Annie Helmes

Original Building Form:

Although my part 2 from Module 5 was a different shape, I chose to go back to the basics and use my solution from part 1 except ensured my scripts changed two parameters. With the twisting triangular mass family, the parameters that can be flexed include the base radius and top height. This figure can be shown below.


Recommended Building Form:


Inputs: Top Height = 530 ft, Base Radius = 220 ft

New Evaluator Metrics:

  1. LEED Rating of my Building
  2. Rent of an SF Commerical Building

Metric #1:

As structural engineers, it is pivotal that we are concious of the carbon footprint of our structures. The LEED Evaluation system, in particular, is a means of which quantifying and rewarding the “greenest” buildings. Thus, I decided for my first evaluation metric that I would look at the overall carbon footprint of my building and with this assign it a LEED rating. Although the LEED system uses a number of metrics to evaluate the overall energy efficiency of the building, I used the square footage of my building to do so.

Using an EPA tool, I found that an average commericial building emits around 10 lbs of CO2 per square foot during construction ( From this, I did a bit more research into seeing how the LEED ratings correspond with the carbon emissions and found the table below from Arc Skoru that I would use as my metric. 10 lbs is equivalent to 0.005 tons so for the sake of simplicity, in the custom node I measured the CO2 emissions in tons.


As a means of maximizing the “score,” I assigned numerical values to the certification levels with 4 corresponding to Platinum and 1 corresponding to Certified. I ran the script initially in order to see what sorts of values I was getting as the carbon emissions initially. Obviously, since all my areas are being multiplied by 0.005 tons, they all fell into the “Gold” category. I expected this, so from an initial passing, I altered the metrics such that I assigned a “carbon value limit” with a LEED Rating: Platinum was <5000 tons, Gold <6000, Silver <7000, Certifed <8000 and then anything greater than 8000 tons was not rated. The script used to create this LEED rating assignments was for me, one of the hardest parts of the assignment but I wanted to challenge myself.

The script of my “BuildingForm.CarbonEmissions” custom node can be found below.


Metric #2:

For my second metric, I wanted to look at the building from a real estate perspective and chose to examine the monthly rent per SF of the space. I did some research regarding SF rent for commercial buildings and found that on average, commercial real estate is around $66 per SF per year. This price, however, varies with floor level. As the floor level increases, the price increases. With a higher floor comes better views and ameneties. With the baseline as $66, the middle levels rent cost $120 with the high-rise levels costing $250. I divided the space into 3 zones of 25 levels.

The script of my “BuildingForm.CostOfRent” custom node can be found below.


By computing both metrics, I was able to produce the summary table below with inputs and outputs.

Summary Table:


Single-Objective Function:

For my single objective function, the objectives I worked to satisfy were maximizing space efficiency (gross area/gross volume), minimizing carbon emission, maximizing LEED rating, and minimizing cost of rent. The carbon emissions and LEED ratings go hand in hand, but I wanted to show both for completion. I did this single objective scheme by adapting the “EvaluationResults.ComputeCombinedEvaluationScore” node from the module videos. I normalized these metrics by using almost the equivalent of a linear interpolation. For the metrics I wanted to minimize, I calculated: (Max - Col Value) / (Max- Min). For the metrics I wanted to maximize, I calculated: (Col Value - Min) / (Max- Min). This can be seen through the code block below with 5 corresponding to Carbon Emissions, 6 corresponding to LEED Rating, and 7 corresponding to Rental Cost:


I then found the combined scores for these four metrics by summing them together. A snip of this custom node can be found below:


For the weights themselves, I assigned them on an order of 1-3 with 1 being the least important and 3 being the most important. My importance metric scoring can be clearly seen below:

  • Space Efficiency: 2
  • Carbon Emissions: 2
  • LEED Rating: 1
  • Cost of Rent: 3

As much as I wish that low carbon and good LEED ratings were valued more, unfortunately the world works around money. Thus, I chose the cost of rent for the office to be the most important. I think efficient use of space as well as low carbon emissions are equally as important in order to create a greener and efficient space. Finally, since the LEED ratings are not required by the state, I made it the least important metric. My personal values may disagree, but I wanted to put this single objective function in the eyes of the consumer. The bulk of the single objective function as used in my main test script can be found below:


Ultimately, the weighting factors worked in conjunction with the goal of my scheme in maximizing efficiency, minimizing carbon, maximizing LEED rating, and minimizing cost. The largest “score” correlates with the desired final result. I didn’t output the space efficiency because I wanted to focus on the metrics I made the custom nodes for but they are included in the score. Also, I added more alternatives during my final run for the sake of thoroughness. The buildings that had a gross floor area that was out of the boundaries of 1,200,000 SF - 1,500,000 SF were assigned a score of 0 as they violated the project guidelines. The final results can be found below with the top 3 recommended design alternatives highlighted in blue with the darker shading being most desirable and lighter being less desirable.


The “Best” Option

The best option was one that had the following parameters and metrics:

  • Top Height: 530 ft
  • Base Radius: 220 ft
  • Gross Floor Area: 1273263.556 SF
  • Carbon Emissions: 6366.32 tons
  • LEED Rating: 2 (Silver)
  • Cost of Rent: $3,361,415.79

This alternative rose to the top based on the way my optimization scheme was scaled in terms of importance metrics. In a non-intuitive sense, the Minimum Key node actually had the maximum values and the Maximum Key node has the minimum. Thus, the Maximum Key Node provided the desired result. The reason that these works almost backwards was simply due to my optimization goals, maximizing and minimizing different metrics. It is important to note that there will always be a sense of bias associated in choosing the best alternative as I had to decide what metrics were important to me. Ultimately the best alternative is not necessary the best option but optimizes the metrics I found important comparative to the alternatives - with a lower carbon emission, higher LEED rating and lower, respectively, cost of rent.

Main Script: