Decision Mathematics 2 - The travelling salesman problem Cards about the travelling salesman 5.0 / 5 based on 2 ratings ? Further MathsASEdexcel Created by: jennahxmaiCreated on: 17-05-12 16:27 Key Words Classical - each vertex is visited only once Practical - each vertex is visited at least once Walk - finite sequence of edges where the end of one edge is the start of the next Tour - A walk that visits every vertex & returns to its starting vertex 1 of 4 Finding an upper bound Minimum spanning tree You can find one of these using either Prim's or Kruskal's algorithm When you have found the MST, double the value that you get (this is effectively going up then down every edge) This can become an improved upper bound by finding a shortcut Nearest Neighbour Choose a starting vertex Move to the nearest unvisited vertex Repeat step 2 until all vertices have been visited Return to the start vertex 2 of 4 Finding a lower bound Choose a vertex and delete it and all of its connected edges Find a minimum spanning tree for the rest of the network Add the vertex back on to the minimum spanning tree by adding the two shorted arcs from the deleted vertex to the weight of the minimum spanning tree 3 of 4 Nearest Neighbour Algorithm Choose a starting vertex Move from your present position to the nearest unvisited vertex Repeat step 2 until every vertex has been visited Return to start vertex in the quickest way possible from your current position 4 of 4
Comments
Report