In a sense, design is about choosing parameters. All the parameters available for adjustment form the basis of the multi-dimensional solution space. The ranges within which the parameters are allowed to change, often due to constraints, sets the volume of the feasible region of the solution space where the designer is supposed to work. Parametric design is, to some extent, a way to convert design processes or subprocesses into algorithms for varying the parameters in order to automatically generate a variety of designs. Once such algorithms are established, users can easily create new designs by tweaking parameters without having to repeat the entire process manually. The reliance on computer algorithms to manipulate design elements is called parametricism in modern architecture.
Parametricism allows people to use a computer to generate a lot of designs for evaluation, comparison, and selection. If the choice of the parameters is driven by a genetic algorithm, then the computer will also be able to spontaneously evolve the designs towards one or more objectives. In this article, I use the design of the heliostat field of a concentrated solar power tower as an example to illustrate how this type of generative design may be used to search for optimal designs in engineering practice. As always, I recorded a screencast video that used the daily total output of such a power plant on June 22 as the objective function to speed up the calculation. The evaluation and ranking of different solutions in the real world must use the annual output or profit as the objective function. For the purpose of demonstration, the simulations that I have run for writing this article were all based on a rather coarse grid (only four points per heliostat) and a pretty large time step (only once per hour for solar radiation calculation). In real-world applications, a much more fine-grained grid and a much smaller time step should be used to increase the accuracy of the calculation of the objective function.
Video: The animation of a generative design process of a heliostat field on an area of 75m×75m for a hypothetical solar power tower in Phoenix, AZ.
Figure 1: A parametric model of the sunflower.
Heliostat fields can take many forms (the radial stagger layout with different heliostat packing density in multiple zones seems to be the dominant one). One of my earlier (and naïve) attempts was to treat the coordinates of every heliostat as parameters and use genetic algorithms to find optimal coordinates. In principle, there is nothing wrong with this approach. In reality, however, the algorithm tends to generate a lot of heliostat layouts that appear to be random distributions (later on, I realized that the problem is as challenging as protein folding if you know what it is -- when there are a lot of heliostats, there are just too many local optima that can easily trap a genetic algorithm to the extent that it would probably never find the global optimum within the computational time frame that we can imagine). While a "messy" layout might in fact generate more electricity than a "neat" one, it is highly unlikely that a serious engineer would recommend such a solution and a serious manager would approve it, especially for large projects that cost hundreds of million of dollars to construct. For one thing, a seemingly stochastic distribution would not present the beauty of the Ivanpah Solar Power Facility through the lens of the famed photographers like Jamey Stillings.
In this article, I chose a biomimetic pattern proposed by Noone, Torrilhon, and Mitsos in 2012 based on Fermat's spiral as the template. The Fermat spiral can be expressed as a simple parametric equation, which in its discrete form has two parameters: a divergence parameter βthat specifies the angle the next point should rotate and a radial parameter b that specifies how far the point should be away from the origin, as shown in Figure 1.
Figure 2: Possible heliostat field patterns based on Fermat's spiral.
When β = 137.508° (the so-called golden angle), we arrive at Vogel's model that shows the pattern of florets like the ones we see in sunflowers and daisies (Figure 1). Before using a genetic algorithm, I first explored the design possibilities manually by using the spiral layout manager I wrote for Energy3D. Figure 2 shows some of the interesting patterns I came up with that appear to be sufficiently distinct. These patterns may give us some ideas about the solution space.
Figure 3: Standard genetic algorithm result.
Figure 4: Micro genetic algorithm result.
Then I used the standard genetic algorithm to find a viable solution. In this study, I allowed only four parameters to change: the divergence parameter β, the width and height of the heliostats (which affect the radial parameter b), and the radial expansion ratio (the degree to which the radial distance of the next heliostat should be relative to that of the current one in order to evaluate how much the packing density of the heliostats should decrease with respect to the distance from the tower). Figure 3 shows the result after evaluating 200 different patterns, which seems to have converged to the sunflower pattern. The corresponding divergence parameter β was found to be 139.215°, the size of the heliostats to be 4.63m×3.16m, and the radial expansion ratio to be 0.0003. Note that the difference between β and the golden angle cannot be used alone as the criterion to judge the resemblance of the pattern to the sunflower pattern as the distribution also depends on the size of the heliostat, which affects the parameter b.
I also tried the micro genetic algorithm. Figure 4 shows the best result after evaluating 200 patterns, which looks quite similar to Figure 3 but performs slightly less. The corresponding divergence parameter β was found to be 132.600°, the size of the heliostats to be 4.56m×3.17m, and the radial expansion ratio to be 0.00033.
In conclusion, genetic algorithms seem to be able to generate Fermat spiral patterns that resemble the sunflower pattern, judged from the looks of the final patterns.
