Order of nodes in graphviz

I am working on this graph:

digraph "example.gsn.yaml" {

  ## Elements
  "G1" [shape="box", label=<<B>G1</B><BR align="left"/>Goal 1>];
  "G2" [shape="box", label=<<B>G2</B><BR align="left"/>Goal 2>];
  "G4" [shape="box", label=<<B>G4</B><BR align="left"/>Goal 4>];
  "G3" [shape="box", label=<<B>G3</B><BR align="left"/>Goal 3>];
  "C1" [shape="box", style="rounded", label=<<B>C1</B><BR align="left"/>Context 1>];
  "S1" [shape="parallelogram", label=<<B>S1</B><BR align="left"/>Strategy 1>];
  "A1" [shape="oval", label=<<B>A1</B><BR align="left"/>Argument 1>];
  "A1":e -> "A1":e [headlabel=< <B>A</B> >, labeldistance=2.5, penwidth=0, arrowhead=none];
  "Sn1" [shape="circle", label=<<B>Sn1</B><BR align="left"/>Solution 1>];
  "Sn2" [shape="circle", label=<<B>Sn2</B><BR align="left"/>Solution 2>];
  "J1" [shape="oval", label=<<B>J1</B><BR align="left"/>Justification 1>];
  "J1":e -> "J1":e [headlabel=< <B>J</B> >, labeldistance=2.5, penwidth=0, arrowhead=none];

  ## Relations
  "G1" -> "G2";
  "G1" -> "G3";
  "G1" -> "G4";
  "G2" -> "S1";
  "G4" -> "Sn2";
  "G3" -> "Sn1";
  "G3" -> "C1" [arrowhead=empty];
  {rank = same; "G3"; "C1"; }
  "S1" -> "Sn1";
  "S1" -> "J1" [arrowhead=empty];
  "S1" -> "A1" [arrowhead=empty];
  {rank = same; "A1"; "S1"; }
  {rank = same; "S1"; "J1"; }
}

I would like to minimize crossings. My preferred layout would be that A1, S1 and J1 are on the same rank in a left-to-right order. However I cannot find out how to do this.

Can anybody help, please? Thanks in advance.

Solution

Many "obvious" solutions did not work (ordering, weight, invisible edges). Putting A1, J1, and S1 inside a cluster does the trick:

digraph "example.gsn.yaml" {
  ## Elements
  "G1" [shape="box", label=<<B>G1</B><BR align="left"/>Goal 1>];
  "G2" [shape="box", label=<<B>G2</B><BR align="left"/>Goal 2>];
  "G4" [shape="box", label=<<B>G4</B><BR align="left"/>Goal 4>];
  "G3" [shape="box", label=<<B>G3</B><BR align="left"/>Goal 3>];
  "C1" [shape="box", style="rounded", label=<<B>C1</B><BR align="left"/>Context 1>];
  "S1" [shape="parallelogram", label=<<B>S1</B><BR align="left"/>Strategy 1>];
  "A1" [shape="oval", label=<<B>A1</B><BR align="left"/>Argument 1>];
  "A1":e -> "A1":e [headlabel=< <B>A</B> >, labeldistance=2.5, penwidth=0, arrowhead=none];
  "Sn1" [shape="circle", label=<<B>Sn1</B><BR align="left"/>Solution 1>];
  "Sn2" [shape="circle", label=<<B>Sn2</B><BR align="left"/>Solution 2>];
  "J1" [shape="oval", label=<<B>J1</B><BR align="left"/>Justification 1>];
  "J1":e -> "J1":e [headlabel=< <B>J</B> >, labeldistance=2.5, penwidth=0, arrowhead=none];

  subgraph clusterg1{
    graph[peripheries=0]  // no box around the cluster
    {rank = same; node[group=g1] edge[style=invis]  "A1" -> "S1" ->  "J1"}
  }

  ## Relations
  "G1" -> "G2";
  "G1" -> "G3";
  "G1" -> "G4";
  "G2" -> "S1";
  "G4" -> "Sn2";
  "G3" -> "Sn1";
  "G3" -> "C1" [arrowhead=empty];
  {rank = same; "G3"; "C1"; }
  "S1" -> "Sn1";
  "S1" -> "J1" [arrowhead=empty];
  "A1" -> "S1" [arrowhead=empty dir=back];
}

p.s. is the A1->S1 arrow correct?