## (Unterschrift Betreuer/in)

### BibTeX

@MISC{Pagacz_(unterschriftbetreuer/in),

author = {Anna Pagacz and Betreuer Univ. -prof and Dr. Günther and R. Raidl and Mitwirkung Univ. -ass and Dr. Bin Hu and Technische Universität Wien and Anna Pagacz},

title = {(Unterschrift Betreuer/in)},

year = {}

}

### OpenURL

### Abstract

an der

### Citations

8573 |
Introduction to Algorithms
- Cormen, Leiserson, et al.
- 2001
(Show Context)
Citation Context ...h or bottom-up approach, which tries to solve the sub-problems first and use their solutions to build-on and finally obtain solutions to bigger sub-problems. For more details please refer to [29] and =-=[3]-=-. 4Figure 1.3: a) Graph G = (V, E) which is not vertex biconnected, b) the corresponding block tree representing block nodes and cut nodes of graph G 1.3 Metaheuristics and population based methods T... |

7415 |
Genetic Algorithms
- Goldberg
- 1989
(Show Context)
Citation Context ..., P ′ ) t ←t+1 until termination condition met Steady state Evolutionary Algorithm As a steady state sort of algorithm is used to solve GMVBCNP, it is briefly introduced in here. Steady state EA [13] =-=[11]-=- is an algorithm with successive population replacement. Strictly speaking there is no offspring population. Instead offspring are generated gradually replacing the worst individual(s) immediately so ... |

434 |
Algorithms
- Sedgewick
- 1998
(Show Context)
Citation Context ... edges of cluster V1 and V2 call repair procedure ( S ′ = (P, T ′ )) 2.7 Cut Nodes Detection and repair procedure In order to deal with feasible solutions a special algorithm, inspired by R.Sedgewick =-=[34]-=- that detects cut nodes has been implemented. The main conclusion regarding graph biconnectivity is: ` ‘The graph is biconnected if and only if there are at least two different paths connecting each p... |

230 |
Future Paths for Integer Programming and Links to Artificial Intelligence
- Glover
- 1986
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Citation Context ...nnected, b) the corresponding block tree representing block nodes and cut nodes of graph G 1.3 Metaheuristics and population based methods The term metaheuristic has been introduced by Glover in 1986 =-=[10]-=-, however for the time being there is no commonly accepted definition. Nevertheless we can outline here some common properties that characterize the metaheuristics: ˆ strategies that guide the search ... |

173 | Metaheuristics in combinatorial optimization: Overview and conceptual comparison
- Blum, Roli
(Show Context)
Citation Context ...management can be involved, which will control population diversity. Such a method is introduced in Chapter 2.9. 1.4 Variable Neighborhood Search Variable Neighborhood Search (VNS) is a metaheuristic =-=[2]-=- that explicitly applies a strategy based on dynamical change of neighborhood structures. The change of neighborhoods leads to exploration of local optima but as well to escape from these valleys in o... |

106 |
Augmentation problems
- Eswaran, Tarjan
- 1976
(Show Context)
Citation Context ...implemented operators is presented. 92.2 Previous work For the time being there are not too many literatures addressing the Generalized Minimum Vertex Biconnected Network Problem. Eswaran and Tarjan =-=[4]-=- were the first to investigate vertex biconnectivity augmentation problem for graphs(V2AUG). By means of a reduction of the Hamiltonian cycle they proved that the decision problem for V2AUG is NP-comp... |

105 |
Genetic algorithms and random keys for sequencing and optimization
- Bean
- 2011
(Show Context)
Citation Context ...ode ni from cluster Vi add node ni to solution.data adjacent list that represents connections between clusters - in other words it represents edges of a clustered graph. A method based on random keys =-=[1]-=- is used to create the initial solutions. In this method, to each gene a random number wi , i = 1, . . . , r drawn uniformly from [0, 1) is assigned (Figure 2.2). A single gene represents a cluster. T... |

104 |
Memetic algorithms: a short introduction
- Moscato
- 1999
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Citation Context ...essful in many optimization problems. The difference between Memetic Algorithm (MA) and EA [13][11] is that MA actually exploits all available knowledge about the problem under study. As mentioned in =-=[25]-=- MA exploits problem knowledge by involving hybridization, that evaluates to the use of pre-existing heuristics, preprocessing data reduction rules, approximation, local search techniques and speciali... |