Everyone loves to maximize the return of investment (ROI). If you can effortlessly find a solution that pays a higher profit -- even only a few dollars more handsomely, why not? The problem is that, in many complicated engineering cases in the real world, such as designing a solar farm, we often don't know exactly what the optimal solutions are. We may know how to get some good solutions based on what textbooks or experts say, but no one in the world can be 100% sure that there aren't any better ones waiting to be discovered beyond the solution space that we have explored. As humans, we can easily get complacent and settled with the solutions that we feel good about, leaving the job (and the reward) of finding better solutions to another time or someone else.
Artificial intelligence (AI) is about to change all that. As design is essentially an evolution of solutions, AI techniques such as genetic algorithms (GA) are an excellent fit to the nature of many design problems and can generate a rich variety of competitive designs in the same way genetics does for biology (no two leaves are the same but they both work). These powerful tools have the potential to help people learn, design, and discover new things. In this article, I demonstrate how GA can be used to design a photovoltaic (PV) solar farm. As always, I first provide a short screencast video in which I used the daily output or profit as the objective function to speed up the animation so that you can see the evolution driven by GA. The actual assessments are based on using the annual output or profit as the objective function, presented in the text that follows the video. Note that the design process is still geared towards a single objective (i.e., the total output in kWh or the total profit in dollars over a given period of time). Design problems with multiple objectives will be covered later.
In GA, the solution depends largely on the choice of the objective function (or the fitness function), which specifies how the main goal is calculated. For example, if the main goal is to generate as much electricity as possible on a given piece of land without the concern of the cost of the solar panels, a design in which the solar panels are closely packed may be a good choice. On the other hand, if the main goal is to generate as much electricity as possible from each individual solar panel because of their high price, a design in which rows of solar panels are far away from one another would be a good choice. Unsurprisingly, in the case shown in the video, a single row of solar panels was found as the best solution. Aiming at maximizing the profit, the real-world problems always lie between these two extremes, which is why they must be solved using the principles of engineering design. The video above clearly illustrates the design evolution driven by GA in the three cases (the two extremes and an intermediate).
Figure 1. An Energy3D model of an existing solar farm in Massachusetts.
To test the usefulness of the GA implementation in Energy3D for solving real-world problems, I picked an existing solar farm in Massachusetts (Figure 1) to see if GA could find better solutions. A 3D model of the solar farm had been created in the Virtual Solar Grid based on the information shown on Google Maps and its annual output calculated using Energy3D. Because I couldn't be exactly sure about the tilt angle, I also tweaked it a bit manually and ensured that an optimal tilt angle for the array be chosen (I found it to be around 32° in this case). The existing solar farm has 4,542 solar panels, capable of generating 2,255 MWh of electricity each year, based on the analysis result of Energy3D. [I must declare here that the selection of this site was purely for the purpose of scientific research and any opinion expressed as a result of this research should be viewed as exploratory and should not be considered as any kind of evaluation of the existing solar farm and its designer(s). There might be other factors beyond my comprehension that caused a designer to choose a particular trade-off. The purpose of this article is to show that, if we know all the factors needed to be considered in such a design task, we can use AI to augment our intelligence, patience, and diligence.]
Figure 2. The results of 10 iterations.
Energy3D has a tool that allows the user to draw a polygon within which the solar farm should be designed. This polygon is marked by white lines. Using this tool, we can ensure that our solutions will always be confined to the specified area. I used this tool to set the boundary of the solar farm under design. This took care of an important spatial constraint and guaranteed that GA would always generate solutions on approximately the same land parcel as is situated by the existing solar farm.
For the objective function, we can select the total annual output, the average annual output of a solar panel, or the annual profit. I chose the annual profit and assumed that the generated electricity would sell for 22.5 cents per kWh (the 2018 average retail price in Massachusetts) and the daily cost of a solar panel (summing up the cost of maintenance, financing, and so on) would be 20 cents. I didn't know how accurate these ROI numbers would be. But let's just go with them for now. The annual profit is the total sale income minus the total operational cost. Qualitatively, we know that a higher electricity price and a lower operational cost would both favor using more solar panels whereas a lower electricity price and a higher operational cost would both favor using less solar panels. Finding the sweet spots in the middle requires quantitative analyses and comparisons of many different cases, which can be outsourced to AI.
Figure 3: The best design from 2,000 solutions
Figure 4: The second best design from 2,000 solutions.
