InsertionTsp< CM > Class Template Reference

Detailed Description

template<typename CM>
class lemon::InsertionTsp< CM >

InsertionTsp implements the insertion heuristic for solving symmetric TSP.

This is a fast and effective tour construction method that has many variants. It starts with a subtour containing a few nodes of the graph and it iteratively inserts the other nodes into this subtour according to a certain node selection rule.

This method is among the fastest TSP algorithms, and it typically provides quite good solutions (usually much better than NearestNeighborTsp and GreedyTsp).

InsertionTsp implements four different node selection rules, from which the most effective one (farthest node selection) is used by default. With this choice, the algorithm runs in O(n²) time. For more information, see SelectionRule.

Template Parameters

CM	Type of the cost map.

#include <lemon/insertion_tsp.h>

Public Types
enum	SelectionRule { NEAREST, FARTHEST, CHEAPEST, RANDOM }
	Constants for specifying the node selection rule. More...
typedef CM	CostMap
	Type of the cost map.
typedef CM::Value	Cost
	Type of the edge costs.

Public Member Functions
	InsertionTsp (const FullGraph &gr, const CostMap &cost)
	Constructor. More...
Execution Control
Cost	run (SelectionRule rule=FARTHEST)
	Runs the algorithm. More...
Query Functions
Cost	tourCost () const
	The total cost of the found tour. More...
const std::vector< Node > &	tourNodes () const
	Returns a const reference to the node sequence of the found tour. More...
template<typename Iterator >
void	tourNodes (Iterator out) const
	Gives back the node sequence of the found tour. More...
template<typename Path >
void	tour (Path &path) const
	Gives back the found tour as a path. More...

Member Enumeration Documentation

enum SelectionRule

Enum type containing constants for specifying the node selection rule for the run() function.

During the algorithm, nodes are selected for addition to the current subtour according to the applied rule. The FARTHEST method is one of the fastest selection rules, and it is typically the most effective, thus it is the default option. The RANDOM rule usually gives slightly worse results, but it is more robust.

The desired selection rule can be specified as a parameter of the run() function.

Enumerator
NEAREST	An unvisited node having minimum distance from the current subtour is selected at each step. The algorithm runs in O(n2) time using this selection rule.
FARTHEST	An unvisited node having maximum distance from the current subtour is selected at each step. The algorithm runs in O(n2) time using this selection rule.
CHEAPEST	An unvisited node whose insertion results in the least increase of the subtour's total cost is selected at each step. The algorithm runs in O(n3) time using this selection rule, but in most cases, it is almost as fast as with other rules.
RANDOM	An unvisited node is selected randomly without any evaluation at each step. The global random number generator instance is used. You can seed it before executing the algorithm, if you would like to. The algorithm runs in O(n2) time using this selection rule.

Constructor & Destructor Documentation

InsertionTsp ( const FullGraph &  gr, const CostMap &  cost  )

inline

Constructor.

Parameters

gr	The full graph the algorithm runs on.
cost	The cost map.

Member Function Documentation

Cost run ( SelectionRule  rule = FARTHEST )

inline

This function runs the algorithm.

Parameters

rule	The node selection rule. For more information, see SelectionRule.

Returns

The total cost of the found tour.

Cost tourCost ( ) const

inline

This function returns the total cost of the found tour.

Precondition

run() must be called before using this function.

const std::vector<Node>& tourNodes ( ) const

inline

This function returns a const reference to a vector that stores the node sequence of the found tour.

Precondition

run() must be called before using this function.

void tourNodes ( Iterator  out ) const

inline

This function copies the node sequence of the found tour into an STL container through the given output iterator. The value_type of the container must be FullGraph::Node. For example,

*  std::vector<FullGraph::Node> nodes(countNodes(graph));
*  tsp.tourNodes(nodes.begin());
*  

or

*  std::list<FullGraph::Node> nodes;
*  tsp.tourNodes(std::back_inserter(nodes));
*  

Precondition

run() must be called before using this function.

void tour ( Path &  path ) const

inline

This function copies the found tour as a list of arcs/edges into the given path structure.

Precondition

run() must be called before using this function.