## A Racing Algorithm for Configuring Metaheuristics (2002)

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Citations: | 127 - 37 self |

### BibTeX

@MISC{Birattari02aracing,

author = {Mauro Birattari and Universit Libre De Bruxelles and Thomas Stützle and Klaus Varrentrapp and Luis Paquete and Technische Universitt Darmstadt},

title = {A Racing Algorithm for Configuring Metaheuristics},

year = {2002}

}

### Years of Citing Articles

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### Abstract

This paper describes a racing procedure for finding, in a limited amount of time, a configuration of a metaheuristic that performs as good as possible on a given instance class of a combinatorial optimization problem. Taking inspiration from methods proposed in the machine learning literature for model selection through cross-validation, we propose a procedure that empirically evaluates a set of candidate configurations by discarding bad ones as soon as statistically sufficient evidence is gathered against them. We empirically evaluate our procedure using as an example the configuration of an ant colony optimization algorithm applied to the traveling salesman problem.

### Citations

3350 |
Probability and measure
- Billingsley
- 1995
(Show Context)
Citation Context ...view. Formally: [ ] ∫ ∫ C(θ) = EI,C c(θ, i) = c(θ, i) dPC(c|θ, i) dPI(i), I (2) where the expectation is considered with respect to both PI and PC, and the integration is taken in the Lebesgue sense (=-=Billingsley, 1986-=-). The measures PI and PC are usually not explicitly available and the analytical solution of the integrals in Equation 2, one for each configuration θ, is not possible. In order to overcome such a li... |

530 |
Practical Nonparametric Statistics
- Conover
- 1971
(Show Context)
Citation Context ...Race The racing algorithm we propose, F-Race in the following, is based on the Friedman test, a statistical method for hypothesis testing also known as Friedman two-way analysis of variance by ranks (=-=Conover, 1999-=-). For giving a description of the test, let us assume that FRace has reached step k, and n = |Θk−1| configurations are still in the race. The Friedman test assumes that the observed costs are k mutua... |

360 | Ant algorithms for discrete optimization - Dorigo, Caro, et al. - 1999 |

329 | The ant colony optimization metaheuristic - Dorigo, Caro - 1997 |

328 |
The Traveling Salesman Problem
- Lawler, Lenstra, et al.
- 1985
(Show Context)
Citation Context ... TSP is symmetric, that is, we have dij = dji for every pair of nodes i and j. The TSP is extensively studied in literature and that serves as a standard benchmark problem (Johnson and McGeoch, 1997; =-=Lawler et al., 1985-=-; Reinelt, 1994). For our study we randomly generate Euclidean TSP instances with a random distribution of city coordinates and a random number of cities. Euclidean TSPs were chosen because such insta... |

285 |
The Travelling Salesman Problem: A case study in local optimization by
- Johnson, Lyle
- 1995
(Show Context)
Citation Context ...de of G once. We assume the TSP is symmetric, that is, we have dij = dji for every pair of nodes i and j. The TSP is extensively studied in literature and that serves as a standard benchmark problem (=-=Johnson and McGeoch, 1997-=-; Lawler et al., 1985; Reinelt, 1994). For our study we randomly generate Euclidean TSP instances with a random distribution of city coordinates and a random number of cities. Euclidean TSPs were chos... |

137 |
Fast Algorithms for Geometric Traveling Salesman Problems
- Bentley
- 1993
(Show Context)
Citation Context ...ettings leads to one particular algorithm config-uration, leading to a total number of 4×4×4×4 = 256 configurations. In our experiments each solution is improved by a 2.5-opt local search procedure (=-=Bentley, 1992-=-). 5 EXPERIMENTAL RESULTS In this section we propose a Monte Carlo evaluation of F-Race based on a resampling technique (Good, 2001). For comparison, we consider two other instances of racing algorith... |

132 | Efficient algorithms for minimizing cross validation error
- Moore, Lee
- 1994
(Show Context)
Citation Context ...izing the number of experiments. The solution we propose is inspired by a class of methods proposed for solving the model selection problem in memory-based supervised learning (Maron and Moore, 1994; =-=Moore and Lee, 1994-=-). Following the terminology introduced by Maron and Moore (1994), we call racing method for selection a method that finds a good configuration (model) from a given finite pool of alternatives through... |

107 | Hoeffding races: Accelerating model selection search for classification and function approximation
- Maron, Moore
- 1994
(Show Context)
Citation Context ...valuations, while minimizing the number of experiments. The solution we propose is inspired by a class of methods proposed for solving the model selection problem in memory-based supervised learning (=-=Maron and Moore, 1994-=-; Moore and Lee, 1994). Following the terminology introduced by Maron and Moore (1994), we call racing method for selection a method that finds a good configuration (model) from a given finite pool of... |

100 | The MAX-MIN Ant system and local search for the travelling salesman problem
- Stützle, Hoos
- 1997
(Show Context)
Citation Context ...over all candidates, to be performed prior to any pairwise test.4 MAX–MIN-ANT-SYSTEM FOR TSP In this paper we illustrate F-Race by using as an example the configuration of MAX–MIN-Ant-System (MMAS) (=-=Stützle and Hoos, 1997-=-; Stützle and Hoos, 2000), a particular Ant Colony Optimization algorithm (Dorigo and Di Caro, 1999; Dorigo and Stützle, 2002), over a class of instances of the Traveling Salesman Problem (TSP). 4.1 A... |

