Avoiding overlapping edges with minimal physics in vis.js

I'm using vis.js to build a story visualization tool, and a key feature is to allow authors to manually position nodes via dragging. There's also often several edges with the same origin and destination nodes. Without physics, these edges overlap.

Currently to avoid edge overlap, I enable physics for a small interval whenever a new edge is created to repel any overlapping edges from each other. Ideally I would have physics always disabled and edges would not overlap, but I don't think that is possible.

Are there any recommendations for how to apply vis physics so that it's disabled on node drag, stabilizes quickly also prevents edge overlap?

If anyone comes across this issue, the solution is to calculate the roundness for each edge, based on how many edges have the same origin and destination node.

example: http://jsbin.com/wojanuboxi/edit?html,js,output

 var nodes = new vis.DataSet([
 {id: 1, label: '1'},
 {id: 2, label: '2'},
 {id: 3, label: '3'}
]);
var edges = new vis.DataSet([
  {id: 1, from: 1, to: 2, smooth: {type: 'curvedCW', roundness: 0.2}},
  {id: 2, from: 1, to: 2, smooth: {type: 'curvedCW', roundness: -2.2}},
  {id: 5, from: 1, to: 2, label: 5,  smooth: {type: 'curvedCW', roundness: 0.4}},
  {id: 6, from: 1, to: 2, label: 6, smooth: {type: 'curvedCW', roundness: -2.4}},

  {id: 3, from: 1, to: 3, smooth: {type: 'curvedCW', roundness: -2.1}},
  {id: 4, from: 1, to: 3, smooth: {type: 'curvedCW', roundness: 0.1}}
]);
var data = {
  nodes: nodes,
  edges: edges
};
var options = {
  physics: false,
  layout: {
    hierarchical: {
      direction: 'UD'
    }
  }
};

var networkContainer = document.getElementById('networkContainer');
var network = new vis.Network(networkContainer, data, options);