Module org.jgrapht.core

Package org.jgrapht.alg.tour

Class NearestInsertionHeuristicTSP<V,E>

java.lang.Object

org.jgrapht.alg.tour.HamiltonianCycleAlgorithmBase<V,E>

org.jgrapht.alg.tour.NearestInsertionHeuristicTSP<V,E>

Type Parameters:

V - the graph vertex type

E - the graph edge type

All Implemented Interfaces:

HamiltonianCycleAlgorithm<V,E>

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.

Author:

Peter Harman

Constructor Summary

Constructors

Constructor	Description
NearestInsertionHeuristicTSP()	Constructor.
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

Method Summary

Modifier and Type	Method	Description
GraphPath<V,E>	getTour(Graph<V,E> graph)	Computes a tour using the nearest insertion heuristic.

Methods inherited from class org.jgrapht.alg.tour.HamiltonianCycleAlgorithmBase

checkGraph, closedVertexListToTour, edgeSetToTour, getSingletonTour, requireNotEmpty, vertexListToTour

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

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

Parameters:

subtour - Initial sub-tour, or null to start with shortest edge

Method Details

getTour

public GraphPath<V,E> getTour(Graph<V,E> graph)

Computes a tour using the nearest insertion heuristic.

Parameters:

graph - the input graph

Returns:

a tour

Throws:

IllegalArgumentException - If the graph is not undirected

IllegalArgumentException - If the graph is not complete

IllegalArgumentException - If the graph contains no vertices

IllegalArgumentException - If the specified sub-tour is for a different Graph instance

IllegalArgumentException - If the graph does not contain specified sub-tour vertices

IllegalArgumentException - If the graph does not contain specified sub-tour edges