Module org.jgrapht.core
Package org.jgrapht.alg.spanning

Class AhujaOrlinSharmaCapacitatedMinimumSpanningTree<V,E>

java.lang.Object
org.jgrapht.alg.spanning.AbstractCapacitatedMinimumSpanningTree<V,E>
org.jgrapht.alg.spanning.AhujaOrlinSharmaCapacitatedMinimumSpanningTree<V,E>
Type Parameters:
V - the vertex type
E - the edge type
All Implemented Interfaces:
CapacitatedSpanningTreeAlgorithm<V,E>
public class AhujaOrlinSharmaCapacitatedMinimumSpanningTree<V,E> extends AbstractCapacitatedMinimumSpanningTree<V,E>
Implementation of an algorithm for the capacitated minimum spanning tree problem using a cyclic exchange neighborhood, based on Ravindra K. Ahuja, James B. Orlin, Dushyant Sharma, A composite very large-scale neighborhood structure for the capacitated minimum spanning tree problem, Operations Research Letters, Volume 31, Issue 3, 2003, Pages 185-194, ISSN 0167-6377, https://doi.org/10.1016/S0167-6377(02)00236-5. (http://www.sciencedirect.com/science/article/pii/S0167637702002365)

A Capacitated Minimum Spanning Tree (CMST) is a rooted minimal cost spanning tree that satisfies the capacity constrained on all trees that are connected to the designated root. The problem is NP-hard. The hard part of the problem is the implicit partition defined by the subtrees. If one can find the correct partition, the MSTs can be calculated in polynomial time.

This algorithm is a very large scale neighborhood search algorithm using a cyclic exchange neighborhood until a local minimum is found. It makes frequently use of a MST algorithm and the algorithm for subset disjoint cycles by Ahuja et al. That is, the algorithm may run in exponential time. This algorithm is implemented in two different version: a local search and a tabu search. In both cases we have to find the best neighbor of the current capacitated spanning tree.

Since:
July 11, 2018
Author:
Christoph Grüne

  • Constructor Details

    • AhujaOrlinSharmaCapacitatedMinimumSpanningTree

      public AhujaOrlinSharmaCapacitatedMinimumSpanningTree(Graph<V,E> graph, V root, double capacity, Map<V,Double> demands, int lengthBound, int numberOfOperationsParameter)
      Constructs a new instance of this algorithm.
      Parameters:
      graph - the base graph
      root - the designated root of the CMST
      capacity - the edge capacity constraint
      demands - the demands of the vertices
      lengthBound - the length bound of the cycle detection algorithm
      numberOfOperationsParameter - the number of operations that are considered in the randomized Esau-Williams algorithm EsauWilliamsCapacitatedMinimumSpanningTree @see EsauWilliamsCapacitatedMinimumSpanningTree

    • AhujaOrlinSharmaCapacitatedMinimumSpanningTree

      public AhujaOrlinSharmaCapacitatedMinimumSpanningTree(CapacitatedSpanningTreeAlgorithm.CapacitatedSpanningTree<V,E> initialSolution, Graph<V,E> graph, V root, double capacity, Map<V,Double> demands, int lengthBound)
      Constructs a new instance of this algorithm with the proposed initial solution.
      Parameters:
      initialSolution - the initial solution
      graph - the base graph
      root - the designated root of the CMST
      capacity - the edge capacity constraint
      demands - the demands of the vertices
      lengthBound - the length bound of the cycle detection algorithm

    • AhujaOrlinSharmaCapacitatedMinimumSpanningTree

      public AhujaOrlinSharmaCapacitatedMinimumSpanningTree(Graph<V,E> graph, V root, double capacity, Map<V,Double> demands, int lengthBound, boolean bestImprovement, int numberOfOperationsParameter, boolean useVertexOperation, boolean useSubtreeOperation, boolean useTabuSearch, int tabuTime, int upperLimitTabuExchanges)
      Constructs a new instance of this algorithm.
      Parameters:
      graph - the base graph
      root - the designated root of the CMST
      capacity - the edge capacity constraint
      demands - the demands of the vertices
      lengthBound - the length bound of the cycle detection algorithm
      bestImprovement - contains whether the best (if true) or the first improvement (if false) is returned in the neighborhood search
      numberOfOperationsParameter - the number of operations that are considered in the randomized Esau-Williams algorithm EsauWilliamsCapacitatedMinimumSpanningTree @see EsauWilliamsCapacitatedMinimumSpanningTree
      useVertexOperation - contains whether the local search uses the vertex operation
      useSubtreeOperation - contains whether the local search uses the subtree operation
      useTabuSearch - contains whether a tabu search is used
      tabuTime - the tabu time that is the number of iterations an element is in the tabu list
      upperLimitTabuExchanges - the upper limit of non-improving exchanges, this is the stopping criterion in the tabu search

    • AhujaOrlinSharmaCapacitatedMinimumSpanningTree

      public AhujaOrlinSharmaCapacitatedMinimumSpanningTree(CapacitatedSpanningTreeAlgorithm.CapacitatedSpanningTree<V,E> initialSolution, Graph<V,E> graph, V root, double capacity, Map<V,Double> demands, int lengthBound, boolean bestImprovement, boolean useVertexOperation, boolean useSubtreeOperation, boolean useTabuSearch, int tabuTime, int upperLimitTabuExchanges)
      Constructs a new instance of this algorithm with the proposed initial solution.
      Parameters:
      initialSolution - the initial solution
      graph - the base graph
      root - the designated root of the CMST
      capacity - the edge capacity constraint
      demands - the demands of the vertices
      lengthBound - the length bound of the cycle detection algorithm
      bestImprovement - contains whether the best (if true) or the first improvement (if false) is returned in the neighborhood search
      useVertexOperation - contains whether the local search uses the vertex operation
      useSubtreeOperation - contains whether the local search uses the subtree operation
      useTabuSearch - contains whether a tabu search is used
      tabuTime - the tabu time that is the number of iterations an element is in the tabu list
      upperLimitTabuExchanges - the upper limit of non-improving exchanges, this is the stopping criterion in the tabu search

  • Method Details