## A Predecessor Coding in an Evolutionary Algorithm for the Capacitated Minimum Spanning Tree Problem (0)

Venue: | Late Breaking Papers at the 2000 Genetic and Evolutionary Computation Conference, pages 309–316, Las Vegas, NV |

Citations: | 5 - 3 self |

### BibTeX

@INPROCEEDINGS{Raidl_apredecessor,

author = {Günther R. Raidl and Christina Drexel},

title = {A Predecessor Coding in an Evolutionary Algorithm for the Capacitated Minimum Spanning Tree Problem},

booktitle = {Late Breaking Papers at the 2000 Genetic and Evolutionary Computation Conference, pages 309–316, Las Vegas, NV},

year = {},

pages = {309--316}

}

### OpenURL

### Abstract

This article presents an evolutionary algorithm (EA) for the capacitated minimum spanning tree problem occurring in telecommunication applications. The EA encodes a solution by a predecessor vector indicating for each node the preceding node at the path to the given central root node. Initialization, crossover, and mutation operators were specifically designed to provide strong locality and to enable an e#ective search in the space of feasible solutions only. Furthermore, local heuristics are applied to promote the inclusion of low-cost links. Empirical results on a set of standard test problems indicate that the EA performs better than two other heuristic techniques.

### Citations

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(Show Context)
Citation Context ...forms better than two other heuristic techniques. 1 Introduction The problem of finding a capacitated minimum spanning tree (CMST) plays an important role in the design of telecommunication networks [=-=Gavish, 1991].-=- In this problem, a central server and a set of n ≥ 1 client machines are given. Each client i (i = 1, . . . , n) has an associated demand di > 0 representing the network traffic that is supposed to... |

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Citation Context ...0 2.02 2.84 2.95 5.93sWe tested the described EA on a standard test data set, which we obtained from the OR-Library 1 of J. E. Beasley. This set has already been used in several other works, such as [=-=Amberg et al., 1996-=-, Ahuja et al., 1998, Rolland et al., 1998]. There are two categories of problem instances named tc and te. In all problem instances nodes have unit demands (di = 1) and links have identical capacitie... |

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Citation Context ...9) from parent q. Since after the completion of step 4 all nodes are connected to a feasible tree, it is not necessary to add entirely new edges (step 5) in this example. A union-find data structure [=-=Kingston, 1990-=-] is used for efficiently checking whether two nodes are already connected via some link(s) or not (steps 4.3 and 5.1). This data structure is initialized with a set of n+1 independent elements repres... |

24 |
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(Show Context)
Citation Context ...mbol were applied. A similar EA for bicriteria topological network design is described in [Kim and Gen, 1999]. Two more elaborated variants of Prüfer-coded EAs for the DegMST problem are proposed in =-=[Krishnamoorthy et al., 1999]-=-. Abuali et al. [1994] used the Prüfer coding in a GA for the probabilistic minimum spanning tree problem. Operators included circular left shift, swap of two random positions, and random modificatio... |

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(Show Context)
Citation Context ...modification of a symbol. However, several researchers have pointed out that the Prüfer number encoding is problematic due to its weakslocality [Palmer and Kershenbaum, 1994, Knowles and Corne, 2000,=-= Raidl and Julstrom, 2000]-=-. Rothlauf and Goldberg [1999] studied the locality properties of the Prüfer encoding in detail. Patterns of symbols do not represent consistent substructures of spanning trees. Usually applied varia... |

18 |
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(Show Context)
Citation Context ...ple subtrees. An exact method based on a branch-and-bound algorithm with column generation and the utilization of cutting planes to strengthen the formulation is proposed in [Chang and Vance, 1998]. [=-=Hall, 1996] -=-presented another cutting plane algorithm for the CMST 0 ❄ problem. Due to the complex nature of the problem, the applicability of such exact techniques is limited to relatively small problem instan... |

15 |
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(Show Context)
Citation Context ..., pn), where pi denotes the predecessor of node i. E.g. the predecessor vector of the spanning tree in Fig. 1 is p=(0,1,1,0,4,5,0,7,0). Note that such a predecessor encoding has already been used in [=-=Abuali et al., 1994-=-] and discussed in [Palmer and Kershenbaum, 1994] and [Krishnamoorthy et al., 1999]. Especially in the latter two works, predecessor encoding has been pointed out to be problematic since an arbitrary ... |

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11 | A new evolutionary approach to the degree constrained minimum spanning tree problem
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(Show Context)
Citation Context ...om positions, and random modification of a symbol. However, several researchers have pointed out that the Prüfer number encoding is problematic due to its weakslocality [Palmer and Kershenbaum, 1994,=-= Knowles and Corne, 2000,-=- Raidl and Julstrom, 2000]. Rothlauf and Goldberg [1999] studied the locality properties of the Prüfer encoding in detail. Patterns of symbols do not represent consistent substructures of spanning tr... |

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(Show Context)
Citation Context ...indicating directly which edges are to be included in a solution have inherent problems with the huge amount of infeasible solutions that are generated by an EA using traditional variation operators [=-=Piggott and Suraweera, 1995]. An o-=-ften applied coding for spanning trees is based on Prüfer’s proof of Cayley’s formula, which identifies the number of distinct spanning trees on a complete graph with k vertices as k k−2 [Cayle... |

3 | Memory adaptive reasoning & greedy assignment techniques for the capacitated minimum spanning tree problem. Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, edited by
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(Show Context)
Citation Context ...relatively small problem instances or special problem subclasses. Recently, Patterson et al. [1999] proposed a hybrid memory adaptive reasoning technique (ART) for solving the CMST problem, see also [=-=Rolland et al., 1998-=-]. In this approach, the classic EW heuristic is iteratively applied to the problem which is augmented with additional non-redundant constraints determined via an adaptive memory. Empirical results in... |

1 |
New neighbourhood search structures for the capacitated minimum spanning tree problem
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(Show Context)
Citation Context ...sWe tested the described EA on a standard test data set, which we obtained from the OR-Library 1 of J. E. Beasley. This set has already been used in several other works, such as [Amberg et al., 1996, =-=Ahuja et al., 1998-=-, Rolland et al., 1998]. There are two categories of problem instances named tc and te. In all problem instances nodes have unit demands (di = 1) and links have identical capacities mi,j. In both cate... |

1 |
A branch-and-price algorithm for the capacitated minimum spanning tree problem
- Chang, Vance
- 1998
(Show Context)
Citation Context ...hanges that involve multiple subtrees. An exact method based on a branch-and-bound algorithm with column generation and the utilization of cutting planes to strengthen the formulation is proposed in [=-=Chang and Vance, 1998].-=- [Hall, 1996] presented another cutting plane algorithm for the CMST 0 ❄ problem. Due to the complex nature of the problem, the applicability of such exact techniques is limited to relatively small ... |

1 | System Technical Journal, 36: 1389–1401 - Bell - 1957 |