## A Study of Evaluation Functions for the Graph K-Coloring Problem

Citations: | 2 - 1 self |

### BibTeX

@MISC{Porumbel_astudy,

author = {Daniel Cosmin Porumbel and Pascale Kuntz},

title = {A Study of Evaluation Functions for the Graph K-Coloring Problem},

year = {}

}

### OpenURL

### Abstract

Abstract. The evaluation or fitness function is a key component of any heuristic search algorithm. This paper introduces a new evaluation function for the well-known graph K-coloring problem. This function takes into account not only the number of conflicting vertices, but also inherent information related to the structure of the graph. To assess the effectiveness of this new evaluation function, we carry out a number of experiments using a set of DIMACS benchmark graphs. Based on statistic data obtained with a parameter free steepest descent, we show an improvement of the new evaluation function over the classical one. 1

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Citation Context ...such that G is K−colorable. The smallest K is the chromatic number of G. From a theoretical viewpoint, K-COL is a very important NP-complete problem as it is one of the 21 NP-complete problems listed =-=[10]-=-. Coloring problems are also at the heart of numerous applications including for instance, scheduling, register allocation in compilers and frequency assignment in mobile networks. The graph coloring ... |

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Citation Context ...n function is the above objective function f which counts the number of conflicting edges of a given K-coloring. Indeed, this evaluation function is largely used by many wellknown coloring algorithms =-=[7,5,2,6,1]-=-. We will show in this paper that this evaluation function is not discriminating enough and can be improved. – Neighborhood: Given a configuration (K-coloring) C = (c(1),c(2), ··· , c(|V |)), a neighb... |

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Citation Context ...n function is the above objective function f which counts the number of conflicting edges of a given K-coloring. Indeed, this evaluation function is largely used by many wellknown coloring algorithms =-=[7,5,2,6,1]-=-. We will show in this paper that this evaluation function is not discriminating enough and can be improved. – Neighborhood: Given a configuration (K-coloring) C = (c(1),c(2), ··· , c(|V |)), a neighb... |

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Citation Context ...n function is the above objective function f which counts the number of conflicting edges of a given K-coloring. Indeed, this evaluation function is largely used by many wellknown coloring algorithms =-=[7,5,2,6,1]-=-. We will show in this paper that this evaluation function is not discriminating enough and can be improved. – Neighborhood: Given a configuration (K-coloring) C = (c(1),c(2), ··· , c(|V |)), a neighb... |

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Citation Context ... in order to identify particular properties that are useful for the design of the evaluation function. Such a problem-specific approach has demonstrated its effectiveness for several NP-hard problems =-=[4,8,13]-=-. N. Monmarché et al. (Eds.): EA 2007, LNCS 4926, pp. 124–135, 2008. c○ Springer-Verlag Berlin Heidelberg 2008sA Study of Evaluation Functions for the Graph K-Coloring Problem 125 In this paper, we co... |

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Citation Context ...in section 4.1. 3 A New Evaluation Function For the graph K-coloring problem, many previous algorithms use f as their evaluation function, although other functions are also proposed (see for instance =-=[12,3]-=-). However, the function f is not sufficiently discriminating since it cannot distinguish configurations having the same number of conflicts while these colorings may have different possibilities for ... |

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Citation Context ...in section 4.1. 3 A New Evaluation Function For the graph K-coloring problem, many previous algorithms use f as their evaluation function, although other functions are also proposed (see for instance =-=[12,3]-=-). However, the function f is not sufficiently discriminating since it cannot distinguish configurations having the same number of conflicts while these colorings may have different possibilities for ... |

2 | An improved evaluation function for the bandwidth minimization problem
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Citation Context ... in order to identify particular properties that are useful for the design of the evaluation function. Such a problem-specific approach has demonstrated its effectiveness for several NP-hard problems =-=[4,8,13]-=-. N. Monmarché et al. (Eds.): EA 2007, LNCS 4926, pp. 124–135, 2008. c○ Springer-Verlag Berlin Heidelberg 2008sA Study of Evaluation Functions for the Graph K-Coloring Problem 125 In this paper, we co... |

1 |
der Hauw, J.K.: Adaptive penalties for evolutionary graph coloring
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(Show Context)
Citation Context ...in section 4.1. 3 A New Evaluation Function For the graph K-coloring problem, many previous algorithms use f as their evaluation function, although other functions are also proposed (see for instance =-=[12,3]-=-). However, the function f is not sufficiently discriminating since it cannot distinguish configurations having the same number of conflicts while these colorings may have different possibilities for ... |

1 |
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Citation Context ... fitness function. Indeed, it is this function that guides the search process to explore an arbitrarily large search space. There are different approaches to design an informative evaluation function =-=[14]-=-. First, the static or dynamic penalty approach is a well established technique for constrained problems. Here relaxed constraints are integrated into the evaluation function with special penalty term... |