Generative Design

Generative Design for AEC Computational Design

1. Generative Design Paradigm

1.1 Definition and Scope

Generative design is a computational design methodology in which a designer defines a problem through goals, constraints, and variable parameters, and an algorithmic system autonomously generates, evaluates, and evolves candidate solutions across a defined design space. Unlike traditional design where the human produces every solution manually, generative design shifts the designer's role from direct form-maker to curator of outcomes — defining what is desired rather than how to achieve it.

In the AEC context, generative design applies to problems ranging from single-building floor plan layouts and structural topologies to neighborhood-scale massing studies and infrastructure routing. The common thread is a design space too large for exhaustive manual exploration.

1.2 Distinction from Parametric Design

The confusion between parametric and generative design is pervasive. The distinction is fundamental:

A parametric model is a prerequisite for generative design — it provides the mechanism by which the solver manipulates geometry. But parametric design alone does not search; it merely responds to human input. Generative design automates the search.

1.3 The Generate-Evaluate-Evolve Loop

Every generative design process follows a three-phase loop:

1. Generate — The solver creates candidate solutions by sampling or evolving design variable values within defined ranges. In evolutionary approaches, this involves applying genetic operators (crossover, mutation) to parent solutions.

2. Evaluate — Each candidate is assessed against one or more fitness functions. This is typically the computational bottleneck: running energy simulations, structural analyses, daylight calculations, or spatial adjacency checks for every individual in every generation.

3. Evolve — Based on evaluation results, the solver selects better-performing candidates and uses them to produce the next generation. Over many iterations, the population converges toward high-performing regions of the design space.

This loop continues until convergence criteria are met: a generation limit is reached, fitness improvements plateau below a threshold, or population diversity drops below a minimum.

1.4 When to Use Generative Design

Generative design is appropriate when:

• The design space is large (more than 5-10 independent variables)
• Multiple conflicting objectives must be balanced simultaneously
• Optimal or near-optimal performance is critical (structural efficiency, energy, cost)
• The relationship between variables and outcomes is non-linear and non-intuitive
• The designer needs evidence-based justification for design decisions
• Time exists for computational exploration (hours to days of compute)

Generative design is not appropriate when:

• The problem is well-understood and a known heuristic suffices
• Only one or two variables are being tuned (manual slider adjustment is faster)
• Evaluation is extremely expensive and no surrogate model is feasible
• Aesthetic or experiential qualities dominate and resist quantification
• The parametric model is unstable or produces invalid geometry frequently

1.5 Design Agency and Authorship

The designer retains authorship because they define the problem, construct the fitness landscape, set constraints, and select solutions. The algorithm is a tool with no intent. However, generative design shifts creative decisions upstream: defining what matters (fitness functions), what is possible (variable ranges), and what is acceptable (feasibility thresholds). This demands deeper understanding of design performance than traditional workflows.

1.6 Human-in-the-Loop vs. Fully Automated Generation

Fully automated: Solver runs autonomously from initialization to convergence. Designer intervenes only at setup and selection. Appropriate for well-defined problems with reliable fitness functions.

Human-in-the-loop (IEC): Designer evaluates candidates subjectively during optimization, guiding evolution toward aesthetically or experientially desirable outcomes.

The hybrid approach — automated fitness for quantifiable metrics, human selection for qualitative criteria — is often most productive in practice.

2. Evolutionary Algorithm Fundamentals

2.1 Genetic Algorithm (GA) — Core Framework

The Genetic Algorithm is the foundational evolutionary optimization method used in AEC generative design. Inspired by Darwinian natural selection, it maintains a population of candidate solutions that evolve over generations through selection, crossover, and mutation.

2.1.1 Encoding Schemes

The encoding (genotype representation) determines how design variables are stored and manipulated:

Binary encoding: Variables as bit strings (e.g., 8-bit = 0-255). Simple operators but suffers from Hamming cliffs and imprecision for continuous variables.

Real-valued encoding: Variables as floating-point numbers directly. Standard for AEC — design variables (dimensions, angles, positions) are inherently continuous. Used by all major Grasshopper solvers.

