title: I need an alternative to the first fit decreasing bin packing algorithm that always finds an optimal solution
body: <p>I have implemented the First-Fit-Decreasing bin packing algorithm to split a list of numbers into two 'bins' of equal size. The algorithm almost always finds the optimal packing arrangement but occasionally it doesn't.</p>
  
  <p>For example:</p>
  
  <p>The set of numbers 4, 3, 2, 4, 3, 2 can obviously be split into this arrangement:
  1) 4, 3, 2
  2) 4, 3, 2</p>
  
  <p>The first fit decreasing algorithm does not find a solution.</p>
  
  <p>It is not acceptable in this circumstance to NOT find the correct solution if one exists.</p>
  
  <p>The original puzzle is to split a sequence of numbers into two sets that have an equal sum.</p>
  
  <p>Is this just a simple bin packing problem or have I used the wrong algorithm?</p>