77 | T.: The Ant Colony Optimization Metaheuristic: Algorithms, Applications and Advances
- Dorigo, Stützle
- 2002
(Show Context)
Citation Context ...-Race by using as an example the configuration of MAX–MIN-Ant-System (MMAS) (Stützle and Hoos, 1997; Stützle and Hoos, 2000), a particular Ant Colony Optimization algorithm (Dorigo and Di Caro, 1999; =-=Dorigo and Stützle, 2002-=-), over a class of instances of the Traveling Salesman Problem (TSP). 4.1 A Class of TSP Instances Given a complete graph G = (N, A, d) with N being the set of n = |N| nodes, A being the set of arcs f... |

54 |
Design and Analysis of Experiments
- Dean, Voss
- 1999
(Show Context)
Citation Context ...n a more technical level, left aside the specific application to metaheuristics, we give some contribution to the general class of racing algorithms. In particular, our method adopts blocking design (=-=Dean and Voss, 1999-=-) in a nonparametric setting. In some sense, therefore, the method fills the gap between Hoeffding race (Maron and Moore, 1994) and BRACE (Moore and Lee, 1994): similarly to Hoeffding race it features... |

40 |
Introduction to Probability Theory and Statistical Inference, 3rd ed
- Larson
- 1982
(Show Context)
Citation Context ...to formulate hypotheses on the distribution of the observations. Discussions on the relative pros and cons of the parametric and nonparametric approaches can be found in most textbooks on statistics (=-=Larson, 1982-=-). For an organic presentation of the topic, we refer the reader, for example, to Conover (1999). Here we limit ourselves to mention some widely accepted facts about parametric and nonparametric hypot... |

24 |
The Travelling Salesman: Computational Solutions for TSP
- Reinelt
- 1994
(Show Context)
Citation Context ...at is, we have dij = dji for every pair of nodes i and j. The TSP is extensively studied in literature and that serves as a standard benchmark problem (Johnson and McGeoch, 1997; Lawler et al., 1985; =-=Reinelt, 1994-=-). For our study we randomly generate Euclidean TSP instances with a random distribution of city coordinates and a random number of cities. Euclidean TSPs were chosen because such instances are used i... |

21 | Lesrnin8 search control knowledge for deep space network scheduling - Chien, S, et al. - 1993 |

20 |
Multiple Comparisons
- Hsu
- 1996
(Show Context)
Citation Context ..., is the first work in which blocking is considered in a nonparametric setting. Further, in all the above mentioned works blocking was always implemented through multiple pairwise paired comparisons (=-=Hsu, 1996-=-), and only in the more recent one (Chien et al., 1995) correction for multiple tests is considered. F-Race is the first racing algorithm to implement blocking through ranking and to adopt an aggregat... |

19 |
On the Efficient Allocation of Resources for Hypothesis Evaluation: A Statistical Approach
- Chien, Gratch, et al.
- 1995
(Show Context)
Citation Context ...idered in a nonparametric setting. Further, in all the above mentioned works blocking was always implemented through multiple pairwise paired comparisons (Hsu, 1996), and only in the more recent one (=-=Chien et al., 1995-=-) correction for multiple tests is considered. F-Race is the first racing algorithm to implement blocking through ranking and to adopt an aggregate test over all candidates, to be performed prior to a... |

17 | Improving the ant-system: A detailed report on the MAX -MIN ant system
- Stützle, Hoos
- 1996
(Show Context)
Citation Context ... problem being solved. The solutions obtained by the ants may then be improved by applying some local search routine. ACO algorithms typically follow the high-level procedure given in Figure 2. MMAS (=-=Stützle and Hoos, 1996-=-, 1997; Stützle and Hoos, 2000) is currently one of the best performing ACO algorithms for the TSP. MAX–MIN-Ant-System constructs tours as follows: Initially, each of the m ants is put on some randoml... |

12 |
8th DIMACS implementation challenge. http://www.research.att.com/~dsj/chtsp
- Johnson, McGeoch, et al.
- 2001
(Show Context)
Citation Context ...ution of city coordinates and a random number of cities. Euclidean TSPs were chosen because such instances are used in a large number of experimental researches on the TSP (Johnson and McGeoch, 1997; =-=Johnson et al., 2001-=-). In our case, city locations are randomly chosen according to a uniform distribution in a square of dimension 10.000 × 10.000, and the resulting distances are rounded to the nearest integer. The num... |

3 |
Resampling Methods. Birkhauser
- Good
- 2001
(Show Context)
Citation Context ...ts each solution is improved by a 2.5-opt local search procedure (Bentley, 1992). 5 EXPERIMENTAL RESULTS In this section we propose a Monte Carlo evaluation of F-Race based on a resampling technique (=-=Good, 2001-=-). For comparison, we consider two other instances of racing algorithms both based on a paired t-test. They are therefore parametric, and they adopt a blocking design. We refer to them as tn-Race and ... |

1 | Introduction to Probability Theory and Statistical lnfi, rence - Larson - 1982 |

1 | The Travelling Salesvan Problem - Lawler, Lenstra, et al. - 1985 |

1 | The Traveling Salesman: Computational Solutionx. j'br TSP - Reinelt - 1994 |

1 | Improving the Ant-System: A detailed report on the .M,A2d-.AdZ. M Ant System - Sttitzle, Hoos - 1996 |