Class NearestNeighborHeuristicTSP<V,​E>

  • Type Parameters:
    V - the graph vertex type
    E - the graph edge type
    All Implemented Interfaces:
    HamiltonianCycleAlgorithm<V,​E>

    public class NearestNeighborHeuristicTSP<V,​E>
    extends HamiltonianCycleAlgorithmBase<V,​E>
    The nearest neighbour 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?".

    This is perhaps the simplest and most straightforward TSP heuristic. The key to this algorithm is to always visit the nearest city.

    The tour computed with a Nearest-Neighbor-Heuristic can vary depending on the first vertex visited. The first vertex for the next or for multiple subsequent tour computations (calls of getTour(Graph)) can be specified in the constructors NearestNeighborHeuristicTSP(Object) or NearestNeighborHeuristicTSP(Iterable). This can be used for example to ensure that the first vertices visited are different for subsequent calls of getTour(Graph). Once each specified first vertex is used, the first vertex in subsequent tour computations is selected randomly from the graph. Alternatively NearestNeighborHeuristicTSP(Random) or NearestNeighborHeuristicTSP(long) can be used to specify a Random used to randomly select the vertex visited first.

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

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

    This algorithm requires that the graph is complete.

    Author:
    Peter Harman, Hannes Wellmann
    • Constructor Detail

      • NearestNeighborHeuristicTSP

        public NearestNeighborHeuristicTSP()
        Constructor. By default a random vertex is chosen to start.
      • NearestNeighborHeuristicTSP

        public NearestNeighborHeuristicTSP​(V first)
        Constructor
        Parameters:
        first - First vertex to visit
        Throws:
        java.lang.NullPointerException - if first is null
      • NearestNeighborHeuristicTSP

        public NearestNeighborHeuristicTSP​(java.lang.Iterable<V> initialVertices)
        Constructor
        Parameters:
        initialVertices - The Iterable of vertices visited first in subsequent tour computations (per call of getTour(Graph) another vertex of the Iterable is used as first)
        Throws:
        java.lang.NullPointerException - if first is null
      • NearestNeighborHeuristicTSP

        public NearestNeighborHeuristicTSP​(long seed)
        Constructor
        Parameters:
        seed - seed for the random number generator
      • NearestNeighborHeuristicTSP

        public NearestNeighborHeuristicTSP​(java.util.Random rng)
        Constructor
        Parameters:
        rng - Random number generator
        Throws:
        java.lang.NullPointerException - if rng is null
    • Method Detail

      • getTour

        public GraphPath<V,​E> getTour​(Graph<V,​E> graph)
        Computes a tour using the nearest neighbour heuristic.
        Parameters:
        graph - the input graph
        Returns:
        a tour
        Throws:
        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 initial vertex is not in the graph