59 | A Branch-and-Cut Algorithm for the Symmetric Generalized Traveling Salesman Problem
- Fischetti, Salazar, et al.
- 1997
(Show Context)
Citation Context ...s complete on each other, however they can be used independently as well. 282.10 Computational results for GMVBCNP The MA was tested on Euclidean TSPlib instances with geographical center clustering =-=[6, 8]-=-. They contain 137 to 431 nodes partitioned into 28 to 87 clusters. The number of nodes per cluster varies. All experiments have been performed on 2× Dual-Core AMD Opteron Processor 2214 with 8GB RAM.... |

53 |
Edge-connectivity augmentation problems
- Watanabe, Nakamura
- 1987
(Show Context)
Citation Context ...te vertex biconnectivity augmentation problem for graphs(V2AUG). By means of a reduction of the Hamiltonian cycle they proved that the decision problem for V2AUG is NP-complete. Watanabe and Nakamura =-=[37]-=- proved that minimum-cost augmentation for edge or vertex k-connectivity is NP-hard, for any k ≥ 2. Some preliminary results of running memetic algorithm for the Generalized Minimum Vertex Biconnected... |

24 |
Comparison of algorithms for the degree constrained minimum spanning tree
- Krishnamoorthy, Ernst, et al.
- 1999
(Show Context)
Citation Context ...ated annealing, multistart hillclimbing and genetic algorithm. Another several heuristics including simulated annealing and genetic algorithms has been presented by Krishnamoorthy, Ernst and Sharaiha =-=[20]-=-. They proposed as well a method based on problem space search (PSS), which as they concluded works best over all the problems. An efficient Evolutionary Algorithm proposed by Raidl [30] produces only... |

23 | An efficient evolutionary algorithm for the degree-constrained minimum spanning tree problem
- Raidl
- 2000
(Show Context)
Citation Context ... and Sharaiha [20]. They proposed as well a method based on problem space search (PSS), which as they concluded works best over all the problems. An efficient Evolutionary Algorithm proposed by Raidl =-=[30]-=- produces only a feasible candidate solutions and provides substantially stronger locality than most previous approaches. Raidl and Julstrom [31] proposed representation of spanning trees in EAs direc... |

20 |
Edge sets: An effective evolutionary coding of spanning trees
- Raidl, Julstrom
(Show Context)
Citation Context ... An efficient Evolutionary Algorithm proposed by Raidl [30] produces only a feasible candidate solutions and provides substantially stronger locality than most previous approaches. Raidl and Julstrom =-=[31]-=- proposed representation of spanning trees in EAs directly as sets of their edges and developed initialization, recombination, and mutation operators for this representation. The operators offer local... |

18 | Generalized Spanning Trees and Extensions
- Feremans
- 2001
(Show Context)
Citation Context ...s complete on each other, however they can be used independently as well. 282.10 Computational results for GMVBCNP The MA was tested on Euclidean TSPlib instances with geographical center clustering =-=[6, 8]-=-. They contain 137 to 431 nodes partitioned into 28 to 87 clusters. The number of nodes per cluster varies. All experiments have been performed on 2× Dual-Core AMD Opteron Processor 2214 with 8GB RAM.... |

18 |
On the Generalized Minimum Spanning Tree Problem
- Myung, Lee, et al.
- 1995
(Show Context)
Citation Context ...1: Example for d-GMST problem, where degree d = 3 GMSTP and d-MSTP this chapter briefly introduces a previous works related to both of them. The GMST problem was first proposed by Myung, Lee and Tcha =-=[26]-=- and they proved that it is NP-hard and they provided Integer Linear Programming formulation. Feremans, Labbe and Laporte provided further formulations in [7] and investigated all eight ILPs. Feremans... |

17 | Generalized network design problems
- Feremans, Labbé, et al.
- 1995
(Show Context)
Citation Context ...as first proposed by Myung, Lee and Tcha [26] and they proved that it is NP-hard and they provided Integer Linear Programming formulation. Feremans, Labbe and Laporte provided further formulations in =-=[7]-=- and investigated all eight ILPs. Feremans in [6] proposed exact solution algorithms based on branch and cut approach, while Pop, Kern and Still in [28] proposed approximation algorithms and heuristic... |

15 | Variable neighborhood search for the degree-constrained minimum spanning tree problem
- Ribeiro, Souza
(Show Context)
Citation Context ... on edge exchange has been proposed by Savelsbergh and Volgenant [33]. Volgenant [36] proposed also edge exchanges used in branch and bound algorithm based on Lagrangian relaxation. Ribeiro and Souza =-=[32]-=- proposed a VNS based on dynamic neighbor42hood model and using a variable neighborhood descent iterative improvement algorithm for local search. Knowles and Corne introduced in [19] a novel tree con... |

