Hyperparameters

Three models explored in this paper are Kernel Ridge Regression, Random Forest, and Neural Network. Kernel Ridge Regression can accommodate nonlinearity in high dimensional space. Two key hyperparameters for that are alpha and gamma. They decide the smoothness of the curve and the size of Kernels. Random Forest operates by constructing a multitude of decision trees at training time and outputting the class that is the mode of the classes. Three hyperparameters to be adjusted for it include n_estimator (number of trees in the forest), max_depth (maximum number of levels in each decision tree), and max_features (max number of features considered for splitting a node). Random Forest is good at accessing and predicting discrete values. This feature will be useful when doing categorical regression, which will be illustrated later. Its hyperparameters include the number of layers, number of neurons in each layer, and activation functions. Take the number of neurons as an example; if there is only one target energy usage, there should only be one neuron in the last layer of the network. The most crucial hyperparameter is the activation function. There are many function options. When doing classification, sigmoid and tanh can be used because they have values ranging from 0 to 1, representing probabilities. In contrast, we cannot use them for numerical predictions since the results may be larger than 1. Instead, we can use ReLus or Softplus. ReLus is the function selected in our neural network. Image representations of three different models are shown in Fig 2.

Fig 2. Representations of Three Algorithms

2.4. Performance Comparison Method

The metric used to look at model performance is mean square error (MSE). It is correlated to some other common factors, such as R square. However, “a single MSE number may not be enough to explain the performance, because people may wonder how big or small value for MSE is compared to the values of the structure score, how the normalization scheme affects it, and about other similar issues” (Brown, 2015, p.282). As a result, this paper will also mention performance visualization choices at the conclusion part.

Methodology

3.1. Data Sampling in Grasshopper

To train the surrogate model, we need to generate data first. The dataset with feature and target values is generated by the Grasshopper script using the energy-plus function. Firstly, the ranges and options of wall features are listed in Grasshopper, as shown in Fig 3. (inside the purple box). Then, the python (inside the pink box) will select combinations of wall features as inputs for Honeybee Construction functions to build the wall assembly. Energy-plus is then used to report the target energy usage for each design solution. It took around 12 hours to finish 800 runs. And this 800-length dataset is used for building the surrogate model. As for the sampling method, grid sampling is used. For example, when selecting a window to wall ratio (WWR), python will select from 10%, 20%, 30% and so on. Other sampling methods include random sampling and Latin Hyper sampling. We will discuss the pros and cons later in the result section.

Fig 3. Grasshopper Script Used for Generating Data

3.2. Modelling Building Process: Numerical

The first approach to train the surrogate model is by using numerical features only: Ext.Wall R-value, Window U-value, WWR%, and Shading Ratio%. The latter three are directly generated by python. In contrast, Ext.Wall R-value is obtained by constructing walls inside Honeybee and then using the existing Honeybee function that calculates assembly R-value.

Then, the dataset will be split into training and test data. The process of finding the best hyperparameters is called cross-validation. The training data is divided into several parts. For each trial, a small portion of the training data will be selected as the validation set, and the others are selected as training sets. The validation set is used to test the trained model at each trail, reporting corresponding MSE. The best model is the option with minimized MSE or optimal hyperparameters. Finally, the test data is used to report the MSE of the best model. Usually, it’s an average value of several runs. A process illustration is shown in Fig 4.

Fig 4. Cross-Validation Process

3.3. Modelling Building Process: Categorical

Another approach to train the models is by using categorical features. In this way, we can skip the Honeybee construction step. Python can directly generate features. However, most of them are “Strings,” instead of numbers. So, we need to encode categories into arrays of 0 and 1. A Python function called OneHotEncode can do this. Take WallType as an example; we use five 0 and one 1 to represent six different wall types. The position of 1 represents the type of wall. We will encode each column and then combine all columns together. The advantage of separately encoding each column is that we can leave numerical columns as numerical. For example, when the insulation thickness numerical values are kept in the feature dataset, users can test whatever thickness they want. In contrast, if the thickness is encoded, users can only select from the existing thickness in the feature dataset. The energy prediction will be made by inputting the long series of the number containing arrays and numerical values.

Fig 5. OneHotEncode Categories to Arrays with 0 and 1

3.4. Modelling Applying Process in Grasshopper

The built model is saved in Jupyter notebook. Pickle is used to loading the saved model from its directory to Grasshopper. Take the categorical approach as an example; the categorical options can be presented as drop-down menus. Before inputting these options to the model, they need to be encoded as well. So, the final input for the model is a list with many arrays with 0 and 1 and some numerical values. The output of the model is the annual electricity usage in GWh, as shown in Fig. 6.

