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## Fitness Landscapes And Performance Of Meta-Heuristics (1999)

Venue: | Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization |

Citations: | 11 - 0 self |

### Citations

13825 |
Computers and Intractability - A Guide to the Theory of NPCompleteness, Bell Telephone Laboratories, Incorporated
- Garey, Johnson
- 1979
(Show Context)
Citation Context ...ies is euclidian. Most studies of the TSP are limited in this manner as most applications of the TSP can be seen as two, or three, dimensional in our physical world. Even in this case, TSP is NP-hard =-=[7]-=-. We name 2ETSP this class of instances of the TSP. A tour is coded by the set of n edges that it is composed of. There are N = (n - 1)!/2 di#erent tours when taking account of symetries and redundanc... |

10040 |
Genetic Algorithms
- Goldberg
- 1989
(Show Context)
Citation Context ... design better search methods. Metaheuristics come in di#erent brands, such as simulated annealing [18], tabu search [8, 9], evolutionary algorithms (including all variants such as genetic algorithms =-=[10]-=-, evolution programming [26]), ant colony systems [5] being the 255 256 META-HEURISTICS 98: THEORY & APPLICATIONS most famous. (See [29, 1] for recent reviews of metaheuristics.) Basically, metaheuris... |

2697 |
Genetic Algorithms + Data Structures = Evolution Programs
- Michalewicz
- 1994
(Show Context)
Citation Context ...s. Metaheuristics come in di#erent brands, such as simulated annealing [18], tabu search [8, 9], evolutionary algorithms (including all variants such as genetic algorithms [10], evolution programming =-=[26]-=-), ant colony systems [5] being the 255 256 META-HEURISTICS 98: THEORY & APPLICATIONS most famous. (See [29, 1] for recent reviews of metaheuristics.) Basically, metaheuristics are composed of a loop.... |

994 | Ant Colony System: A cooperative learning approach to the traveling salesman problem
- Dorigo, Gambardella
- 1997
(Show Context)
Citation Context ...di#erent brands, such as simulated annealing [18], tabu search [8, 9], evolutionary algorithms (including all variants such as genetic algorithms [10], evolution programming [26]), ant colony systems =-=[5]-=- being the 255 256 META-HEURISTICS 98: THEORY & APPLICATIONS most famous. (See [29, 1] for recent reviews of metaheuristics.) Basically, metaheuristics are composed of a loop. The body of the loop is ... |

646 | Tabu search part I
- Glover
- 1989
(Show Context)
Citation Context ...e.g. [13, 6, 31]). We wish to go on further on this kind of studies and use them to design better search methods. Metaheuristics come in di#erent brands, such as simulated annealing [18], tabu search =-=[8, 9]-=-, evolutionary algorithms (including all variants such as genetic algorithms [10], evolution programming [26]), ant colony systems [5] being the 255 256 META-HEURISTICS 98: THEORY & APPLICATIONS most ... |

405 |
An effective heuristic algorithm for the traveling salesman problem
- Lin, Kernighan
- 1973
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Citation Context ...Bock in 1958 exchanges up to 3 edges [21]. We can go on and define the k-opt which exchanges k edges. In practice, values of k > 4 are seldomly used. The LK-move, defined by Lin and Kernighan in 1973 =-=[22]-=-, is based on the exchange of edges, the number of edges to exchange being evaluated to get the best possible improvement. Since 1973, it is the best move known for the TSP and is at the core of the m... |

378 |
Modern Heuristic Techniques for Combinatorial Problems
- Reeves
- 1993
(Show Context)
Citation Context ...y algorithms (including all variants such as genetic algorithms [10], evolution programming [26]), ant colony systems [5] being the 255 256 META-HEURISTICS 98: THEORY & APPLICATIONS most famous. (See =-=[29, 1]-=- for recent reviews of metaheuristics.) Basically, metaheuristics are composed of a loop. The body of the loop is based on the following elements: a current state which is a point, or a collection of ... |

350 |
TSPLIB A traveling salesman problem library
- Reinelt
- 1991
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Citation Context ...nd RDW starting from points sampled at random and we examine the length of the walks, the cost of the local optima that are reached, the distance between each others. We use instances from the Tsplib =-=[28]-=- for which we know the shortest tour, att48, kroA100, tsp225. Though these instances are very few and of small size, the results obtained here are in accord with what we observed on many other instanc... |

341 |
Computer solution of the traveling salesman problem
- Lin
- 1965
(Show Context)
Citation Context ...d reconstruct a new di#erent tour (there is always one and only one way to reconstruct a new valid tour that is di#erent from the original). The 3-opt proposed by Bock in 1958 exchanges up to 3 edges =-=[21]-=-. We can go on and define the k-opt which exchanges k edges. In practice, values of k > 4 are seldomly used. The LK-move, defined by Lin and Kernighan in 1973 [22], is based on the exchange of edges, ... |