Permutation encoding: For ordering problems (room sequencing, scheduling). Requires order-preserving operators (PMX, OX, CX).

Tree/graph encoding: For evolving solution topology itself (bracing patterns, connectivity graphs). Enables topological innovation but complex to implement.

2.1.2 Selection Methods

Selection determines which individuals become parents for the next generation:

Tournament selection: Randomly pick k individuals (tournament size, typically k=2 to 7), select the best. Larger k increases selection pressure. This is the most commonly used method in AEC tools — simple, efficient, no global fitness sorting required.

Roulette wheel (fitness-proportionate) selection: Selection probability proportional to fitness. Problem: premature convergence when one individual dominates.

Rank-based selection: Selection probability proportional to rank rather than raw fitness. Avoids scaling issues of roulette wheel.

Stochastic universal sampling (SUS): Like roulette wheel but uses equally spaced pointers, reducing selection variance.

2.1.3 Crossover (Recombination) Operators

Crossover combines genetic material from two parents to produce offspring:

Single-point crossover: Choose a random point; offspring gets genes from parent A before the point and parent B after.

Two-point crossover: Two random points; segment between points from one parent, rest from the other. Better gene block preservation.

Uniform crossover: Each gene independently chosen from either parent with equal probability. Maximum mixing — good when variables are independent.

Simulated Binary Crossover (SBX): Standard for NSGA-II. Operates directly on real numbers. Distribution index eta_c (typically 2-20) controls offspring distance from parents. Higher eta_c = offspring closer to parents (exploitation); lower = larger jumps (exploration).

Blend Crossover (BLX-alpha): Offspring sampled uniformly from [min(p1,p2) - alphad, max(p1,p2) + alphad]. Alpha=0.5 is typical.

2.1.4 Mutation Operators

Mutation introduces random variation to maintain diversity:

Bit-flip mutation: For binary encoding. Each bit has probability 1/L of flipping.

Gaussian mutation: For real-valued encoding. Add N(0, sigma) noise to each gene. Most common mutation in AEC problems. Sigma can be fixed or adaptive.

Polynomial mutation: Used in NSGA-II. Distribution index eta_m (typically 20-100) controls perturbation magnitude. Higher eta_m = smaller perturbations.

Swap / Scramble mutation: For permutation encoding. Swap exchanges two positions; scramble randomly rearranges a subset.

Adaptive mutation: Rate or step size adjusts during the run — higher early (exploration), lower later (exploitation).

2.1.5 Elitism

Elitism ensures the best individual(s) from the current generation survive unchanged into the next generation. Without elitism, the best solution found can be lost through crossover and mutation. Typically, the top 1-5% of the population is preserved. NSGA-II implements elitism through its combined parent+offspring selection scheme.

2.2 Population Sizing

Population size determines the balance between solution diversity and computational cost:

• Rule of thumb: 50-200 individuals for most AEC problems
• Small populations (20-50): Faster per generation but higher risk of premature convergence and loss of diversity. Acceptable for problems with few variables (<10) and smooth fitness landscapes
• Medium populations (50-200): Standard range. Provides sufficient diversity for most problems with 10-50 variables
• Large populations (200-1000): Necessary for highly multimodal landscapes, many-objective problems, or when each variable has a large range. Computationally expensive if evaluation is slow
• Adaptive population sizing: Start small, increase if diversity drops. Some frameworks support this

The critical trade-off: larger populations explore more of the design space per generation but require more evaluations per generation. If a single evaluation takes 30 seconds (e.g., energy simulation), a population of 200 requires nearly 2 hours per generation.