Fig 6. Apply Categorical Model in Grasshopper

Results

4.1. Model Performance Comparison

The main criteria to evaluate model performance is MSE. The average target value is 1.4 GWh. All models show an error of around 1%, which is very good. There are several findings by looking at the average MSE chart in Fig 7. Firstly, for both Kernel Ridge Regression and Random Forest, MSE for the numerical approach is lower than the one for the categorical approach, but the difference is not huge. Secondly, for both numerical and categorical approaches, Random Forest performs better than Kernel Ridge Regression, especially for the categorical approach. This is probably because Random Forest is good at analyzing binary data. When encoding categorical values, it generates a series of arrays containing 0 and 1. Random Forest uses > 0.5 or < 0.5 to distinguish these inputs. The nature of grid sampling may also be the other reason since Random Forest is good at accessing discrete values. However, when switching to random sampling, the performance of different models may change correspondingly. Moreover, the Neural Network performs better than both Kernel

Fig 7. Model Performance Comparison by MSE

Ridge Regression and Random Forest. However, it requires more time to build the model. Considering both response time and accuracy, Random Forest is selected as the optimal model.

4.2. Other Available Analysis

Apart from predictions, some other analysis can be done with a huge amount of data as well. For example, we can explore the sensitivity of different features, which feature has a larger influence on energy usage. Since the model is not a simple equation, we cannot determine the sensitivity by looking at coefficients. Instead, we can explore that by visualizing the design space. A parallel coordinate diagram might be a good option. When hovering on the high score range, we could see the design patterns. For example, most WWR% ranges between 20 and 40 percent, which means that WWR is a sensible feature.

Fig 8. Design Solution Exploration & Sensibility

Conclusion

5.1. Possible Improvements

5.1.1 Sampling Method

In this paper, Random Forest is selected as the optimal model. One reason for that is because we are using grid sampling, and Random Forest is good at analyzing discrete values. However, when testing the model in Grasshopper, I found that the model works well when predicting features that exist in the training dataset, for example, 30% and 40% WWR. It doesn’t work well when predicting continuous values, for example, 33% or 35.6%. Thus, to analyze design options exhaustively, a better sampling method to use is random sampling. Although Latin-Hyper sampling will lead to a more even distribution, it is not considered due to higher complexity and more time required.

5.1.2 Separate Models

Based on surrogate modelling precedents in Joshua’s paper, the performance of heating energy predictions is always better than the one for cooling predictions. When predicting cooling and heating together, the performance might seem good because of the heating part; however, it doesn’t mean that the predictions for cooling are good enough. To address this, a possible option is to predict heating and cooling separately, so we can make sure that we are getting good models for both parts.

5.1.3 Normalization

During the model building process, it’s found that training the model with features and target at the same magnitude leads to better performance. To ensuring all variables to be on a similar scale, I am currently adjusting variables by changing units. For example, kWh can be changed to GWh to decrease the energy usage to a smaller magnitude around 1.4, like the R-value or U-value around 2.0 or 3.0. However, in Brown’s paper, the authors introduce a better method to do that, and it is called normalization. So, the value is normalized by using the variable itself reduced by its mean and then divided by its standard deviation. Normalization is important because “it brings all the variables in the same magnitude and prevent assigning unrealistic importance or bias toward some variables” (Brown, 2015, p.280).

5.1.4 Performance Visualizations

As mentioned before, MSE values might not be enough when comparing model performance. There are several options suggested in Brown's paper to visualize the model performance. For example, a plotting with predicted values versus real values can be useful. As explained by Brown, "the correlation of the two variables is a way to quantify the proximity of the points to the slope 1 line. This correlation metric is often referred to as the R2. The closer this value is to 1, the better the performance is. And good performance features points accumulating near the slope 1 line" (Brown, 2015, p.284). Another option is to plot an MSE bar graph. Brown also suggests that there can be a flat model to be established as a benchmark when comparing model MSE. Since this flat model is calculating the mean of the dataset every time. It does not reflect in any way the structure of the data, and a surrogate model must surely have a considerably lower error than this flat model's to be considered adequate" (Brown, 2015, p.285). These are all possible options to be done for better performance visualizations.

5.2. Contributions

The use of the surrogate model will speed up the energy simulation process significantly. We can use the energy usage results as part of the lifecycle cost and environmental impact calculation. By facilitating the process to generate a huge amount of data, we could better optimize life cycle cost and impact, meanwhile analyzing the sensitivity of different features.

Reference

Brown, Nathan, Caitlin T. Mueller, and Stavros Tseranidis. “Data-driven approximation algorithms for rapid performance evaluation and optimization of civil structures.” Automation in Construction 72 (2016) 279–293. Amsterdam, Netherlands: August 2015.

Hester, Joshua, Jeremy Gregory, and Randolph Kirchain. “Sequential Early-design Guidance for Residential Single-family Buildings Using a Probabilistic Metamodel of Energy Consumption.” Energy and Buildings. vol. 134 (2017): pp. 202-211. https://www.sciencedirect.com/science/article/abs/pii/S037877881631369X.

Hester, Joshua, et al. “Building Design-space Exploration Through Quasi-optimization of Life

Cycle Impacts and Costs.” Building and Environment. vol. 144 (2018): pp. 34-44. https://www.sciencedirect.com/science/article/abs/pii/S0360132318304712.

Brown, Nathan, Caitlin T. Mueller, and Jonathas Felipe. “Early-stage Integration of Architectural

and Structural Performance in a Parametric Multi-objective Design Tool.” In Proceedings of the 3rd International Conference on Structures and Architecture ICSA, edited by Paulo J.S. Cruz, 1103-1111. CRC Press/Balkema: Jan 1, 2016.