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13
A New Evolutionary Approach to the Degree Constrained Minimum Spanning Tree Problem
 IEEE Transactions on Evolutionary Computation
, 2000
"... Finding the degreeconstrained minimum spanning tree (dMST) of a graph is a well studied NPhard problem which is important in network design. We introduce a new method which improves on the best technique previously published for solving the dMST, either using heuristic or evolutionary app ..."
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Finding the degreeconstrained minimum spanning tree (dMST) of a graph is a well studied NPhard problem which is important in network design. We introduce a new method which improves on the best technique previously published for solving the dMST, either using heuristic or evolutionary approaches. The basis of this encoding is a spanningtree construction algorithm which we call the Randomised Primal Method (RPM), based on the wellknown Prim's algorithm [6], and an extension [4] which we call `dPrim's'. We describe a novel encoding for spanning trees, which involves using the RPM to interpret lists of potential edges to include in the growing tree. We also describe a random graph generator which produces particularly challenging dMST problems. On these and other problems, we find that an evolutionary algorithm (EA) using the RPM encoding outperforms the previous best published technique from the operations research literature, and also outperforms simulated...
A New Evolutionary Approach to the DegreeConstrained Minimum Spanning Tree Problem
 IEEE Transactions on Evolutionary Computation
, 1999
"... Finding the degreeconstrained minimum spanning tree (dMST) of a graph is a wellstudied NPhard problem of importance in communications network design and other networkrelated problems. In this paper we describe some previously proposed algorithms for solving the problem, and then introduce a nove ..."
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Cited by 10 (2 self)
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Finding the degreeconstrained minimum spanning tree (dMST) of a graph is a wellstudied NPhard problem of importance in communications network design and other networkrelated problems. In this paper we describe some previously proposed algorithms for solving the problem, and then introduce a novel tree construction algorithm called the Randomised Primal Method (RPM) which builds degreeconstrained trees of low cost from solution vectors taken as input. RPM is applied in three stochastic iterative search methods: simulated annealing, multistart hillclimbing, and a genetic algorithm. While other researchers have mainly concentrated on finding spanning trees in Euclidean graphs, we consider the more general case of random graph problems. We describe two random graph generators which produce particularly challenging dMST problems. On these and other problems we find that the genetic algorithm employing RPM outperforms simulated annealing and multistart hillclimbing. Our experimental ...
Graph Matching and Clustering Using Spectral Partitions
 Pattern Recognition
"... Although inexact graphmatching is a problem of potentially exponential complexity, the problem may be simplified by decomposing the graphs to be matched into smaller subgraphs. If this is done, then the process may cast into a hierarchical framework and hence rendered suitable for parallel computat ..."
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Cited by 9 (0 self)
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Although inexact graphmatching is a problem of potentially exponential complexity, the problem may be simplified by decomposing the graphs to be matched into smaller subgraphs. If this is done, then the process may cast into a hierarchical framework and hence rendered suitable for parallel computation. In this paper we describe a spectral method which can be used to partition graphs into nonoverlapping subgraphs. In particular, we demonstrate how the Fiedlervector of the Laplacian matrix can be used to decompose graphs into nonoverlapping neighbourhoods that can be used for the purposes of both matching and clustering.
A Comparison of Encodings and Algorithms for Multiobjective Minimum Spanning Tree Problems
 In Proceedings of the 2001 Congress on Evolutionary Computation (CEC'01
, 1997
"... this paper we apply (appropriately modified) the best of recent methods for the (degreeconstrained) single objective MST problem to the multiobjective MST problem, and compare with a method based on Zhou and Gen's approach. Our evolutionary computation approaches, using the different encodings ..."
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Cited by 9 (1 self)
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this paper we apply (appropriately modified) the best of recent methods for the (degreeconstrained) single objective MST problem to the multiobjective MST problem, and compare with a method based on Zhou and Gen's approach. Our evolutionary computation approaches, using the different encodings, involve a new populationbased variant of Knowles and Corne's PAES algorithm. We find the direct encoding to considerably outperform the Prufer encoding. And we find that a simple iterated approach, based on Prim's algorithm modified for the multiobjective MST, also significantly outperforms the Prufer encoding.
