Body: <p>Sorry, the title is bad because I don't even know what to call this problem.</p>
  
  <p>I have a set of <code>n</code> objects <code>{obj_0, obj_1, ......, obj_(n-1)}</code>, where <code>n</code> is an even number.</p>
  
  <p>Any two objects can be paired together to produce an output score. So for instance, you might take <code>obj_j</code> and <code>obj_k</code>, and pair them together giving a score of <code>S_j,k</code>. All scores are independent, so the previous example doesn't tell you anything about what the score for combining <code>obj_j</code> and <code>obj_i</code>, <code>S_j,i</code> might be. </p>
  
  <p>There is no ordering in the combination, so <code>S_j,i</code> and <code>S_i,j</code> are the same.</p>
  
  <p>All scores for all pairing possibilities are known.</p>
  
  <p>The whole set of objects is to be taken and organised into pairs (leaving no objects unpaired). The total score, <code>S_tot</code> is the sum of all scores of individual pairs.</p>
  
  <p>What's the most efficient way to find the score-maximising pairing configuration for a large set of such objects? (does this problem have a name?)</p>
  
  <p>Is there a method which works with the version of this problem where objects are grouped into triplets?</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2018-07-15T07:59:10.557Z
Comments.Text: It seems similar to [N-grams](https://en.wikipedia.org/wiki/N-gram)
Comments.UserDisplayName: kiner_shah
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2018-07-15T14:51:54.423Z
Comments.Text: Thanks @kiner_shah
  For anyone interested, I've found this: https://en.wikipedia.org/wiki/Vehicle_routing_problem 
  If you search for "Set partitioning problem" you'll find what I was looking for
Comments.UserDisplayName: Alexander Soare
Tags: <problem-solving>
Title: How to solve problem: pairwise grouping to maximise score
UserDisplayName: Alexander Soare
ThreadText: # How to solve problem: pairwise grouping to maximise score
  
  (Asked by: username_0 on 2018-07-14)
  
  Sorry, the title is bad because I don't even know what to call this problem.
  
  I have a set of `n` objects `{obj_0, obj_1, ......, obj_(n-1)}`, where `n` is an even number.
  
  Any two objects can be paired together to produce an output score. So for instance, you might take `obj_j` and `obj_k`, and pair them together giving a score of `S_j,k`. All scores are independent, so the previous example doesn't tell you anything about what the score for combining `obj_j` and `obj_i`, `S_j,i` might be.
  
  There is no ordering in the combination, so `S_j,i` and `S_i,j` are the same.
  
  All scores for all pairing possibilities are known.
  
  The whole set of objects is to be taken and organised into pairs (leaving no objects unpaired). The total score, `S_tot` is the sum of all scores of individual pairs.
  
  What's the most efficient way to find the score-maximising pairing configuration for a large set of such objects? (does this problem have a name?)
  
  Is there a method which works with the version of this problem where objects are grouped into triplets?
  
  **Tags:** problem-solving
  > **Comments:**
  > **username_1**: It seems similar to [N-grams](https://en.wikipedia.org/wiki/N-gram)  
  > **username_0**: Thanks @kiner_shah For anyone interested, I've found this: https://en.wikipedia.org/wiki/Vehicle_routing_problem  If you search for "Set partitioning problem" you'll find what I was looking for  
  
  ---
  
  ## 0 answers
  
  