Bin Packing

   Despite its name, the Worst Fit Algorithm produces result that are consistently better than the First Fit Algorithm.  This does come with some extra processing though (on small data sets it doesn't really matter).  The only difference between the two algorithms is that Worst Fit picks the Bin with the most amount of free space (or creates a new Bin if no existing one can fit the Element) instead of just picking the first Bin available.

   Private Sub WorstFit()
      'Checks to make sure everything is initialized
      If Elements Is Nothing Then Exit Sub

      Dim ElementsCopy(Elements.GetUpperBound(0)) As Integer
      ReDim Bins(0)
      'Bin Number we are on, Bin Element we are on, Amount placed in the current Bin
      Dim BinNumber, BinElement, BinCount As Integer
      Dim WorstBin, WorstBinAmount As Integer
      Dim i, j, k As Integer

      'Make a copy of the array incase we need to sort it
      DeepCopyArray(Elements, ElementsCopy)

      'Sort in descending order if needed
      If Me.Decreasing = True Then
         Array.Sort(ElementsCopy)
         Array.Reverse(ElementsCopy)
      End If

      'Declare the first element in the first Bin
      ReDim Bins(0)(0)

      'Loop through each Element and place in a Bin
      For i = 0 To ElementsCopy.GetUpperBound(0)
         WorstBin = -1
         WorstBinAmount = Me.BinHeight + 1

         For j = 0 To BinNumber
            BinElement = Bins(j).GetUpperBound(0)

            'Count the amount placed in this Bin
            BinCount = 0
            For k = 0 To BinElement
               BinCount += Bins(j)(k)
            Next

            'Find the least full Bin that can hold this Element
            If WorstBinAmount > BinCount AndAlso BinCount + ElementsCopy(i) <= Me.BinHeight Then
               WorstBinAmount = BinCount
               WorstBin = j
            End If
         Next


         If WorstBin = -1 Then
            'There wasn't room for the Element in any existing Bin
            'Create a new Bin
            ReDim Preserve Bins(BinNumber + 1)
            BinNumber += 1

            'Initialize first element of new bin
            ReDim Bins(BinNumber)(1)
            BinElement = 0

            Bins(BinNumber)(BinElement) = ElementsCopy(i)
         Else
            'There's room for this Element in an existing Bin
            'Place Element in "Best Bin"
            BinElement = Bins(WorstBin).GetUpperBound(0)
            ReDim Preserve Bins(WorstBin)(BinElement + 1)
            Bins(WorstBin)(BinElement) = ElementsCopy(i)
         End If
      Next

      'All Elements have been place, now we go back and remove unused Elements
      For i = 0 To BinNumber
         For j = 0 To Bins(i).GetUpperBound(0)
            If Bins(i)(j) = 0 Then
               ReDim Preserve Bins(i)(j - 1)
            End If
         Next
      Next

      GC.Collect()
   End Sub

With the same set of data as the last example, this algorithm will lay out something like this in memory: