如何根据所需邻域的程度对单元进行重新排序？（进行中）

我需要帮助来实现允许生成建筑计划的算法，最近在阅读Kostas Terzidis教授的最新出版物《置换设计：建筑，文本和上下文》（2014）时，我偶然发现了该算法。

语境

• 考虑一个划分为网格系统（a）的站点（b）。
• 我们还考虑要在站点限制内放置的空间列表（c）和邻接矩阵，以确定这些空间的放置条件和相邻关系（d）

引用Terzidis教授的话：

"A way of solving this problem is to stochastically place spaces within the grid until all spaces are fit and the constraints are satisfied"

The figure above shows such a problem and a sample solution (f).

ALGORITHM (as briefly described in the book)

1/ "Each space is associated with a list that contains all other spaces sorted according to their degree of desirable neighborhood."

2/ "Then each unit of each space is selected from the list and then one-by-one placed randomly in the site until they fit in the site and the neighboring conditions are met. (If it fails then the process is repeated)"

Example of nine randomly generated plans:

I should add that the author explains later that this algorithm doesn't rely on brute force techniques.

PROBLEMS

As you can see, the explanation is relatively vague and step 2 is rather unclear (in terms of coding). All I have so far are "pieces of a puzzle":

• a "site" (list of selected integers)
• an adjacency matrix (nestled lists)
• "spaces" (dictionnary of lists)

for each unit:

• a function that returns its direct neighbors
• a list of its desirable neighbors with their indices in sorted order

• a fitness score based on its actual neighbors

  from random import shuffle
  
  n_col, n_row = 7, 5
  to_skip = [0, 1, 21, 22, 23, 24, 28, 29, 30, 31]
  site = [i for i in range(n_col * n_row) if i not in to_skip]
  fitness, grid = [[None if i in to_skip else [] for i in range(n_col * n_row)] for e in range(2)]
  
  n = 2
  k = (n_col * n_row) - len(to_skip)
  rsize = 50
  
  #Adjacency matrix
  adm = [[0, 6, 1, 5, 2],
         [6, 0, 1, 4, 0],
         [1, 1, 0, 8, 0],
         [5, 4, 8, 0, 3],
         [2, 0, 0, 3, 0]]
  
  
  spaces = {"office1": [0 for i in range(4)], 
            "office2": [1 for i in range(6)], 
            "office3": [2 for i in range(6)],
            "passage": [3 for i in range(7)],
            "entry": [4 for i in range(2)]}
  
  
  def setup():
      global grid
      size(600, 400, P2D)
      rectMode(CENTER)
      strokeWeight(1.4)
  
      #Shuffle the order for the random placing to come
      shuffle(site)
  
      #Place units randomly within the limits of the site
      i = -1   
      for space in spaces.items():
          for unit in space[1]:    
              i+=1
              grid[site[i]] = unit
  
  
      #For each unit of each space... 
      i = -1   
      for space in spaces.items():
          for unit in space[1]:    
              i+=1
  
              #Get the indices of the its DESIRABLE neighbors in sorted order
              ada = adm[unit]
              sorted_indices = sorted(range(len(ada)), key = ada.__getitem__)[::-1]
  
              #Select indices with positive weight (exluding 0-weight indices)
              pindices = [e for e in sorted_indices if ada[e] > 0] 
  
              #Stores its fitness score (sum of the weight of its REAL neighbors)
              fitness[site[i]] = sum([ada[n] for n in getNeighbors(i) if n in pindices])
  
      print 'Fitness Score:', fitness
  
  def draw():
      background(255)
  
      #Grid's background
      fill(170)
      noStroke()
      rect(width/2 - (rsize/2) , height/2 + rsize/2 + n_row , rsize*n_col, rsize*n_row)
  
  
      #Displaying site (grid cells of all selected units) + units placed randomly
      for i, e in enumerate(grid):
          if isinstance(e, list): pass
          elif e == None: pass
          else:
              fill(50 + (e * 50), 255 - (e * 80), 255 - (e * 50), 180)
              rect(width/2 - (rsize*n_col/2) + (i%n_col * rsize), height/2 + (rsize*n_row/2) + (n_row - ((k+len(to_skip))-(i+1))/n_col * rsize), rsize, rsize)
              fill(0)
              text(e+1, width/2 - (rsize*n_col/2) + (i%n_col * rsize), height/2 + (rsize*n_row/2) + (n_row - ((k+len(to_skip))-(i+1))/n_col * rsize))
  
  
  
  
  def getNeighbors(i):
      neighbors = []
  
      if site[i] > n_col and site[i] < len(grid) - n_col:
          if site[i]%n_col > 0 and site[i]%n_col < n_col - 1:
              if grid[site[i]-1] != None: neighbors.append(grid[site[i]-1])
              if grid[site[i]+1] != None: neighbors.append(grid[site[i]+1])
              if grid[site[i]-n_col] != None: neighbors.append(grid[site[i]-n_col]) 
              if grid[site[i]+n_col] != None: neighbors.append(grid[site[i]+n_col])
  
      if site[i] <= n_col:
          if site[i]%n_col > 0 and site[i]%n_col < n_col - 1:
              if grid[site[i]-1] != None: neighbors.append(grid[site[i]-1])
              if grid[site[i]+1] != None: neighbors.append(grid[site[i]+1])
              if grid[site[i]+n_col] != None: neighbors.append(grid[site[i]+n_col])
  