309 |
The Traveling Salesman Problem: A Case Study
- Johnson, McGeoch
- 1997
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Citation Context ...xcellent local optima: for instances of up to 10 5 cities, solutions which length are not more than 1% in excess to that of the shortest tour length are reached within minutes on typical workstations =-=[14]-=-. Metaheuristics do also perform very well on problems such as vehicle routing problem, quadratic assignment problem, graph coloring problem, set partitioning problem, VLSI layout design, ... Facing t... |

129 |
Scheduling problems and traveling salesman: The genetic edge recombination operator, in
- Whitley, Starkweather, et al.
- 1989
(Show Context)
Citation Context .... New individuals are then created by cross-over using a slightly refined version of the well-known enhanced-edge recombination (EER). We don't recall here the details of EER, and refer the reader to =-=[34]-=-. Our modification to EER relies on the fact that edges not belonging to any parents may have to be introduced in order to satisfy the tour constraint. It has been noted that this fact tend to decreas... |

128 |
The genetic algorithm and the structure of the fitness landscape
- Manderick, Weger, et al.
- 1991
(Show Context)
Citation Context ...of local optima and their quality. We consider this first work, its followers (such as [33, 30, 12]), and some other works dealing with the study of the correlation of the cost of neighborhing points =-=[25, 11]-=- as complementary to ours. In the following, we first present our study of the structure of the planar, euclidian TSP. From it, we derive a search algorithm and provide experimental results and compar... |

86 |
A method for solving traveling salesman problems
- Croes
- 1958
(Show Context)
Citation Context ...es and redundancies in the coding of solutions. This is also the number of points in the search space for the algorithms that are considered in this paper. The basic move of local search is the 2-opt =-=[4]-=- move which consists in removing two edges from a tour and reconstruct a new di#erent tour (there is always one and only one way to reconstruct a new valid tour that is di#erent from the original). Th... |

79 | Combining simulated annealing with local search heuristics
- Martin, Otto
- 1996
(Show Context)
Citation Context ... instead of recombining tours of very low quality. This speeds-up our hybrid GA a lot as will be seen below. Our approach has much to be compared with Martin et al.'s Chained Local Optimization (CLO) =-=[23, 24]-=- and Johnson's Iterated LK [14]. In the next section, we first present our hybrid GA, briefly review Johnson's version of ILK and Junger et al.'s ILK, and provide some experimental results comparing t... |

64 | Towards a theory of landscapes
- Stadler
- 1995
(Show Context)
Citation Context ... of these walks is able to bring some interesting information about the structure of the space, the distribution of local optima and their quality. We consider this first work, its followers (such as =-=[33, 30, 12]-=-), and some other works dealing with the study of the correlation of the cost of neighborhing points [25, 11] as complementary to ours. In the following, we first present our study of the structure of... |

62 | A Measure of Landscapes
- Hordijk
- 1996
(Show Context)
Citation Context ... of these walks is able to bring some interesting information about the structure of the space, the distribution of local optima and their quality. We consider this first work, its followers (such as =-=[33, 30, 12]-=-), and some other works dealing with the study of the correlation of the cost of neighborhing points [25, 11] as complementary to ours. In the following, we first present our study of the structure of... |

51 |
Local Search and Local Structure of NP-Complete Problems
- Grover
- 1992
(Show Context)
Citation Context ...of local optima and their quality. We consider this first work, its followers (such as [33, 30, 12]), and some other works dealing with the study of the correlation of the cost of neighborhing points =-=[25, 11]-=- as complementary to ours. In the following, we first present our study of the structure of the planar, euclidian TSP. From it, we derive a search algorithm and provide experimental results and compar... |

48 | Configuration space analysis of travelling salesman problems, Journal de Physique 46
- Kirkpatrick, Toulouse
- 1985
(Show Context)
Citation Context ..., where lots of local optima are concentrated around one, or more, shortest tour(s). In itself, this result is not new since the discovery of a "deep valley" by S. Kirkpatrick and G. Toulous=-=e in 1985 [19]-=-. However, the way we obtain this result is very di#erent, relying on statistics. One may feel that this approach is very weak and does not prove anything. Though perfectly aware of this weakness, we ... |

48 |
The Landscape of the Traveling Salesman Problem
- Stadler, Schnabl
- 1992
(Show Context)
Citation Context ...ximations of optimal solutions to numerous NP-hard problems. Some authors have tried to explain these performances by a study of the topology of the research space associated to the problem (see e.g. =-=[13, 6, 31]-=-). We wish to go on further on this kind of studies and use them to design better search methods. Metaheuristics come in di#erent brands, such as simulated annealing [18], tabu search [8, 9], evolutio... |

41 |
Models for Iterative Global Optimization
- Boese
- 1996
(Show Context)
Citation Context ... 2opt (t2, t1). FITNESS LANDSCAPES AND PERFORMANCE OF META-HEURISTICS 259 This distance is very attractive but we know of no polynomial way to compute it. So, we use # as an approximation of # as did =-=[19, 2]-=-. [2] prooves the following inequalities: #(t1, t2)/2 # # 2opt (t1, t2) # #(t1, t2). This all implies that when in the sequel we say that two tours are close to each others (that is, their distance # ... |

