Class NearestInsertionHeuristicTSP<V,​E>

  • Type Parameters:
    V - the graph vertex type
    E - the graph edge type
    All Implemented Interfaces:

    public class NearestInsertionHeuristicTSP<V,​E>
    extends HamiltonianCycleAlgorithmBase<V,​E>
    The nearest insertion heuristic algorithm for the TSP problem.

    The travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?".

    Insertion heuristics are quite straightforward, and there are many variants to choose from. The basics of insertion heuristics is to start with a tour of a subset of all cities, and then inserting the rest by some heuristic. The initial sub-tour is often a triangle or the convex hull. One can also start with a single edge as sub-tour. This implementation uses the shortest edge by default as the initial sub-tour.

    The implementation of this class is based on:
    Nilsson, Christian. "Heuristics for the traveling salesman problem." Linkoping University 38 (2003)

    This implementation can also be used in order to augment an existing partial tour. See constructor NearestInsertionHeuristicTSP(GraphPath).

    The runtime complexity of this class is $O(V^2)$.

    This algorithm requires that the graph is complete.

    Peter Harman
    • Constructor Detail

      • NearestInsertionHeuristicTSP

        public NearestInsertionHeuristicTSP()
        Constructor. By default a sub-tour is chosen based on the shortest edge
      • NearestInsertionHeuristicTSP

        public NearestInsertionHeuristicTSP​(GraphPath<V,​E> subtour)
        Constructor Specifies an existing sub-tour that will be augmented to form a complete tour when getTour(org.jgrapht.Graph) is called
        subtour - Initial sub-tour, or null to start with shortest edge
    • Method Detail

      • getTour

        public GraphPath<V,​E> getTour​(Graph<V,​E> graph)
        Computes a tour using the nearest insertion heuristic.
        graph - the input graph
        a tour
        java.lang.IllegalArgumentException - If the graph is not undirected
        java.lang.IllegalArgumentException - If the graph is not complete
        java.lang.IllegalArgumentException - If the graph contains no vertices
        java.lang.IllegalArgumentException - If the specified sub-tour is for a different Graph instance
        java.lang.IllegalArgumentException - If the graph does not contain specified sub-tour vertices
        java.lang.IllegalArgumentException - If the graph does not contain specified sub-tour edges