2.3 Convergence Criteria

Optimization terminates when:

• Generation limit: Fixed number of generations (e.g., 50-500). Simple and predictable but may stop too early or waste time
• Fitness plateau: Average or best fitness has not improved by more than epsilon over the last N generations. Typical: epsilon = 0.1%, N = 10-20 generations
• Diversity threshold: Population diversity (measured by genotypic or phenotypic distance) drops below a minimum, indicating convergence
• Computational budget: Total evaluation count reaches a limit (e.g., 10,000 evaluations). Useful when evaluation cost is the binding constraint
• Target fitness: A satisfactory fitness value is reached. Rarely used in multi-objective optimization

2.4 Exploration vs. Exploitation Balance

The fundamental tension in optimization:

• Exploration: Searching broadly across the design space for promising regions. Promoted by: large populations, high mutation rates, low selection pressure, diverse initialization
• Exploitation: Intensifying search near known good solutions. Promoted by: small populations, low mutation rates, high selection pressure, elitism

Effective optimization requires both. Early generations should favor exploration; later generations should favor exploitation. This can be achieved through:

• Adaptive operator rates (decreasing mutation rate over time)
• Island models (separate subpopulations with periodic migration)
• Restart strategies (re-initialize if stuck)
• Niching methods (fitness sharing, clearing) to maintain diverse subpopulations

2.5 Schema Theorem and Building Blocks

Holland's Schema Theorem: short, low-order, above-average schemata (building blocks) receive exponentially increasing trials in subsequent generations. Implication for encoding: variables that interact strongly should be positioned near each other in the genotype to reduce disruption by crossover.

3. Multi-Objective Optimization

3.1 Pareto Optimality

Most AEC design problems involve multiple conflicting objectives. A building cannot simultaneously minimize cost, minimize energy consumption, and maximize floor area — these objectives conflict. Multi-objective optimization acknowledges this and seeks the set of best trade-off solutions.

Pareto dominance: Solution A dominates solution B if A is at least as good as B in all objectives and strictly better in at least one. A solution that is not dominated by any other solution in the population is called non-dominated or Pareto optimal.

Pareto front: The set of all non-dominated solutions forms the Pareto front (or Pareto frontier) in objective space. This front represents the best achievable trade-offs — improving one objective requires worsening another.

3.2 Pareto Front Visualization

For 2 objectives: a 2D scatter plot with each axis representing one objective. The Pareto front appears as a curve along the boundary of the feasible region.

For 3 objectives: a 3D scatter plot or parallel coordinate plot. The Pareto front is a surface.

For 4+ objectives: direct visualization is impossible. Use parallel coordinate plots, radar charts, heatmaps, or dimensionality reduction (PCA, t-SNE) to explore the solution set. Wallacei provides built-in multi-dimensional Pareto analytics.

3.3 NSGA-II (Non-dominated Sorting Genetic Algorithm II)

NSGA-II (Deb et al., 2002) is the most widely used multi-objective evolutionary algorithm in AEC. It is the engine behind Wallacei and many other tools.

Key mechanisms:

1. Non-dominated sorting: The combined parent+offspring population is sorted into fronts. Front 1 contains all non-dominated solutions. Front 2 contains solutions dominated only by Front 1, and so on
2. Crowding distance: Within each front, solutions are ranked by crowding distance — a measure of how isolated a solution is in objective space. Solutions with larger crowding distances are preferred to maintain diversity along the Pareto front
3. Selection: Binary tournament selection using (front rank, crowding distance) as the comparison key. Lower front rank is better; within the same front, higher crowding distance is better
4. Elitism: The next generation is filled by taking solutions front-by-front from the combined population until the population size is reached. The last front that fits may be truncated using crowding distance

Typical NSGA-II parameters for AEC:

• Population size: 50-200
• Crossover: SBX with eta_c = 20, probability = 0.9
• Mutation: Polynomial with eta_m = 20, probability = 1/n (n = number of variables)
• Generations: 50-300

3.4 SPEA2 (Strength Pareto Evolutionary Algorithm 2)

SPEA2 maintains an external archive of non-dominated solutions. Fitness based on domination strength and density (k-th nearest neighbor distance). Often produces better-distributed Pareto fronts than NSGA-II for many-objective problems. Available in Octopus for Grasshopper.

3.5 MOEA/D (Multi-Objective Evolutionary Algorithm based on Decomposition)

Decomposes the multi-objective problem into single-objective subproblems using weight vectors. Each subproblem optimized simultaneously with information sharing between neighbors. Efficient for many-objective problems (4+) where NSGA-II's crowding distance becomes less effective.

