Generative Design Primer
  • Welcome
  • Introduction to Generative Design
    • Computational Design
    • Generative Design
      • What is Generative Design?
      • Why should I use Generative Design?
      • What goes into a Generative Design Process?
        • Anatomy of each stage
      • Examples of Generative Design
        • MaRs Innovation District of Toronto
        • Furniture Design
        • A Further Analogy
      • Anatomy of a Good Generative Design Process
    • Visual Programming
    • Dynamo
    • Generative Design for Revit and Dynamo
  • Deeper Dive to Generative Design
    • Algorithms
      • What are Algorithms?
      • Generators
      • Evaluators
      • Solvers
    • Optioneering
    • Optimization
      • What is Optimization?
      • Objective Function
      • Constraints
      • Data
      • Defining Goals
    • Genetic Algorithms
      • What is a Genetic Algorithm?
      • Initialization phase
      • Evaluation Phase
      • Selection Phase
      • Crossover Phase
      • Mutation Phase
    • Other Techniques
    • Genetic Algorithm Q&A
  • Hello Generative Design for Revit and Dynamo!
    • Installing Generative Design
    • Setting up a Graph for Generative Design
    • Running Generative Design
    • Visualizing Results in Generative Design
    • Refinery Toolkit
      • Installing the Refinery Toolkit from the Dynamo Package Manager
      • Using the Refinery Toolkit
    • Space Analysis for Dynamo
      • Installing the Space Analysis for Dynamo package from the Dynamo Package Manager
      • Using the Space Analysis Package
    • Using Revit alongside Generative Design
      • Using Data from Revit
      • Remember Node Inputs
      • How to Test Revit Data Capture
      • Detailed Example Workflow
      • Sharing Logic and Results
      • Current Limitations
      • Accessing Generative Design Directly From Revit
  • Sample Workflows
    • Getting Started Workflows
      • Highest Point of a Surface
      • Minimum Volume and Maximum Surface
    • Architectural Workflows
      • Building Mass Generator
      • Building Positioning based on Solar Analysis
      • Office Layout
      • Grid Object Placement in a Room
      • Entourage Placement Exploration
    • MEP Workflows
      • Distributing Spotlights in an Office Space
    • Structural Workflows
    • BIM Workflows
      • Placement of views on sheets
    • Community Examples
      • Guidelines
      • List Of Examples
  • Generative Design in Your Office
    • What Generative Design Can Be Used For?
    • What Generative Design Can’t Be Used For?
    • How to Convince Senior Stakeholders of Using Generative Design?
    • The Role of a Generative Designer
    • Hiring a Generative Designer
  • Next Steps
    • Machine Learning
      • What is Machine Learning?
      • Is Generative Design Machine Learning?
      • Can Machine Learning and Generative Design Work Together?
  • Appendix
    • Glossary
    • Reference Material
    • Need Professional Help?
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  • Single Objective Optimization
  • Multi-Objective Optimization

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  1. Deeper Dive to Generative Design
  2. Optimization

Objective Function

PreviousWhat is Optimization?NextConstraints

Last updated 5 years ago

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An objective function is the output that you want to maximize or minimize. It is what you will measure designs against to decide which option is best.

The objective function can be thought of as the goal of your generative design process.

In finance, the objective function is usually to maximize portfolio value; in aerospace engineering the objective is often to minimize weight.

The key to objective function is that it must be quantifiable - you must be able to put a number to it.

In generative design workflows, we are not limited to one objective ('single objective optimization') - we can also have multiple objectives or goals that we are trying to optimise our design against ('multi-objective optimization').

Single Objective Optimization

Single objective optimization is when we have only one objective function.

In this scenario, the computer will return a single optimal solution e.g. the surface with largest area.

Multi-Objective Optimization

Multi-objective optimization involves using multiple objective functions.

Usually, optimizing designs involves multiple objectives that compete simultaneously. In this context, optimization becomes a matter of finding the best trade-off between objectives, rather than finding the single best solution.

Even though adding more objectives makes the optimization process more complex, it also means the designer can choose from a set of optimal solutions instead of just one.

Imagine having to optimize a structural design. We want the structure to be as light as possible, but at the same time we want it to be as rigid as possible. Here we have have two competing objectives where one will produce the lightest solution and the other the most rigid solution. In between those, there will be a huge number of designs that vary in weight and stiffness.

The designs that cannot be improved in one objective without compromising the other are known as a 'pareto optimal solutions'. For a solution to be placed in the 'pareto optimal set', it cannot be dominated by another solution.

If a solution is worse than another solution on all objectives, it is dominated and will not be included in the pareto optimal set.