In Energy3D, GA always starts with the current design as part of the first generation (so if you already have a good design, it will converge quickly). In order for GA not to inherit anything from the existing solar farm, I created an initial model that had only a rack with a few solar panels on it and a zero tilt angle. The size of the population was set to be 20. So at the beginning, this initial model would compete with 19 randomly generated solutions and was almost guaranteed to lose the chance to enter the next generation. In order to stop and check the results, I let GA run for only 10 generations. For convenience, let's call every 10 generations of GA evolution an iteration. Figure 2 shows that GA generated solutions below the supposed human performance in the first two iterations but quickly surpassed it after that. The solution kept improving but got stuck in iterations 5-7 and then it advanced again and stagnated again in iterations 8-10. This process could continue indefinitely, but I decided to terminate it after 10 iterations, or 100 generations. By this time, the software had generated and evaluated 2,000 solutions, which took a few hours as it had to run 2,000 annual simulations for thousands of solar panels.
The best solution (Figure 3) that emerged from these 2,000 generated solutions used 5,420 solar panels fixed at a tilt angle of 28.3° to generate 2,667 MWh per year and was about 16% better than the existing one based on the ROI model described above. The second best solution (Figure 4) used 4,670 solar panels fixed at a tilt angle of 38.6° to generate 2,340 MWh per year and was about 5.5% better than the existing one based on the ROI model. Note that if we use the average annual output per solar panel as the criterion, the second best solution would actually be better than the best one, but we know that the average panel output is not a good choice for the fitness function as it can result in an optimal solution with very few solar panels.
In conclusion, the generative design tools in Energy3D powered by AI can be used to search a large volume of the solution space and find a number of different solutions for the designer to pick and choose. The ability of AI to transcend human limitations in complex design is a significant application of AI and cannot be more exciting! We predict that future work will rely more and more on this power and today's students should be ready for the big time.
The National Science Foundation issued a statement on May 10, 2018 in which the agency envisions that "The effects of AI will be profound. To stay competitive, all companies will, to some extent, have to become AI companies. We are striving to create AI that works for them, and for all Americans." This is probably the strongest message and the clearest matching order from a top science agency in the world about a particular area of research thus far. The application of AI to the field of design, and more broadly, creativity, is considered by many as the moonshot of the ongoing AI revolution, which is why I have chosen to dedicate a considerable portion of my time and effort to this strategically important area.
I have added two more application categories of using genetic algorithms (GAs) to assist engineering design in Energy3D, the main platform based on which I am striving to create a "designerly brain." One example is to find the optimal position to add a new building with glass curtain walls to an open space in an existing urban block so that the new building would use the least amount of energy. The other example is to find the optimal sizes of the windows on different sides of a building so that the building would use the least amount of energy. To give you a quick idea about how GAs work in these cases, I recorded the following two screencast videos from Energy3D. To speed up the search processes visualized in the videos, I chose the daily energy use as the objective function and only optimized for the winter condition. The solutions optimized for the annual energy use are shown later in this article.
Figure 1: A location of the building recommended by GA if it is in Boston.
Figure 2: A location of the building recommended by GA if it is in Phoenix.
For the first example, the energy use of a building in an urban block depends on how much solar energy it receives. In the winter, solar energy is good for the building as it warms up the building and saves the heating energy. In the summer, excessive heating caused by solar energy must be removed through air conditioning, increasing the energy use. The exact amount of energy use per year depends on a lot of other factors such as the fenestration of the building, its insulation, and its size. In this demo, we only focus on searching a good location for a building with everything else fixed. I chose a population with 32 individuals and let GA run for only five generations. Figures 1 and 2 show the final solutions for Boston (a heating-dominant area) and Phoenix (a cooling-dominant area), respectively. Not surprisingly, the GA results suggest that the new building be placed in a location that has more solar access for the Boston case and in location that has less solar access for the Phoenix case.
Figure 3: Window sizes of a building recommended by GA for Chicago.
Figure 4: Window sizes of a building recommended by GA for Phoenix.
For the second example, the energy use of a building depends on how much solar energy it receives through the windows and how much thermal energy transfers through the windows (since windows typically have less thermal resistance than walls). In the winter, while a larger window allows more solar energy to shine into the building and warm it up during the day, it also allows more thermal energy to escape through the larger area, especially at night. In the summer, both solar radiation and heat transfer through a larger window will contribute to the increase of the energy needed to cool the building. And this complicated relationship changes when the solution is designed for a different climate. Figures 3 and 4 show the final solutions for Chicago and Phoenix as suggested by the GA results, respectively. Note that not all GA results are acceptable solutions, but they can play advisory roles during a design process, especially for novice designers who do not have anyone to consult with.
In conclusion, artificial intelligence such as GA provides automated procedures that can help designers find optimal solutions more efficiently and thereby free them up from tedious, repetitive tasks if an exhaustive search of the solution space is necessary. Energy3D provides an accessible platform that integrates design, visualization, and simulation seamlessly to demonstrate these potential and capabilities. Our next step is to figure out how to translate this power into instructional intelligence that can help students and designers develop their abilities of creative thinking.