3.6 Trade-Off Analysis and Decision-Making

The Pareto front provides options, not answers. Decision-making methods:

• Knee point selection: Point of maximum curvature where marginal trade-offs are most balanced
• Aspiration-based: Define acceptable thresholds per objective, select solutions satisfying all
• TOPSIS: Rank by distance to ideal point and from anti-ideal point
• Clustering: Group similar Pareto-optimal solutions, select representatives. Wallacei provides K-means and agglomerative clustering
• Designer preference: Review phenotype geometry and select on qualitative judgment

3.7 Weighted Sum vs. Epsilon-Constraint Methods

Weighted sum: F = w1f1 + w2f2 + ... + wn*fn. Simple but cannot find solutions on non-convex Pareto front regions. Galapagos uses this approach.

Epsilon-constraint: Optimize f1 subject to f2 <= epsilon_2, f3 <= epsilon_3. Can find non-convex Pareto front solutions. Requires choosing which objective to optimize and setting constraint bounds.

4. Fitness Function Design

4.1 The Most Critical Step

The fitness function is the single most consequential decision in generative design. It encodes what the designer values. A poorly designed fitness function will efficiently produce solutions that are technically "optimal" but designically irrelevant. The fitness function is the designer's proxy — it must faithfully represent design intent.

4.2 Common AEC Fitness Criteria

Structural Objectives

• Total weight / material volume: Minimize structural material usage (steel tonnage, concrete volume)
• Maximum deflection: Minimize peak deflection under service loads (L/360, L/240 limits)
• Stress utilization ratio: Minimize peak stress/capacity ratio across all members (target: 0.6-0.85 range)
• Material efficiency: Maximize load-carried-per-unit-material (structural efficiency index)
• Natural frequency: Maximize first natural frequency to avoid resonance (target: >3 Hz for floors)
• Redundancy: Maximize structural redundancy (number of alternative load paths)

Environmental Objectives

• Annual daylight hours: Maximize useful daylight illuminance (300-3000 lux) across floor area
• Solar heat gain: Minimize unwanted solar gain in cooling season; maximize in heating season
• Energy use intensity (EUI): Minimize annual energy demand per unit floor area (kWh/m2/year)
• View factor: Maximize percentage of floor area with quality views to exterior
• Daylight autonomy (DA): Maximize percentage of occupied hours when daylight exceeds 300 lux
• Useful Daylight Illuminance (UDI): Maximize hours in 100-2000 lux range (avoid glare)
• Embodied carbon: Minimize total embodied CO2 of structural and envelope materials (kgCO2e)

Spatial Objectives

• Area efficiency: Maximize net-to-gross floor area ratio (usable area / total area)
• Circulation ratio: Minimize circulation area relative to total area (target: 15-25%)
• Adjacency satisfaction: Maximize satisfaction of programmatic adjacency requirements (percentage of required adjacencies achieved)
• Daylight factor: Maximize average daylight factor across occupied spaces (target: >2%)
• Spatial connectivity: Maximize/minimize integration values from space syntax analysis
• Room proportion: Minimize deviation from target aspect ratios (1:1 to 1:1.5 for offices)

Fabrication Objectives

• Panel planarity: Minimize maximum deviation of quad panels from planar (target: <panel-diagonal/500)
• Unique element count: Minimize number of unique panel types / structural members
• Material waste: Minimize cutting waste when nesting panels on stock sheets
• Assembly complexity: Minimize number of distinct connection types or assembly steps
• Curvature variation: Minimize rate of curvature change across surface (smoother = easier to build)

Cost Objectives

• Material quantity: Minimize total material volume/weight across all systems
• Construction duration: Minimize critical path length in construction schedule
• Lifecycle cost: Minimize 30-year total cost (construction + operation + maintenance + demolition)
• Operational cost: Minimize annual energy + maintenance + staffing costs

4.3 Normalization Strategies

When combining multiple objectives, normalization is essential to prevent one objective from dominating due to scale differences:

Min-max: f_norm = (f - f_min) / (f_max - f_min). Maps to [0,1]. Requires estimating bounds. Z-score: f_norm = (f - mean) / std_dev. Maps to ~[-3, 3]. Dynamic per generation. Target-based: f_norm = |f - f_target| / f_target. For absolute performance targets. Rank-based: Replace values with population rank. Eliminates scale differences but loses magnitude.

