Group number to create specified sum (galapagos?)

I was wondering if it’s possible to group numbers into a list so that each list would have a sum close to a number i specified?

for example, i have numbers:
and i want a sum of list to be as close to 12 as possible
so it’d split these number into lists like:
[0] 12
[1] 9, 3
[2] 7, 5
[3] 6,1

is this possible?

That’s a combinatorial problem (more specifically 1-D bin packing), and I don’t think there’s a simple way to to express it in a form that can be directly accepted by Galapagos.

It’s definitely possible though, and there are lots of heuristics for solving these problems - you can google them, but they would definitely involve some scripting.


Here’s a simple Python implementation of “first fit decreasing” algorithm, copied directly from (6.8 KB)

''' Partition a list into sublists whose sums don't exceed a maximum 
    using a First Fit Decreasing algorithm. See
    for a simple description of the method.

class Bin(object):
    ''' Container for items that keeps a running sum '''
    def __init__(self):
        self.items = []
        self.sum = 0
    def append(self, item):
        self.sum += item

    def __str__(self):
        ''' Printable representation '''
        return 'Bin(sum=%d, items=%s)' % (self.sum, str(self.items))
def pack(values, maxValue):
    values = sorted(values, reverse=True)
    bins = []
    for item in values:
        # Try to fit item into a bin
        for bin in bins:
            if bin.sum + item <= maxValue:
                #print 'Adding', item, 'to', bin
            # item didn't fit into any bin, start a new bin
            #print 'Making new bin for', item
            bin = Bin()
    return bins

from Grasshopper import DataTree
from Grasshopper.Kernel.Data import GH_Path
result = DataTree[float]()
for path, bin in enumerate(pack(values, maxValue)):
    result.AddRange(bin.items, GH_Path(path))