A.1.1.1. Principle and process of data distillation#

Data distillation reduces repetitive data into a single set. It is used to build new profiles—for example, to determine interest rates in banking or select optimal materials in manufacturing (Inmon et al., 2020).

A.1.1.2. Principle and process of data subsetting#

Following distillation, data is further filtered into subsets to avoid bias and simplify analysis. This aids in selecting relevant and insightful data (Inmon et al., 2020).

A.1.2.1. Definition and working principle#

LS is a geometry-based algorithm that reorganizes and smooths meshes by adjusting node positions. It improves mesh quality while preserving the original topology (Huang et al., 2020; Xiao et al., 2019).

A.1.2.2. Iterative process of LS#

In the repositioning process, point A is the initial coordinate and point B is the final coordinate, computed iteratively from the previous point (Xiao et al., 2019).

Where $N$ is the number of neighboring nodes and $\overline{x_i^{(q+1)}}$ is the new coordinate after smoothing and iteration $(q+1)$ (Xiao et al., 2019).

Where $N_q$ and $N_{(q+1)}$ are derived from $q$ and $(q+1)$. If $N_{(q+1)} = 0$, then Equation A.1 applies (Xiao et al., 2019).

A.1.2.3. Purpose and Application of LS#

LS can be used in geometric modeling via software such as Rhino and Grasshopper. Though lacking a linear algebra library, the algorithm’s iterations let users create balanced models between accuracy and speed. LS is also flexible and applicable across various design phases (Huang et al., 2020).

A.1.3.1. Historical development#

SPA emerged from network modeling needs to identify shortest routes:

• 1955 – Dantzig formalized the shortest path problem.
• 1957 – Minty used web string and knot representations.
• 1959 – Ford introduced negative arc lengths.
• 1959 – Dijkstra created a simpler version with minimal data storage, still widely used today.
• 1968 – Hart et al. introduced A* with cost estimation for route completion.

In the past 50 years, A* has been refined and applied to telephone routing, communication networks, and transport systems (Zeng and Church, 2009).

A.1.3.2. Function and strengths of A*#

A* finds shortest routes by aligning paths with existing networks (Schneider et al., 2011).

• Optimization can be achieved using evolutionary algorithms like Galapagos.
• A* advantages over Dijkstra: - Searches for sub-optimal solutions, not just the optimal. - Faster and more efficient in directed search ([^Alieksieiev/2019]; [^Mittal-etal/2021]).

A.1.3.3. A* working process#

A* combines heuristic $h(n)$ and actual cost $g(n)$ (Hart et al., 1968):

• $g(n)$ – Actual shortest route from source $s$ to node $n$.
• $h(n)$ – Estimated distance from $n$ to goal $a$.
• $f(n)$ – Total temporary shortest cost, updated until algorithm finishes.

A.1.4.1. Wallacei#

Wallacei was developed by Mohammed Makki during his PhD at the Architectural Association (AA), supervised by Dr. Michael Weinstock (Makki et al., 2019).

• Built on evolutionary computation to solve design problems.
• Focuses on:
  1. Problem formulation.
  2. Output analysis.
  3. Optimized solution selection.

A.1.4.2. Wallacei data analysis#

Wallacei generates several analytic graphs, such as:

• SDG – Standard Deviation Graph (real-time FO visualization).
• SDT – Standard Deviation Trendline (trendline for standard deviation across generations).
• MVT – Mean Value Trendline (average value trend).
• PCP – Parallel Coordinate Plot (PCP visualization from first to last generation).
• DF – Diamond Fitness Chart (DF graph for selected solutions).
• FVG – Fitness Values Graph (fitness values of all population solutions).

A.1.4.3. Wallacei simulation process#

During the input phase, required data includes: Genes, Fitness Objectives/FO, Data, and Phenotypes. After processing in Wallacei X, output values are: Genomes, Fitness Values/FV, Data, and Phenotypes.