4.4 Constraint Handling

Not all variable combinations produce valid designs. Constraint handling manages infeasible solutions:

Penalty method: F_penalized = F_original + penalty * violation_magnitude. Penalty coefficient must balance discouraging infeasibility without undervaluing near-boundary feasible solutions. Adaptive penalties that increase over generations are effective.

Repair method: Map infeasible solutions to nearest feasible solution (e.g., clip oversized rooms to maximum). Effective but requires domain-specific logic.

Decoder method: Genotype maps to feasible phenotypes via a decoder function. Feasibility guaranteed by construction. Example: floor plan decoder ensures rooms tile without overlaps.

Feasibility rules (Deb's rules): Feasible beats infeasible; between infeasible, smaller violation wins; between feasible, better fitness wins. Used in NSGA-II.

Multi-objective constraint handling: Treat constraint satisfaction as an additional objective in Pareto ranking.

4.5 Weighted Aggregation

For single-objective solvers (Galapagos): F_total = w1f1_norm + w2f2_norm + ... + wn*fn_norm where sum(wi) = 1.0. Start with equal weights, then adjust to reflect priorities. Warning: cannot discover solutions on non-convex Pareto front regions.

4.6 Feasibility Thresholds

Hard boundaries: minimum room areas (code), maximum stress (safety), minimum daylight factor (LEED/BREEAM), maximum height (zoning), minimum setbacks (zoning), fire egress distances (life safety). These are constraints defining the feasible region, not objectives.

5. Design Space Exploration

5.1 Parameter Space Definition

The design space is the set of all possible solutions defined by the design variables and their ranges. Each variable defines one dimension of the space. A problem with 20 variables defines a 20-dimensional space.

Variable types:

• Continuous: Position, dimension, angle (e.g., column spacing from 6.0m to 12.0m)
• Discrete: Count, selection (e.g., number of floors from 3 to 15)
• Categorical: Type choice (e.g., structural system: steel frame, concrete frame, timber)
• Boolean: On/off (e.g., include atrium: yes/no)

5.2 Dimensionality and the Curse of Dimensionality

As the number of variables increases, the volume of the design space grows exponentially. A problem with 10 variables, each with 10 possible values, has 10^10 = 10 billion possible solutions. Exhaustive search is impossible.

Practical implications:

• < 5 variables: Grid search or full factorial DOE may be feasible
• 5-15 variables: Evolutionary algorithms work well with moderate populations (50-100)
• 15-50 variables: Larger populations (100-300) and more generations needed. Sensitivity analysis to identify and fix unimportant variables is valuable
• 50+ variables: Decompose the problem, use surrogate models, or apply dimensionality reduction before optimization

5.3 Sampling Strategies

Initial population generation affects convergence speed and solution quality:

Random sampling: Each variable sampled uniformly and independently. Simple but leaves gaps in high dimensions.

Latin Hypercube Sampling (LHS): Each variable's range divided into N equal intervals with exactly one sample per interval. Standard for DOE in AEC. Better coverage than random sampling.

Sobol sequences: Quasi-random low-discrepancy sequences with superior space-filling properties. Available in Python (scipy.stats.qmc.Sobol).

Orthogonal sampling: Extension of LHS ensuring uniform distribution in multi-dimensional subspaces, not just marginal distributions.

5.4 Sensitivity Analysis

Before full optimization, sensitivity analysis identifies which variables most influence the objectives, enabling dimensionality reduction:

Morris method (Elementary Effects): Screening method computing mean and standard deviation of elementary effects per variable. Large mean = influential variable; large std = variable interacts with others. Cost: O(k*(n+1)) evaluations.

Sobol indices: Variance-based global sensitivity. First-order index S_i measures variance due to variable i alone. Total-order index ST_i includes all interactions involving i. Computationally expensive (thousands of evaluations); use surrogate models to reduce cost.