          if site[i]%n_col == 0:
              if grid[site[i]+1] != None: neighbors.append(grid[site[i]+1])
              if grid[site[i]+n_col] != None: neighbors.append(grid[site[i]+n_col])
  
          if site[i] == n_col-1:
              if grid[site[i]-1] != None: neighbors.append(grid[site[i]-1])
              if grid[site[i]+n_col] != None: neighbors.append(grid[site[i]+n_col])
  
      if site[i] >= len(grid) - n_col:
          if site[i]%n_col > 0 and site[i]%n_col < n_col - 1:
              if grid[site[i]-1] != None: neighbors.append(grid[site[i]-1])
              if grid[site[i]+1] != None: neighbors.append(grid[site[i]+1])
              if grid[site[i]-n_col] != None: neighbors.append(grid[site[i]-n_col])
  
          if site[i]%n_col == 0:
              if grid[site[i]+1] != None: neighbors.append(grid[site[i]+1])
              if grid[site[i]-n_col] != None: neighbors.append(grid[site[i]-n_col])
  
          if site[i]%n_col == n_col-1:
              if grid[site[i]-1] != None: neighbors.append(grid[site[i]-1])
              if grid[site[i]-n_col] != None: neighbors.append(grid[site[i]-n_col])
  
      if site[i]%n_col == 0:
          if site[i] > n_col and site[i] < len(grid) - n_col:
              if grid[site[i]+1] != None: neighbors.append(grid[site[i]+1])
              if grid[site[i]+n_col] != None: neighbors.append(grid[site[i]+n_col])
              if grid[site[i]-n_col] != None: neighbors.append(grid[site[i]-n_col])
  
      if site[i]%n_col == n_col - 1:
          if site[i] > n_col and site[i] < len(grid) - n_col:
              if grid[site[i]-1] != None: neighbors.append(grid[site[i]-1])
              if grid[site[i]+n_col] != None: neighbors.append(grid[site[i]+n_col])
              if grid[site[i]-n_col] != None: neighbors.append(grid[site[i]-n_col])
  
      return neighbors
  

I would really appreciate if someone could help connect the dots and explain me:

• how to re-order the units based on their degree of desirable neighborhood ?

EDIT

As some of you have noticed the algorithm is based on the likelihood that certain spaces (composed of units) are adjacent. The logic would have it then that for each unit to place randomly within the limits of the site:

• we check its direct neighbors (up, down, left right) beforehand
• compute a fitness score if at least 2 neighbors. (=sum of the weights of these 2+ neighbors)
• and finally place that unit if the adjacency probability is high

Roughly, it would translate into this:

    i = -1   
    for space in spaces.items():
        for unit in space[1]:    
            i+=1

            #Get the indices of the its DESIRABLE neighbors (from the adjacency matrix 'adm') in sorted order
            weights = adm[unit]
            sorted_indices = sorted(range(len(weights)), key = weights.__getitem__)[::-1]

            #Select indices with positive weight (exluding 0-weight indices)
            pindices = [e for e in sorted_indices if weights[e] > 0] 


            #If random grid cell is empty
            if not grid[site[i]]:

                #List of neighbors
                neighbors = [n for n in getNeighbors(i) if isinstance(n, int)]

                #If no neighbors -> place unit
                if len(neighbors) == 0:
                    grid[site[i]] = unit 

                #If at least 1 of the neighbors == unit: -> place unit (facilitate grouping)
                if len(neighbors) > 0 and unit in neighbors:
                    grid[site[i]] = unit  

                #If 2 or 3 neighbors, compute fitness score and place unit if probability is high
                if len(neighbors) >= 2 and len(neighbors) < 4:

                    fscore = sum([weights[n] for n in neighbors if n in pindices]) #cumulative weight of its ACTUAL neighbors
                    count = [1 for t in range(10) if random(sum(weights)) < fscore] #add 1 if fscore higher than a number taken at random between 0 and the cumulative weight of its DESIRABLE neighbors

                    if len(count) > 5: 
                        grid[site[i]] = unit

                #If 4 neighbors and high probability, 1 of them must belong to the same space
                if len(neighbors) > 3:

                    fscore = sum([weights[n] for n in neighbors if n in pindices]) #cumulative weight of its ACTUAL neighbors                    
                    count = [1 for t in range(10) if random(sum(weights)) < fscore] #add 1 if fscore higher than a number taken at random between 0 and the cumulative weight of its DESIRABLE neighbors

                    if len(count) > 5 and unit in neighbors:                       
                        grid[site[i]] = unit


            #if random grid cell not empty -> pass
            else: pass

Given that a significant part of the units won't be placed on the first run (because of low adjacency probability), we need to iterate over and over until a random distribution where all units can be fitted is found.

After a few thousand iterations a fit is found and all the neighboring requirements are met.

Notice however how this algorithm produces separated groups instead of non-divided and uniform stacks like in the example provided. I should also add that nearly 5000 iterations is a lot more than the 274 iterations mentioned by Mr. Terzidis in his book.

Questions:

• Is there something wrong with the way I'm approaching this algorithm ?
• If no then what implicit condition am I missing ?