12 |
Edge exchanges in the degree-constrained minimum spanning tree problem
- Savelsbergh, Volgenant
- 1985
(Show Context)
Citation Context ...stic procedures and a branch and bound algorithm. The branch and bound algorithm which makes use of an edge elimination procedure based on edge exchange has been proposed by Savelsbergh and Volgenant =-=[33]-=-. Volgenant [36] proposed also edge exchanges used in branch and bound algorithm based on Lagrangian relaxation. Ribeiro and Souza [32] proposed a VNS based on dynamic neighbor42hood model and using ... |

11 | The Generalized Minimum Spanning Tree Problem
- Pop
- 2002
(Show Context)
Citation Context ...n approach or bottom-up approach, which tries to solve the sub-problems first and use their solutions to build-on and finally obtain solutions to bigger sub-problems. For more details please refer to =-=[29]-=- and [3]. 4Figure 1.3: a) Graph G = (V, E) which is not vertex biconnected, b) the corresponding block tree representing block nodes and cut nodes of graph G 1.3 Metaheuristics and population based m... |

10 | A new evolutionary approach to the degree-constrained minimum spanning tree problem
- Knowles, Corne
(Show Context)
Citation Context ...ibeiro and Souza [32] proposed a VNS based on dynamic neighbor42hood model and using a variable neighborhood descent iterative improvement algorithm for local search. Knowles and Corne introduced in =-=[19]-=- a novel tree construction algorithm called the Randomized Principal Method (RPM) which builds degree constrained trees of low cost from solution vectors. They applied RPM in three iterative methods: ... |

10 | Exact and memetic algorithms for two network design problems - Ljubić - 2004 |

9 |
A lagrangean approach to the degree-constrained minimum spanning tree problem
- Volgenant
- 1989
(Show Context)
Citation Context ...and a branch and bound algorithm. The branch and bound algorithm which makes use of an edge elimination procedure based on edge exchange has been proposed by Savelsbergh and Volgenant [33]. Volgenant =-=[36]-=- proposed also edge exchanges used in branch and bound algorithm based on Lagrangian relaxation. Ribeiro and Souza [32] proposed a VNS based on dynamic neighbor42hood model and using a variable neigh... |

7 | Solving Medium to Large Sized Euclidean Generalized Minimum Spanning Tree Problems
- Ghosh
- 2003
(Show Context)
Citation Context ...ying idea of his MIP formulation in a Simulated Annealing approach which allows solving larger instances. To solve more general and larger instances several metaheuristics has been suggested by Ghosh =-=[9]-=-. In his paper he studied performance of neighborhood searches based on tabu search and variable neighborhood search (VNS). He implemented and compared Tabu Search that incorporates recently based mem... |

7 |
Heuristic Search for the Generalized Minimum Spanning Tree Problem
- Golden, Raghavan, et al.
- 2005
(Show Context)
Citation Context ...investigated problem only does an exhaustive search on the subset of clusters. Comparing this approaches Ghosh concluded that TS2 and VNDS perform best on the average. Golden, Raghavan and Stanojevic =-=[12]-=- presented two heuristic search techniques - local search and a genetic algorithm. They proposed as well a simple lower and upper bound heuristics for GMST problem. Hu, Leitner and Raidl [15] proposed... |

6 | Effective neighborhood structures for the generalized traveling salesman problem
- Hu, Raidl
- 2008
(Show Context)
Citation Context ...N. If Vred is empty, then the global structure is a round trip and all spanned nodes can be determined by using the shortest path calculation analogously to the generalized traveling salesman problem =-=[16]-=- [25] and NON is not searched at all. Cluster Re-Arrangement Neighborhood With this neighborhood structure I try to optimize a solution with respect to the arrangement of the clusters. Given a solutio... |

5 | Solving two generalized network design problems with exact and heuristic methods
- Leitner
- 2006
(Show Context)
Citation Context ...f neighborhood structures. The change of neighborhoods leads to exploration of local optima but as well to escape from these valleys in order to reach under-explored areas to find even better results =-=[21]-=-. The VNS main cycle is composed basically of three steps: shaking, local search and move. The VNS can be combined with Variable Neighborhood Descent (VND) that applies a best improvement local search... |