5.5 Design of Experiments (DOE)

DOE provides structured approaches to sample the design space before or instead of optimization:

• Full factorial: All combinations of variable levels. Exponential cost, feasible for <5 variables
• Fractional factorial: Systematic subset, aliases some interactions but drastically reduces evaluations
• Central composite design (CCD): Full factorial + axial + center points. For response surface models
• Box-Behnken design: Alternative to CCD with fewer points, excludes corner points
• Optimal designs (D-optimal, I-optimal): Algorithmically selected points maximizing information per evaluation

5.6 Surrogate Models

When fitness evaluation is expensive (minutes per evaluation for energy simulation or FEA), surrogate models approximate the fitness function with a cheap-to-evaluate mathematical model:

Kriging (Gaussian Process Regression): Interpolates known points with uncertainty estimates, enabling intelligent sampling via expected improvement criterion. Gold standard for expensive optimization.

Radial Basis Functions (RBF): Weighted sums of radial functions centered at known points. Faster than Kriging for large datasets. Used by Opossum (RBFOpt).

Polynomial regression: Low-order polynomials. Fast but limited to smooth, low-dimensional landscapes. Useful for initial screening.

Neural networks: Approximate complex, high-dimensional landscapes. Require hundreds to thousands of training points.

5.7 Visualization Methods

Parallel coordinate plots: Each axis = one variable/objective; each solution = a polyline. Reveals correlations and preferred ranges. Wallacei provides interactive versions. Scatter matrix: Grid of pairwise scatter plots revealing correlations and trade-offs. Heatmaps: Fitness values across 2D variable slices. Identifies ridges, valleys, optima. t-SNE / UMAP: Dimensionality reduction grouping similar solutions, revealing clusters.

6. Tools for Generative Design in AEC

6.1 Tool Comparison Table

6.2 Detailed Tool Notes

Galapagos: The entry point for most designers. Drag a fitness output and a set of sliders into the Galapagos component. It handles GA setup automatically. For multi-objective problems, manually combine objectives into a weighted sum. Best for: quick single-objective explorations, learning generative workflows, problems with <15 variables.

Wallacei: The professional standard for multi-objective generative design in Grasshopper. Provides NSGA-II with full Pareto front analytics including: generation-by-generation convergence tracking, objective value distributions, parallel coordinate filtering, K-means clustering of solutions, phenotype (geometry) preview for any solution. Wallacei X adds enhanced analytics. Best for: serious multi-objective AEC optimization, research, design competitions.

Octopus: Supports many-objective optimization (4+ objectives) better than Wallacei through HypE (Hypervolume-based) algorithm. Interactive Pareto front allows the designer to steer evolution in real time. Best for: many-objective problems, interactive exploration.

Opossum: Uses surrogate-based optimization (RBFOpt) to minimize the number of true evaluations. Instead of evaluating thousands of solutions, it builds a surrogate model from dozens of evaluations and optimizes the surrogate. Best for: problems where each evaluation takes minutes (energy simulation, CFD, detailed structural analysis).

Refinery (Autodesk): Cloud-based generative design for Dynamo. Offloads computation to Autodesk servers. Provides multi-objective optimization with result visualization in a web interface. Best for: Revit/Dynamo users, teams without powerful local hardware.

Autodesk Forma: Cloud platform for early-stage urban and building design. Provides real-time performance feedback (wind, daylight, energy, noise) and generative exploration of massing options. Best for: urban-scale generative studies, early concept design, non-specialist users.

7. Generative Design Workflow

Step 1: Define Design Problem and Objectives

Clearly articulate what you are optimizing and why. Write out:

• The design context (building type, site, program)
• The performance objectives (what to minimize/maximize)
• The constraints (hard limits that must be satisfied)
• The evaluation criteria (how will you judge the results beyond fitness)

Example: "Optimize the floor plan layout of a 2,000 m2 office floor to maximize daylight autonomy, maximize programmatic adjacency satisfaction, and minimize circulation area, subject to minimum room sizes per the brief and maximum distance-to-exit per fire code."

