Class AhujaOrlinSharmaCapacitatedMinimumSpanningTree<V,E>
- java.lang.Object
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- org.jgrapht.alg.spanning.AbstractCapacitatedMinimumSpanningTree<V,E>
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- org.jgrapht.alg.spanning.AhujaOrlinSharmaCapacitatedMinimumSpanningTree<V,E>
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- Type Parameters:
V
- the vertex typeE
- 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 GrĂ¼ne
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Nested Class Summary
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Nested classes/interfaces inherited from class org.jgrapht.alg.spanning.AbstractCapacitatedMinimumSpanningTree
AbstractCapacitatedMinimumSpanningTree.CapacitatedSpanningTreeSolutionRepresentation
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Nested classes/interfaces inherited from interface org.jgrapht.alg.interfaces.CapacitatedSpanningTreeAlgorithm
CapacitatedSpanningTreeAlgorithm.CapacitatedSpanningTree<V,E>, CapacitatedSpanningTreeAlgorithm.CapacitatedSpanningTreeImpl<V,E>
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Field Summary
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Fields inherited from class org.jgrapht.alg.spanning.AbstractCapacitatedMinimumSpanningTree
bestSolution, capacity, demands, graph, root
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Constructor Summary
Constructors Constructor Description AhujaOrlinSharmaCapacitatedMinimumSpanningTree(CapacitatedSpanningTreeAlgorithm.CapacitatedSpanningTree<V,E> initialSolution, Graph<V,E> graph, V root, double capacity, java.util.Map<V,java.lang.Double> demands, int lengthBound)
Constructs a new instance of this algorithm with the proposed initial solution.AhujaOrlinSharmaCapacitatedMinimumSpanningTree(CapacitatedSpanningTreeAlgorithm.CapacitatedSpanningTree<V,E> initialSolution, Graph<V,E> graph, V root, double capacity, java.util.Map<V,java.lang.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.AhujaOrlinSharmaCapacitatedMinimumSpanningTree(Graph<V,E> graph, V root, double capacity, java.util.Map<V,java.lang.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.AhujaOrlinSharmaCapacitatedMinimumSpanningTree(Graph<V,E> graph, V root, double capacity, java.util.Map<V,java.lang.Double> demands, int lengthBound, int numberOfOperationsParameter)
Constructs a new instance of this algorithm.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description CapacitatedSpanningTreeAlgorithm.CapacitatedSpanningTree<V,E>
getCapacitatedSpanningTree()
Computes a capacitated spanning tree.
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Constructor Detail
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AhujaOrlinSharmaCapacitatedMinimumSpanningTree
public AhujaOrlinSharmaCapacitatedMinimumSpanningTree(Graph<V,E> graph, V root, double capacity, java.util.Map<V,java.lang.Double> demands, int lengthBound, int numberOfOperationsParameter)
Constructs a new instance of this algorithm.- Parameters:
graph
- the base graphroot
- the designated root of the CMSTcapacity
- the edge capacity constraintdemands
- the demands of the verticeslengthBound
- the length bound of the cycle detection algorithmnumberOfOperationsParameter
- the number of operations that are considered in the randomized Esau-Williams algorithmEsauWilliamsCapacitatedMinimumSpanningTree
@see EsauWilliamsCapacitatedMinimumSpanningTree
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AhujaOrlinSharmaCapacitatedMinimumSpanningTree
public AhujaOrlinSharmaCapacitatedMinimumSpanningTree(CapacitatedSpanningTreeAlgorithm.CapacitatedSpanningTree<V,E> initialSolution, Graph<V,E> graph, V root, double capacity, java.util.Map<V,java.lang.Double> demands, int lengthBound)
Constructs a new instance of this algorithm with the proposed initial solution.- Parameters:
initialSolution
- the initial solutiongraph
- the base graphroot
- the designated root of the CMSTcapacity
- the edge capacity constraintdemands
- the demands of the verticeslengthBound
- the length bound of the cycle detection algorithm
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AhujaOrlinSharmaCapacitatedMinimumSpanningTree
public AhujaOrlinSharmaCapacitatedMinimumSpanningTree(Graph<V,E> graph, V root, double capacity, java.util.Map<V,java.lang.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 graphroot
- the designated root of the CMSTcapacity
- the edge capacity constraintdemands
- the demands of the verticeslengthBound
- the length bound of the cycle detection algorithmbestImprovement
- contains whether the best (if true) or the first improvement (if false) is returned in the neighborhood searchnumberOfOperationsParameter
- the number of operations that are considered in the randomized Esau-Williams algorithmEsauWilliamsCapacitatedMinimumSpanningTree
@see EsauWilliamsCapacitatedMinimumSpanningTreeuseVertexOperation
- contains whether the local search uses the vertex operationuseSubtreeOperation
- contains whether the local search uses the subtree operationuseTabuSearch
- contains whether a tabu search is usedtabuTime
- the tabu time that is the number of iterations an element is in the tabu listupperLimitTabuExchanges
- the upper limit of non-improving exchanges, this is the stopping criterion in the tabu search
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AhujaOrlinSharmaCapacitatedMinimumSpanningTree
public AhujaOrlinSharmaCapacitatedMinimumSpanningTree(CapacitatedSpanningTreeAlgorithm.CapacitatedSpanningTree<V,E> initialSolution, Graph<V,E> graph, V root, double capacity, java.util.Map<V,java.lang.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 solutiongraph
- the base graphroot
- the designated root of the CMSTcapacity
- the edge capacity constraintdemands
- the demands of the verticeslengthBound
- the length bound of the cycle detection algorithmbestImprovement
- contains whether the best (if true) or the first improvement (if false) is returned in the neighborhood searchuseVertexOperation
- contains whether the local search uses the vertex operationuseSubtreeOperation
- contains whether the local search uses the subtree operationuseTabuSearch
- contains whether a tabu search is usedtabuTime
- the tabu time that is the number of iterations an element is in the tabu listupperLimitTabuExchanges
- the upper limit of non-improving exchanges, this is the stopping criterion in the tabu search
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Method Detail
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getCapacitatedSpanningTree
public CapacitatedSpanningTreeAlgorithm.CapacitatedSpanningTree<V,E> getCapacitatedSpanningTree()
Description copied from interface:CapacitatedSpanningTreeAlgorithm
Computes a capacitated spanning tree.- Specified by:
getCapacitatedSpanningTree
in interfaceCapacitatedSpanningTreeAlgorithm<V,E>
- Specified by:
getCapacitatedSpanningTree
in classAbstractCapacitatedMinimumSpanningTree<V,E>
- Returns:
- a capacitated spanning tree
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