This class can perform a one dimensional bin packing. It could be
used to: Sort pakages of a certain weight into containers that can
carry a given weight, cut 2x4s of a certain length into the required
pieces, fill floppy disks with a list of files...
A mix between standard Best Fit and Worst Fit algorithms is used.
Data must be entered and sorted descending before calling the main
Time Complexity (TC) of this function where
N = # of items
If the average size of an item is 1/2 bin size then TC = N * N/2 or more generally:
TC = N * N * Save% (where S is the percentage of average item size relative to bin capacity)
So if average item size doesn't change doubling the number of items quadruples time spent. Using the second test time above would mean 5 million items would take 17.4 days to sort (5mil/5000 > 10002 * 1.5sec). However, we could assume that not much is gained by considering all items together. You could instead break it down to 5000 reps of the 1000 item problem which would give 0.06s * 5000 = 5min. You might save the results of each repetition, but remove the items in the last bin if not near full and return them to the items remaining to be sorted.
Also note that as S is decreased the number of bins needed will approach the optimum. And as S is increased the assumption above is less true; it becomes more important to check as many items as possible to reduce the number of bins needed. I lack the math skills to prove it, but it's not difficult to see that if you have 1000 items with values ranging from 0 to 1000 and the bin capacity is 1000, there will be many bins with a large first item that won't have a near perfect match which will result in extra bins needed. So given a maximum item size Smax there should be a point at which checking more items causes a huge time penalty without doing much to optimize the number of bins needed: Iopt = Smax * M (where if Save% is large M > 1).
One last note: It is perfectly possible that the number of bins needed far excedes the predicted optimum without implying that the sort did a bad job. Consider a problem where bin capacity is 10 and you have 4 items of size 6. 28/10 predicts that 3 bins will be needed while it is clear that 4 bins are needed.
|Main function of class module|
Public Function PackBins() Dim i As Long, j As Long, tot As Long Dim iBestBin As Long, iWorstBin As Long, qBestBin As Long, qWorstBin As Long, x As Long Dim iSize As Long '=m_Items(i).Size Dim prevUbound As Long pTightenPackageList If UBound(m_Items) = 0 Then '1 item ReDim m_Bins(m_iUItem To m_iUItem) 'so BinsNeeded will give correct val Exit Function End If If m_BinReasonablyFull = 0 Then m_BinReasonablyFull = 0.95 * m_BinCapacity For i = 0 To UBound(m_Items) If m_Items(i).size <= m_BinCapacity Then tot = tot + m_Items(i).size Next 'start with one less than min bins necessary to hold all items 'when remainder of tot / m_BinCapacity < 0.5 ReDim m_Bins(Int(tot / m_BinCapacity) + CLng((tot Mod m_BinCapacity) < m_BinCapacity / 2)) Debug.Print FormatNumber(tot / m_BinCapacity, 3) & "(i.e. " & Int(tot / m_BinCapacity) + IIf(tot Mod m_BinCapacity, 1, 0) & ") bins optimum - though not necessarily possible" 'place all items over 1/2 capacity in their own bin qBestBin = Int(m_BinCapacity / 2) For i = 0 To UBound(m_Items) iSize = m_Items(i).size If iSize > qBestBin Then If iSize <= m_BinCapacity Then m_Items(i).lBin = i If i > UBound(m_Bins) Then pNewBin m_Bins(i) = iSize 'mark bin usage Else m_Items(i).lBin = -1 'oversized End If Else Exit For ' <= 1/2 bin capacity End If Next 'place the rest of the items For i = i To UBound(m_Items) 'loop until a bin has been found m_Items(i).lBin = -1 'no bin chosen yet iBestBin = -1 'best bin index and flag that best bin found iWorstBin = -1 'worst bin index and flag that fits in bin qBestBin = m_BinReasonablyFull - 1 'a best bin has to be > this qWorstBin = m_BinCapacity + 1 iSize = m_Items(i).size j = 0 'current bin to check Do x = m_Bins(j) + iSize 'if fits in bin If x <= m_BinCapacity Then 'is it most full bin If x > qBestBin Then 'NOW qBestBin always= m_BinReasonablyFull-1 m_Items(i).lBin = j m_Bins(j) = x ' m_Bins(j) + iSize Exit Do End If 'is it least full bin If x < qWorstBin Then qWorstBin = x iWorstBin = j End If End If 'if current bin is empty or last bin and don't need new one it's time to decide where to place item If (m_Bins(j) = 0) Or (j = UBound(m_Bins)) Then If iWorstBin >= 0 Then m_Items(i).lBin = iWorstBin m_Bins(iWorstBin) = m_Bins(iWorstBin) + iSize Exit Do Else 'didn't fit - place in the empty bin or in new bin If m_Bins(j) <> 0 Then 'we need a new bin (rare since we start with min bins pNewBin j = j + 1 End If m_Items(i).lBin = j m_Bins(j) = m_Bins(j) + iSize Exit Do End If End If 'try next bin j = j + 1 Loop 'While m_Items(i).lBin = -1 'now exit do takes care 15%faster in IDE Next '-------------------------------------------------------------- If m_Bins(UBound(m_Bins)) = 0 And UBound(m_Bins) > 0 Then ReDim Preserve m_Bins(UBound(m_Bins) - 1) End If 'try and place last items as 1st fit 'keep last bin as empty as possible x = 0 ': j = 0 i = 0 Do 'For i = 0 To UBound(m_Items) If m_Items(i).lBin = UBound(m_Bins) Then If x Then iSize = m_Items(i).size For j = 0 To UBound(m_Bins) - 1 If m_Bins(j) + iSize <= m_BinCapacity Then m_Bins(j) = m_Bins(j) + iSize m_Bins(UBound(m_Bins)) = m_Bins(UBound(m_Bins)) - iSize m_Items(i).lBin = j Debug.Print "moved an item out of last bin" 'leave if only the first item remains in last bin If m_Bins(UBound(m_Bins)) = x Then Exit Do Exit For End If Next Else x = m_Items(i).size 'flag that we found and skipped first (largest) item in last bin End If End If i = i + 1 Loop While i <= UBound(m_Items) 'Next ' SortPackagesByBin 'let user call this so we can see how binsort was executed Debug.Print End Function