Step 2: Identify Design Variables and Ranges

List every parameter the solver can manipulate. For each variable, specify:

• Name and description
• Type (continuous, discrete, categorical)
• Range (minimum, maximum, or list of options)
• Whether it interacts with other variables

Aim for 5-30 variables. Fewer than 5 may not need generative design; more than 30 may require decomposition or dimensionality reduction.

Step 3: Build Parametric Model

Construct the parametric model in Grasshopper, Dynamo, or a scripting environment. The model must:

• Accept all design variables as inputs
• Produce valid geometry for all variable combinations within ranges
• Be robust (no crashes or null geometry for edge cases)
• Run in reasonable time (seconds, not minutes, per evaluation — or use surrogates)

Model robustness is critical. If 10% of variable combinations crash the model, the solver wastes 10% of evaluations and may converge to regions that avoid crashes rather than regions with high fitness.

Step 4: Design Fitness Functions

Implement computable functions that evaluate each objective. Use simulation plugins (Ladybug/Honeybee for environmental, Karamba for structural, custom scripts for spatial) to compute performance metrics. Normalize all fitness values to comparable scales.

Test fitness functions manually with a few known configurations to verify they produce sensible values and rankings.

Step 5: Configure Solver

Select the solver based on the problem:

• Single objective: Galapagos
• Multi-objective (2-3 objectives): Wallacei (NSGA-II)
• Many-objective (4+ objectives): Octopus (HypE/SPEA2)
• Expensive evaluation: Opossum (RBFOpt)

Set parameters:

• Population size: start with 50, increase if diversity is insufficient
• Generations: start with 50, increase if convergence is not reached
• Crossover rate: 0.8-0.95 (SBX with eta_c = 15-20)
• Mutation rate: 1/n to 3/n where n is the number of variables

Step 6: Run Optimization

Launch the solver. Monitor:

• Best fitness per generation (should improve and plateau)
• Average fitness per generation (should improve, indicating population-wide learning)
• Diversity metrics (should decrease gradually, not crash)
• Computation time per generation (estimate total runtime)

For long runs (hours/days), save checkpoints. Most tools allow pausing and resuming.

Step 7: Analyze Results

For single-objective: examine the best solution and compare to the initial design.

For multi-objective:

• Visualize the Pareto front. Is it well-distributed? Are there gaps?
• Apply clustering to group similar solutions on the Pareto front
• Use parallel coordinates to identify common patterns among high-performing solutions
• Preview phenotypes (geometries) for diverse Pareto-optimal solutions
• Compute hypervolume indicator to measure Pareto front quality across runs

Step 8: Select and Refine Solutions

Choose 3-5 solutions from the Pareto front that represent distinct trade-off strategies. For each:

• Document objective values and how they compare to baseline
• Generate high-quality geometry for presentation
• Identify refinement opportunities not captured by the fitness function (aesthetics, constructability details, user experience)
• Iterate manually or run a focused local optimization around the selected solution

8. Case Study Examples

8.1 Floor Plan Layout Optimization

Problem: Optimize the layout of 12 rooms on a 40m x 30m rectangular floor plate for an educational building.

Variables (18 total):

• Room centroid positions: 12 rooms x (x, y) = 24 variables, reduced to 18 by fixing corridors and constraining room connectivity
• Room proportions: 12 aspect ratios (1.0 to 2.0)

Objectives:

1. Maximize adjacency satisfaction — percentage of required adjacencies (e.g., labs near prep rooms, offices near classrooms) achieved based on centroid distances
2. Maximize average daylight factor — computed via Radiance/Honeybee for each room based on window exposure
3. Minimize circulation area — area consumed by corridors and lobbies as a percentage of total

Constraints: Minimum room areas per educational standards. Maximum distance to nearest exit. No room overlaps (enforced by decoder).

Solver: Wallacei, NSGA-II, population 100, 80 generations = 8,000 evaluations.

Results: Pareto front with 45 non-dominated solutions. Three clusters emerge: (A) high-daylight layouts with rooms along perimeter, higher circulation; (B) compact layouts with minimal circulation but reduced daylight for interior rooms; (C) balanced layouts with light wells providing daylight to interior rooms. Cluster C reveals a design strategy (light wells) that was not initially considered — a generative discovery.