22 |
Shmoys (Eds.), The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization
- Lawler, Lenstra, et al.
- 1985
(Show Context)
Citation Context ...ory. Though, as it is now suspected, the TSP is rather atypical in its structure, it is often used due its intuitive appeal. We define it very briefly, pointing the reader to Lawler et al.'s TSP book =-=[20]-=- for (much) more precisions, and also the book from Junger et al.'s [16]. Given a set of n cities c i,0#i in a d dimensional space, one has to find the shortest tour that goes through each city. From ... |

21 |
The analysis of local search problems and their heuristics
- Yannakakis
- 1990
(Show Context)
Citation Context ...ial state is either taken at random in the research space, or obtained from a construction heuristic. The theoretical background of local search is not yet sheding much light on their actual behavior =-=[35, 36]-=-. Given a starting point, we can neither predict the number of iterations that will be done before reaching a local optimum, nor predict the quality of this local optimum. Assuming P #= NP , the numbe... |

15 | Near-Optimal Solutions to Very Large Traveling Salesman Problems," presented at the TIMS-ORSA joint national meeting - Johnson, McGeoch, et al. - 1987 |

11 |
A new Adaptive Multi-Start Technique for
- Boese, Kahng, et al.
- 1994
(Show Context)
Citation Context ...n of local optimum in this region. Such a concentration was dubbed as a "deep valley" by Kirkpatrick and Toulouse [19], or "massif central" by Kau#man [17]. This experimental resul=-=t is is accord with [19, 3]-=-, as well as with Stadler and Schnabl conjecture that there exists a massif central in the 2ETSP [31]. 3. the distribution of the quality of the local optima that are reached by either the SDW and the... |

6 |
Jaumard B, de Aragão M. Local optima topology for the k-coloring problem
- Hertz
(Show Context)
Citation Context ...ximations of optimal solutions to numerous NP-hard problems. Some authors have tried to explain these performances by a study of the topology of the research space associated to the problem (see e.g. =-=[13, 6, 31]-=-). We wish to go on further on this kind of studies and use them to design better search methods. Metaheuristics come in di#erent brands, such as simulated annealing [18], tabu search [8, 9], evolutio... |

6 |
The Traveling Salesman Problem", in \Networks Models
- Junger, Reinelt, et al.
(Show Context)
Citation Context ...tructure, it is often used due its intuitive appeal. We define it very briefly, pointing the reader to Lawler et al.'s TSP book [20] for (much) more precisions, and also the book from Junger et al.'s =-=[16]-=-. Given a set of n cities c i,0#i in a d dimensional space, one has to find the shortest tour that goes through each city. From any city, all other cities may 258 META-HEURISTICS 98: THEORY & APPLICAT... |

3 |
Correlated and Uncorrelated Fitness Landscapes and How to
- Weinberger
- 1990
(Show Context)
Citation Context ...h to study the structure of search space can be used to tackle many combinatorial optimization problems, even if one has to be very careful with the conclusions he/she can draw from it. E. Weinberger =-=[32]-=- has initiated studies on random walks (in a random walk, the pivoting rule takes a neighbor at random) in various search spaces. Though this algorithm is completely useless for the purpose of optimiz... |

3 |
Local properties of Kau man's N-k model: A tunably rugged energy landscape
- Weinberger
- 1991
(Show Context)
Citation Context ... of these walks is able to bring some interesting information about the structure of the space, the distribution of local optima and their quality. We consider this first work, its followers (such as =-=[33, 30, 12]-=-), and some other works dealing with the study of the correlation of the cost of neighborhing points [25, 11] as complementary to ours. In the following, we first present our study of the structure of... |

1 |
When Gravity Fails
- Frank, Cheeseman, et al.
- 1997
(Show Context)
Citation Context ...ximations of optimal solutions to numerous NP-hard problems. Some authors have tried to explain these performances by a study of the topology of the research space associated to the problem (see e.g. =-=[13, 6, 31]-=-). We wish to go on further on this kind of studies and use them to design better search methods. Metaheuristics come in di#erent brands, such as simulated annealing [18], tabu search [8, 9], evolutio... |

1 |
Adaptation on Rugged Fitness Landscapes, and Principles of Adaptation
- Kauman
- 1989
(Show Context)
Citation Context ...he search space, resulting in a high concentration of local optimum in this region. Such a concentration was dubbed as a "deep valley" by Kirkpatrick and Toulouse [19], or "massif centr=-=al" by Kau#man [17]-=-. This experimental result is is accord with [19, 3], as well as with Stadler and Schnabl conjecture that there exists a massif central in the 2ETSP [31]. 3. the distribution of the quality of the loc... |

1 |
Genetic Algorithms
- Mulhenbein
- 1997
(Show Context)
Citation Context ... this stage, we can iterate the whole process to progress further inside the valley. We end-up with some kind of hybrid genetic algorithm. However, we have the advantage over standard approaches (see =-=[27]-=- for a review) to begin recombination in an area of the search space where it is really useful, instead of recombining tours of very low quality. This speeds-up our hybrid GA a lot as will be seen bel... |