Package org.jgrapht.alg.spanning

Class 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 Detail

      • 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