Answers.Body: <p>I understood your question as being &quot;I have a fitness function based on 8 parameters&quot; how can I display that graphically.</p>
  <p>Visualising a multi-dimensional landscape is a hard problem.
  If you convert it to some kind of 3d plot you are inevitably losing information.
  It would help to consider what you are actually trying to achieve by doing so.
  Do you have a practical use for the plot or is it just a <a href="https://en.wiktionary.org/wiki/bright_shiny_object" rel="nofollow noreferrer">bright shiny</a>.</p>
  <p>If you want to show something specific such as how one algorithm is better than another, you may be better off trying to visualise something else entirely.
  Commonly you can look at the average fitness over time instead.</p>
  <p>A better algorithm is typically one that increases fitness more quickly and/or with fewer resources.</p>
  <p>So you could plot fitness by time by population with different coloured lines for each algorithm variation say.</p>
  <p>That said if you really want to visualise the fitness landscape:</p>
  <p>There a some useful information on or linked to the wikipedia page on <a href="https://en.wikipedia.org/wiki/Fitness_landscape" rel="nofollow noreferrer">Fitness_landscapes</a></p>
  <p>You could also try:</p>
  <h3>Dimensionality Reduction</h3>
  <p>You could try [dimensionality reduction](Dimensionality reduction) to reduce the number of parameters down to something you can plot.</p>
  <h3>Identify dimensions with the most interesting properties</h3>
  <p>Look at which dimensions have the most intersting changes over time</p>
  <h3>Plot individual dimensions</h3>
  <p>Create multiple plots for different interesting pairs fo dimensions</p>
  <h3>Innovate ways to plot other dimensions</h3>
  <p>Why stick with 3D? Consider using:</p>
  <ul>
  <li>colour</li>
  <li>size</li>
  <li>texture</li>
  </ul>
  <h3>Make your model interactive</h3>
  <p>Look <a href="http://worrydream.com/#!2/LadderOfAbstraction" rel="nofollow noreferrer">here</a> and elsewhere for inspiration</p>
  <p>Why not provide a way of controlling which dimensions are displayed and how.</p>
  
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Answers.Text: Can you explain why plotting a 3d fitness landscape (the OP's problem) is a hard problem? Because it shouldn't. If the individuals have more than 2 dimensions, then yes I agree that you may need some dimensionality reduction. So, I think you should address the OP's problem directly too in this answer. In any case, they don't explain what x and y are. It's unclear if their individuals are 2d points or not (probably yes).
Answers.UserDisplayName: nbro
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Answers.Text: I understood the individuals as having 8 dimensions.
Answers.UserDisplayName: Bruce Adams
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Answers.Text: thank you this makes sense. I kind of knew it wouldn't really make sense to try as 8 is not the same as 2. Ill go with the option to use multiple plots. It is mostly to generate something shiny, a figure which makes the whole objective of the algorithm easy to understand.
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Body: <p>I'm using a GA to find the best set of parameters to maximize a fitness function. I want to draw a fitness landscape to visualize the effectiveness of the algorithm. The fitness function, calculated using a DNN, has 8 input variables. The landscape I want to plot is 3 dimensional (x,y,fitness). What data should I assign to the x and y axes? Or should I avoid such a plot entirely? Which other types of plots would be better?</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2023-07-18T10:26:42.087Z
Comments.Text: Can you clarify what you mean by "The landscape I want to plot is 3 dimensional"? Why is it 3d? How can we know what you should assign to x and y, if we don't actually know what these axes are supposed to represent in your context? Are your individuals 2d points? If yes, then having a 3d fitness landscape may make sense.
Comments.UserDisplayName: nbro
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2023-07-18T21:52:47.597Z
Comments.Text: @nbro the individuals have 8 dimensions. Thats why I wasn't sure how to plot them on 2 axis. Thank you,
Comments.UserDisplayName: program1232123
Tags: <optimization><genetic-algorithms><fitness-functions><data-visualization>
Title: Best way to generate fitness landscape when using higher dimensional data
UserDisplayName: program1232123
ThreadText: # Best way to generate fitness landscape when using higher dimensional data
  
  (Asked by: username_0 on 2023-07-17)
  
  I'm using a GA to find the best set of parameters to maximize a fitness function. I want to draw a fitness landscape to visualize the effectiveness of the algorithm. The fitness function, calculated using a DNN, has 8 input variables. The landscape I want to plot is 3 dimensional (x,y,fitness). What data should I assign to the x and y axes? Or should I avoid such a plot entirely? Which other types of plots would be better?
  
  **Tags:** optimization, genetic-algorithms, fitness-functions, data-visualization
  
  > **Comments:**
  > **username_1**: Can you clarify what you mean by "The landscape I want to plot is 3 dimensional"? Why is it 3d? How can we know what you should assign to x and y, if we don't actually know what these axes are supposed to represent in your context? Are your individuals 2d points? If yes, then having a 3d fitness landscape may make sense.  
  > **username_0**: @username_1 the individuals have 8 dimensions. Thats why I wasn't sure how to plot them on 2 axis. Thank you,  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_2 on 2023-07-17. Score: 1 | Accepted answer
  
  I understood your question as being "I have a fitness function based on 8 parameters" how can I display that graphically.
  
  Visualising a multi-dimensional landscape is a hard problem.
  If you convert it to some kind of 3d plot you are inevitably losing information.
  It would help to consider what you are actually trying to achieve by doing so.
  Do you have a practical use for the plot or is it just a [bright shiny](https://en.wiktionary.org/wiki/bright_shiny_object).
  
  If you want to show something specific such as how one algorithm is better than another, you may be better off trying to visualise something else entirely.
  Commonly you can look at the average fitness over time instead.
  
  A better algorithm is typically one that increases fitness more quickly and/or with fewer resources.
  
  So you could plot fitness by time by population with different coloured lines for each algorithm variation say.
  
  That said if you really want to visualise the fitness landscape:
  
  There a some useful information on or linked to the wikipedia page on [Fitness\_landscapes](https://en.wikipedia.org/wiki/Fitness_landscape)
  
  You could also try:
  
  ### Dimensionality Reduction
  
  You could try [dimensionality reduction](Dimensionality reduction) to reduce the number of parameters down to something you can plot.
  
  ### Identify dimensions with the most interesting properties
  
  Look at which dimensions have the most intersting changes over time
  
  ### Plot individual dimensions
  
  Create multiple plots for different interesting pairs fo dimensions
  
  ### Innovate ways to plot other dimensions
  
  Why stick with 3D? Consider using:
  
  * colour
  * size
  * texture
  
  ### Make your model interactive
  
  Look [here](http://worrydream.com/#!2/LadderOfAbstraction) and elsewhere for inspiration
  
  Why not provide a way of controlling which dimensions are displayed and how.
  
  > **Comments:**
  > **username_1**: Can you explain why plotting a 3d fitness landscape (the OP's problem) is a hard problem? Because it shouldn't. If the individuals have more than 2 dimensions, then yes I agree that you may need some dimensionality reduction. So, I think you should address the OP's problem directly too in this answer. In any case, they don't explain what x and y are. It's unclear if their individuals are 2d points or not (probably yes).  
  > **username_2**: I understood the individuals as having 8 dimensions.  
  > **username_0**: thank you this makes sense. I kind of knew it wouldn't really make sense to try as 8 is not the same as 2. Ill go with the option to use multiple plots. It is mostly to generate something shiny, a figure which makes the whole objective of the algorithm easy to understand.  
  
  ---
  
  