Explanation in MOEA = Planning

                                                                           
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  /     .-''"'-.  `. .   .-.   .'   '. /'   /  \ \        / (_/   / /      
 /     /________\   \|  '   '  ||    |'    /    \ \      / /     / /       
 |                  ||  |   |  ||    ||    |     \ \    / /     / /        
 \    .-------------'|  |   |  |'.   `'   .'      \ \  / /     . '         
  \    '-.____...---.|  |   |  | \        /        \ `  /     / /    _.-') 
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     `''-...... -'   |  |   |  |   '----'           / /    /  /.-'_.'      
                     |  |   |  |                |`-' /    /    _.'         
                     '--'   '--'                 '..'    ( _.-'       
  

Here's  problem :

The above shows 93 projects (with 23 decisions and 3 objectives) mapped into a 2-d space. 

• The x-axis is the cosine dimension (where the two end points are found via the FastMap heuristic)
• The y-axis is the Pythagorus dimension: sqrt(a^2 -x^2)
• The colors denote clusters (so all the red ones at the bottom left are in one cluster). 
• Clustering done via 4-way recursive splits on mean x,y points

The principle of envy says

• Find your nearest cluster with a better class score
• We use the mean IBEA score of the objectives = sum_i e^(obj[i] - min[i]) where all objectives have been normalized (x-min)/(max - min).
• Find the the delta from you to them
• That is is your plan on how to make your life better.

And here's the problem: 

• how to explain that plan 
• when "nearest" is expressed in the above weirdo  cosine and Pythagorus dimensions.

Here's one solution:

• Given a pair  of centroids (asIs, Envied)
• Sample:
• N times repeat
• Generate  an example Eg at random from the examples in those two clusters
• Let value(Eg) be the score of each example (and  its expressed as the distance to the Envied cluster)
• So smallest scores are better
• For each range in the example
• Add value(Eg) to value(range)
• Prune:
• Sort ranges by their value
• Let gap = distance(centroid(asIs), centroid(Envied))
• Score ranges by their ability to move rows in asIs towards Envied, as follows.
• For i = 1 to 10 (some magic number) 
• Let elite be the best i ranges e.g. 
• ((colNum, range), 
   [(18, 'l'),  
    (15, 'vh'),  
    (19, 'n'), 
    (8, 'xh'), ....]
• For each row in asIs (i.e. the things you want to change)
• Let before = distance(row,centroid(Envied))
• Let mutant = copy(row)
• Inject all the ranges into elite into mutant
• Let after = distance(mutant, centroid(Envied))
• Let movement(elite) = (before - after)/gap
• Policy = the ranges with  most movement

Details:

• Estimates of defect, effort, months from Vasil's algorithm (interpolation between 2 nearest clusters)
• To generate an example, I used the DE trick of interpolating between values. This has the benefit of preserving known distributions

def smear(rows,cols,cr=0.5,f=0.5):
  i    = one(rows)
  j    = one(rows)
  k    = one(rows)
  must = any(0, len(i))
  new  = []
  for n,(a,b,c,col) in enumerate(zip(i,j,k,cols)):
    if a == "?" or b == "?" or c == "?":
      x = "?"
    else:
      x = a
      if n == must or rand() < cr:
        if isa(col,Num):
          x = a + f*(b-c)
        else:
          if rand() < f: 
            x = b if rand() < 0.5 else c 
    new += [x]
  return new

Results

When applied in a 5*5 cross-val, the 25,50,75,100th percentiles of defect, effort, months were as follows. Note the large decreases at the 75th percentile:

effort
before: [0.44, 0.98, 4.52, 199.5]
after: [0.39, 0.76, 2.01, 120.2]

defects
before: [0.34, 0.84, 3.57, 124.76]
after: [0.37, 0.72, 2.09, 127.61]

months
before: [0.15, 0.33, 0.58, 3.7]
after: [0.16, 0.35, 0.51, 3.76]