# The Design Environment: Genetic Algorithm Solver

The success of my thesis is contingent upon the capability of multi-objective algorithms to be solved and drive the creation of façade geometry directly within the digital design environment. Therefore the digital design environment, of the selected three dimensional modeling software Rhino, combined with visual programming agent Grasshopper, must have algorithmic capabilities that provide beneficial application to this thesis; particularly in the realms of conditional multi-variable solving, processing time, geometry creation, and logic building from climatic data sets.

It was determined that the best type of algorithm to use for my thesis is a genetic algorithm. Genetic algorithms, also known as evolutionary algorithms, are able to gain knowledge and build off of that knowledge in each consecutive analysis run in route to finding an optimized solution. The algorithm evolves with each new pass in finding a solution, and reduces computation time to find a solution as a result. For this reason they are commonly found in computational environments that are conducting an immense amount of analysis and simulations to find a performance driven result.

Considering Grasshopper has a preconfigured command that is a genetic algorithm solver titled Galapagos, Galapagos is used as a departure point for studying how genetic algorithms could interact with climatic data, and generate optimized geometry using multi-objective search criteria inside the digital design space.

# Analysis of the Algorithmic Solver

Galapagos uses a typical input-output relationship that is common to most genetic multi-objective algorithm solvers. A ‘fitness function’ is defined as the goal to be solved for, and parametric variable relationships are defined as outputs. Galapagos defines the output relationships as Genomes. These outputs, utilizing Galapagos are restricted to slider parametric function inside the Grasshopper environment. The fitness function is single variable, where the parametric outputs (genomes) can be multivariable. In Galapagos, fitness functions can be defined with search criteria seeking a maximum, minimum, or specified numerical value.

Galapagos offers further features that entail record keeping of each evolutionary pass as it works through analysis, run time restricting, and various conditionally criteria for controlling the mating and offspring behavior of stepping through evolutionary generations (maximum of stagnant generations, maximum population per generation, population multiplication for first generation, individual carryover between population runs, and percentage of inbreeding between generations).

To test the suitability of Galapagos for the thesis project at hand, it must interact with climatic data, author optimized geometry, solve multi-objective criteria, and seek solutions by processing large collections of climate data efficiently. Therefore three experiments were conducted testing Galapagos’s capabilities to sort through data sets, author geometry from climate data, and optimize with multi-criteria restraints.

The first experiment had Galapagos identify the date, month, and time the greatest amount of collective solar radiation was falling on a tilted portion of a building façade. Date, month, and time served as the parametric slider adjustments that Galapagos was adjusting, and a solar radiation test point provided the comparison to identify if the fitness function, the maximum, was being achieved.

The second experiment investigated Galapagos’s ability to optimize and author geometry from climate data. The experiment set a desired solar radiation value (.2 kWh/M2) on a fixed date and time that served as the fitness function, and geometry parametrics were established for vertical fin shading devices. Galapagos had the ability to adjust the rotation, width, and depth of each vertical fin independently as it worked towards resolving a solution that obtained the closest average of .2 kWh/M2 across the façade sample. The façade sample curved and rotated to the North-East to get variation of solar radiation across the façade.

FINAL STATS: Genome[29], Fitness=0.25, Genes [53% · 47% · 48% · 63% · 31% · 33% · 60% · 63% · 91% · 53% · 89% · 96% · 39% · 48% · 92% · 68% · 99% · 45% · 58% · 57% · 18% · 14% · 48% · 65% · 99% · 59% · 71% · 20% · 18% · 65% · 40% · 19% · 77%]

The final experiment sought to explore Galapagos’s handling of multi-objective criteria. It was conducted by combining the first two experiments. Vertical shading fins were created along a façade with parametric sliders, and a range of months, dates, and times were provided as sliders as well. Galapagos’s task was to optimize and author façade geometry while also identifying the ideal date and time for a fitness function of .3 kWh/M2 of cumulative solar radiation.

# Evidential Results

Experiment 1: Seeking and Finding from Data

Running the analysis for over two hours yielded desirable results. Galapagos identified September 9th at 9:00am in the morning the date that receives the greatest amount of solar radiation on the selected façade portion. This output seems logical because the selected area exists on the eastern side of the building. Therefore it would make sense it receives more radiation in the morning. It also makes sense a date near the Fall equinox was selected because theoretical the equinox would provide the greatest shortest distance away from the sun, for the greatest amount of time. Because the surface plane being analyzed is angled and receives shading from surrounding geometry, it also makes sense the equinox was not selected exactly.

Experiment 2: Form Finding from Climate Data

Galapagos worked through various iterations in an attempt to optimize the geometry to meet the conditional criteria. However, it never fully reached the fitness function; as evident from final output percentages. Likely this is the result of needing to run the analysis with a larger population for a greater period of time. But Galapagos was certainly successful in authoring façade geometry that was directly responding to climatic conditions. Much improvement could also be observed from the beginning and end solar radiation readings.

Experiment 3:Multi-Criteria Optimization

Experiment was not completed in completeness due to the time required to complete analysis. However, Galapagos did indicate promise in being able to respond to the multi-objective criteria of authoring geometry, while sorting through data sets.

# Architectural Application

Galapagos has clear ability to support the architectural design process from an output standpoint. Performance based geometry, and numerical values, can be found with automatization using Galapagos as a genetic algorithmic solver. It doing so, architecture can be crafted digitally for climate responsiveness by defining parametric relationships and establishing performative goals to optimize for.

# References

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