## A Comparative Assessment of Memetic, Evolutionary, and Constructive Algorithms for the Multiobjective d-MST Problem (1997)

Venue: | Proc. of 2001 Genetic and Evolutionary Computation Conference Workshop Program |

Citations: | 2 - 0 self |

### BibTeX

@INPROCEEDINGS{Knowles97acomparative,

author = {Joshua D. Knowles and David W. Corne},

title = {A Comparative Assessment of Memetic, Evolutionary, and Constructive Algorithms for the Multiobjective d-MST Problem},

booktitle = {Proc. of 2001 Genetic and Evolutionary Computation Conference Workshop Program},

year = {1997},

pages = {162--167}

}

### OpenURL

### Abstract

Finding a minimum-weight spanning tree

### Citations

532 |
Shortest connection networks and some generalizations
- Prim
- 1957
(Show Context)
Citation Context ...thm mcd-Prim, used for benchmarking the EA results, is described briefly below, as are the initialization procedure, direct encoding and operators used in the EAs. Algorithm mcd-Prim Prim's algorithm =-=[9]-=- is a well-known polynomial time constructive algorithm for solving the (singleobjective, unconstrained) MST problem. It can be adapted to the d-MST by changing it so that at each step, in its constru... |

236 | Approximating the nondominated front using the pareto archived evolution strategy
- Knowles, Corne
- 2000
(Show Context)
Citation Context ...chmark instances developed by us, with constraints and other difficult problem features. Using the same initialization, encoding and operators developed previously, we compare the performance of PAES =-=[5]-=- - a local search strategy, AESSEA [8], and our multiobjective MA, M-PAES [6]. All of the problem instances, generators, and results sets are available for others to use by e-mail contact with the fir... |

81 | On the performance assessment and comparison of stochastic multiobjective optimizers
- Fonseca, Fleming
- 1996
(Show Context)
Citation Context ...two different methods to analyse the statistical performance of the three algorithms over multiple runs on the 15 different problems. Both methods rely on a technique developed by Fonseca and Fleming =-=[2]-=-, and later implemented and extended by us [5]. The technique relies on the notion that the nondominated points from any approximation to a Pareto set define a surface (called the attainment surface),... |

70 |
Neuer Beweis eines Satzes uber Permutationen
- Prufer
- 1918
(Show Context)
Citation Context ...nstances). In a recently published paper by us [8], we extended on the work of Zhou and Gen by developing a new multiobjective EA for the mc-MST problem, called AESSEA, and compared a Prufer encoding =-=[10]-=- (as used by Zhou and Gen) with a direct encoding and specialized operators that we adapted from those of Raidl [11] for the degree-constrained MST (dMST) . Our results demonstrated clear superiority ... |

52 | M-PAES: A memetic algorithm for multiobjective optimization
- Knowles, Corne
(Show Context)
Citation Context ...m features. Using the same initialization, encoding and operators developed previously, we compare the performance of PAES [5] - a local search strategy, AESSEA [8], and our multiobjective MA, M-PAES =-=[6]-=-. All of the problem instances, generators, and results sets are available for others to use by e-mail contact with the first author. 2 Multiobjective Degree-Constrained Spanning Tree Problem A spanni... |

26 |
On spanning tree problems with multiple objectives. Annals of Operations Research 52,209–230
- Hamacher, Ruhe
- 1994
(Show Context)
Citation Context ...ntly, the multiobjective minimum spanning tree (mc-MST) problem, in which there are multiple weights defined on each edge, has become subject to considerable attention. Several papers on this subject =-=[1, 3, 12]-=- have proposed both approximate polynomial algorithms, and worstcase exponential time exact methods, for tackling the problem. Zhou and Gen [13] have also proposed a multiobjective GA approach to the ... |

23 | An efficient evolutionary algorithm for the degree-constrained minimum spanning tree problem
- Raidl
- 2000
(Show Context)
Citation Context ...iobjective EA for the mc-MST problem, called AESSEA, and compared a Prufer encoding [10] (as used by Zhou and Gen) with a direct encoding and specialized operators that we adapted from those of Raidl =-=[11]-=- for the degree-constrained MST (dMST) . Our results demonstrated clear superiority of the direct encoding method on some simple problem instances without constraints. However, the simple instances co... |

13 | Genetic algorithm approach on multi-criteria minimum spanning tree problem
- Zhou, Gen
- 1999
(Show Context)
Citation Context ...derable attention. Several papers on this subject [1, 3, 12] have proposed both approximate polynomial algorithms, and worstcase exponential time exact methods, for tackling the problem. Zhou and Gen =-=[13]-=- have also proposed a multiobjective GA approach to the mc-MST. However, the instances tackled were very simple and could, in fact, be much better solved using good exact methods [12] (smaller instanc... |

10 | A new evolutionary approach to the degree-constrained minimum spanning tree problem
- Knowles, Corne
(Show Context)
Citation Context ...periments reported below, we always run mcd-Prim five times, each time with a different start vertex. Randomized primal method for initialization The randomized primal method (RPM) was put forward in =-=[4]-=- (where it is described in detail) as an encoding for solving the d-MST problem using any metaheuristic search method. It is a decoder type of representation, that is, the chromosome encodes for choic... |

8 | K.: Connectedness of efficient solutions in multiple criteria combinatorial optimization
- Ehrgott, Klamroth
- 1997
(Show Context)
Citation Context ...ntly, the multiobjective minimum spanning tree (mc-MST) problem, in which there are multiple weights defined on each edge, has become subject to considerable attention. Several papers on this subject =-=[1, 3, 12]-=- have proposed both approximate polynomial algorithms, and worstcase exponential time exact methods, for tackling the problem. Zhou and Gen [13] have also proposed a multiobjective GA approach to the ... |

8 | A comparison of encodings and algorithms for multiobjective minimum spanning tree problems
- Knowles, Corne
(Show Context)
Citation Context ...y simple and could, in fact, be much better solved using good exact methods [12] (smaller instances), or heuristic approximation methods [1, 3] (larger instances). In a recently published paper by us =-=[8]-=-, we extended on the work of Zhou and Gen by developing a new multiobjective EA for the mc-MST problem, called AESSEA, and compared a Prufer encoding [10] (as used by Zhou and Gen) with a direct encod... |

6 |
The problem of the optimal biobjective spanning tree
- Ramos, Alonso, et al.
- 1998
(Show Context)
Citation Context ...ntly, the multiobjective minimum spanning tree (mc-MST) problem, in which there are multiple weights defined on each edge, has become subject to considerable attention. Several papers on this subject =-=[1, 3, 12]-=- have proposed both approximate polynomial algorithms, and worstcase exponential time exact methods, for tackling the problem. Zhou and Gen [13] have also proposed a multiobjective GA approach to the ... |

2 | Benchmark problem generators and results for the multiobjective degree-constrained minimum spanning tree problem
- Knowles, Corne
- 2001
(Show Context)
Citation Context ...tances Four types of problems were considered: Correlated, Anti-Correlated, M-Correlated, and Concave. Each presents a particular difficulty to an optimizer. These problems are described in detail in =-=[7]-=-. Three graphs for each of the problem types were generated: one each at sizes of 10, 25, and 50 vertices, giving 12 graphs in all, from which 15 instances are created by setting degree constraints of... |