5 | A memetic algorithm for minimum-cost vertex-biconnectivity augmentation of graphs
- Ljubić, Raidl
(Show Context)
Citation Context ...tion without violating the vertex-biconnectivity feature. As a minimum vertex biconnected network we denote a graph that contains no cut nodes and no redundant edges. The block cut graph Referring to =-=[23]-=-, a block is denoted as maximal subgraph of a graph G that is already vertex biconnected. If the graph is vertex biconnected the whole graph represents one block. If any two blocks of G share at least... |

3 | Combining variable neighborhood search with integer linear programming for the generalized minimum spanning tree problem
- Hu, Leitner, et al.
- 2006
(Show Context)
Citation Context ...anojevic [12] presented two heuristic search techniques - local search and a genetic algorithm. They proposed as well a simple lower and upper bound heuristics for GMST problem. Hu, Leitner and Raidl =-=[15]-=- proposed VNS approach which uses three different types of neighborhoods. Two of them work in complementary ways in order to maximize search effectiveness whereas for the third they applied Mixed Inte... |

3 |
Degree constrained minimum spanning tree
- Narula, Ho
- 1980
(Show Context)
Citation Context ...y applied Mixed Integer Programming (MIP) to optimize local parts within candidate tree’s solution. The application of d-MST in the design of electrical circuits has been pointed out by Narula and Ho =-=[27]-=-. They proposed primal and dual heuristic procedures and a branch and bound algorithm. The branch and bound algorithm which makes use of an edge elimination procedure based on edge exchange has been p... |

2 |
The generalized minimum edge biconnected network problem: Efficient neighborhood structures for variable neighborhood search. accepted for Networks
- Hu, Leitner, et al.
(Show Context)
Citation Context ...ntified and removed. In order to minimize the search area, not all edges are checked against redundancy, but only the edges (pi, pj) ∈ TN , where deg(pi) > 2 ∧ deg(pj) > 2 are considered. Inspired by =-=[14]-=-, to minimize the connection cost, before the edges are examined against its removal possibility, all edges adjacent to nodes with degree deg > 2 are put in particular order: ˆ alfa - decreasing costs... |

2 |
Transitions in geometric minimum spanning trees (extended abstract
- Monma, Suri
- 1991
(Show Context)
Citation Context ...in318 318 50403 64 rd400 400 79800 80 fl417 417 86736 84 gr431 432 92665 87 The preliminary tests showed that the best obtained results for all instances have average degree 3 ≥ d ≥ 4. Monma and Suri =-=[24]-=- proved that there always exist a MST with degree no more than five for trees in Euclidean plane. As the GMST is an extension of the MST the definition holds. The set of tests have been performed on a... |

1 |
A networkflow technique for finding low-weight bounded-degree spanning trees
- Feketea, Khullerb, et al.
- 1997
(Show Context)
Citation Context ...utation operators for this representation. The operators offer locality, heritability, and computational efficiency. The adapting edges procedure presented further in this thesis has been inspired by =-=[5]-=-. Feketea, Khullerb, Klemmsteina, Raghavacharic and Young considered degree constraint for a graph and proposed modification of a given spanning tree representing an unfeasible solution by using adopt... |

1 |
A memetic algorithm for the generalized minimum vertexbiconnected network problem
- Hu, Raidl
- 2009
(Show Context)
Citation Context ...ation for edge or vertex k-connectivity is NP-hard, for any k ≥ 2. Some preliminary results of running memetic algorithm for the Generalized Minimum Vertex Biconnected Network Problem can be found in =-=[17]-=-. The vertex biconnectivity as well as the edge biconnectivity problem has been attacked by Ljubic in [22]. Because the Generalized Minimum Vertex Biconnected Network Problem and the Generalized Minim... |

1 |
Ma—pm: memetic algorithms with population management
- Soerensena, Sevauxb
- 2006
(Show Context)
Citation Context ...lution graph may change. The pseudocode is given in Algorithm 13. 2.9 Population Management There is not much literature about population management techniques. Some theoretical ideas can be found in =-=[35]-=-. It has been observed that the quality of metaheuristics is the result of cooperation between intensification and diversifiation strategies. The use of the memetic algorithm can upset the balance bet... |

1 |
Ein loesungsarchiv-unterstuetzter evolutionaerer algorithmus fuer das generalized minimum spanning tree-problem
- Wolf
- 2009
(Show Context)
Citation Context ...e current population, however once the individual is withdrawn from population, the information about its existence is lost as well. Here comes up the idea of an archive creation, implemented by Wolf =-=[38]-=-. He proposed a complete solution archive for GAs that effectively transforms duplicates into similar so far unconsidered candidate solutions. I use this concept for MA as well. Each 53time a new sol... |