8.2 Facade Shading System Optimization

Problem: Optimize a parametric louver shading system on a south-facing office facade (20m wide x 15m tall, Latitude 40N).

Variables (8 total):

• Louver depth: 0.2m to 1.0m
• Louver spacing: 0.3m to 1.5m
• Louver tilt angle: 0 to 60 degrees
• Number of louver zones (horizontal divisions): 2 to 5
• Per-zone depth multiplier: 0.5 to 1.5 (2-5 variables depending on zone count)

Objectives:

1. Minimize annual cooling load contribution from solar gain (kWh/m2/yr) — computed via EnergyPlus/Honeybee
2. Maximize annual average useful daylight illuminance at desk level (% floor area >300 lux)
3. Minimize material cost — proportional to total louver surface area (cost/m2 of aluminum louver)

Solver: Wallacei, NSGA-II, population 80, 60 generations. Each evaluation requires a Radiance simulation (10 seconds) and an EnergyPlus simulation (30 seconds). Total runtime: approximately 27 hours.

Results: Pareto front reveals that deeper louvers dramatically reduce cooling load but at diminishing returns beyond 0.6m depth. View and daylight preservation is best achieved with variable-depth zoning — deeper louvers at eye level and shallower louvers above. The cost-optimal region suggests 0.45m depth at 0.6m spacing as the knee point of the cost-performance trade-off.

8.3 Structural Form-Finding Optimization

Problem: Optimize the shape of a long-span roof shell (50m x 50m footprint) for a sports hall.

Variables (12 total):

• Control point heights for a 4x4 NURBS surface: 16 control points, of which 4 corners are fixed and edge midpoints are symmetric, yielding 12 free variables
• Height range: 3m to 20m per control point

Objectives:

1. Minimize total structural weight (steel shell + supporting structure) — computed via Karamba3D finite element analysis
2. Minimize maximum deflection under dead + live load combination
3. Maintain minimum interior clearance of 8m (constraint, handled via penalty)

Solver: Octopus (HypE), population 120, 100 generations. Each evaluation requires a Karamba3D analysis (~2 seconds). Total runtime: approximately 6.5 hours.

Results: The Pareto front shows a clear trade-off between weight and deflection. Minimum-weight solutions tend toward anticlastic (saddle-shaped) surfaces that carry load efficiently through membrane action but have higher deflections. Minimum-deflection solutions tend toward synclastic (dome-like) shapes that are stiffer but heavier. The knee point reveals a hybrid form — a shallow dome with edge curvature — that achieves 85% of the minimum weight at only 120% of the minimum deflection. This form was not intuitively predictable.

9. Advanced Topics

9.1 Interactive Evolutionary Computation (IEC)

In IEC, the human designer serves as the fitness function for some or all objectives. Each generation, the designer views rendered phenotypes and selects preferred solutions. Evolution is guided by aesthetic, experiential, or cultural criteria that resist quantification.

Challenges: human fatigue limits populations to 10-20 individuals and runs to 20-30 generations. Solutions: pre-filter with computational fitness to reduce the set the human must evaluate; use surrogate models trained on human selections to automate subsequent generations.

9.2 Co-Evolution

Multiple populations evolve simultaneously, with fitness depending on interactions between populations. Applications in AEC:

• Structure-envelope co-evolution: The structural system and the facade system evolve in separate populations, with fitness evaluated on the combined design
• Building-landscape co-evolution: Building massing and site design evolve together
• Supply-demand co-evolution: Space layouts and circulation networks evolve interdependently

Co-evolution can discover emergent synergies between subsystems that would be missed by optimizing them sequentially.

9.3 Novelty Search

Instead of optimizing fitness, novelty search rewards solutions that are different from all previously found solutions. The archive of encountered solutions grows over time, and fitness is defined as the distance from the nearest archived solution in behavior space.

Application: when the fitness landscape is deceptive (local optima trap conventional optimization), novelty search explores more broadly and often finds globally optimal solutions as a side effect. In AEC: generating diverse facade patterns, exploring

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