The 1Factorization Problem and some related Conjectures
, 2004
"... E dalla crisalide sbucó una farfalla meravigliosa, tanto che tutti i fiori si aprirono ad essa. Out of the chrysalis there came a beautiful butterfly. It was so beautiful that all the flowers opened up to it. Daniela Rigato (19511996) The Classification Problem is the problem of determining whether ..."
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Cited by 7 (4 self)
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E dalla crisalide sbucó una farfalla meravigliosa, tanto che tutti i fiori si aprirono ad essa. Out of the chrysalis there came a beautiful butterfly. It was so beautiful that all the flowers opened up to it. Daniela Rigato (19511996) The Classification Problem is the problem of determining whether or not a given graph is ∆edge colourable, where ∆ is the maximum degree. This problem is known to be NPhard, even when restricted to the class of cubic simple graphs. A theorem of Chetwynd and Hilton states that all regular graphs of order 2n and degree at least ( √ 7−1 2
Application of Loop Frame of Reference to Power Flow Tracing and Loss Allocation
"... This paper introduces a new power flow tracing and subsequently loss allocation method based on loop analysis. The knowledge of the loop paths aids in the visualisation of presumed transfer of power throughout the transmission network. A formalised process of loop identification, based on graph the ..."
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This paper introduces a new power flow tracing and subsequently loss allocation method based on loop analysis. The knowledge of the loop paths aids in the visualisation of presumed transfer of power throughout the transmission network. A formalised process of loop identification, based on graph theory, is introduced to ensure that each loop contains at least one active source. This way, the system losses can be readily and justifiably allocated to the active sources in the network without involving any approximations. The proposed method is applied to both a small test system and the IEEE 14bus test system, demonstrating the features and limitations of the proposed methodology.
Evolutionary Approaches to OffLine Routing in Backbone Communications Networks
, 1999
"... Offline routing in backbone communications networks is an important combinatorial optimisation problem. It has three main uses: first, offline routing provides reference benchmark results for dynamic (online) routing strategies. Second, and more interestingly, offline routing is becoming more an ..."
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Cited by 1 (1 self)
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Offline routing in backbone communications networks is an important combinatorial optimisation problem. It has three main uses: first, offline routing provides reference benchmark results for dynamic (online) routing strategies. Second, and more interestingly, offline routing is becoming more and more investigated and employed in its own right as a way of quickly finding significantly improved routings for live networks which can then be imposed on the network to offer a net improvement in quality of service. Third, it can be used in networks where bandwidth may be booked in advance. In this paper we introduce and investigate a number of heuristic techniques applicable to the routing problem for use in stochastic, iterative search. Results are presented which indicate that these heuristics significantly improve the search for solutions, particularly when online performance is considered. We also investigate how computation time can be further reduced by the use of deltaevaluation...
OneMother Vertex Graphs
"... Abstract: In this paper we will define a new type of graph. The idea of this definition is based on when we illustrate the cardiovascular system by a graph we find that not all vertices have the same important so we define this new graph and call it 1 mother vertex graph. ..."
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Abstract: In this paper we will define a new type of graph. The idea of this definition is based on when we illustrate the cardiovascular system by a graph we find that not all vertices have the same important so we define this new graph and call it 1 mother vertex graph.
Recovery of Software Architecture Using Partitioning Approach by Fiedler Vector and Clustering
"... Software Architecture Recovery includes the extraction of design patterns. Patterns may be found using many techniques such as fielder vectors, using clustering methods, query languages etc. In this chapter, for evaluating design patterns clustering methods and the general notion of fielder vector a ..."
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Software Architecture Recovery includes the extraction of design patterns. Patterns may be found using many techniques such as fielder vectors, using clustering methods, query languages etc. In this chapter, for evaluating design patterns clustering methods and the general notion of fielder vector are used.