%0 Book Section
%B Studies in Computational Intelligence
%D 2008
%T Contraction-Based Heuristics to Improve the Efficiency of Algorithms Solving the Graph Colouring Problem
%A Juhos, I.
%A van Hemert, J. I.
%E Cotta, C.
%E van Hemert, J. I.
%K constraint satisfaction
%K evolutionary computation
%K graph colouring
%B Studies in Computational Intelligence
%I Springer
%P 167--184
%G eng
%9 incollection
%0 Conference Paper
%B Lecture Notes in Computer Science
%D 2008
%T Graph Colouring Heuristics Guided by Higher Order Graph Properties
%A Juhos, Istv\'{a}n
%A van Hemert, Jano
%E van Hemert, Jano
%E Cotta, Carlos
%K evolutionary computation
%K graph colouring
%X Graph vertex colouring can be defined in such a way where colour assignments are substituted by vertex contractions. We present various hyper-graph representations for the graph colouring problem all based on the approach where vertices are merged into groups. In this paper, we show this provides a uniform and compact way to define algorithms, both of a complete or a heuristic nature. Moreover, the representation provides information useful to guide algorithms during their search. In this paper we focus on the quality of solutions obtained by graph colouring heuristics that make use of higher order properties derived during the search. An evolutionary algorithm is used to search permutations of possible merge orderings.
%B Lecture Notes in Computer Science
%I Springer
%V 4972
%P 97--109
%G eng
%9 inproceedings
%0 Conference Paper
%B Springer Lecture Notes on Computer Science
%D 2006
%T Improving Graph Colouring Algorithms and Heuristics Using a Novel Representation
%A Juhos, I.
%A van Hemert, J. I.
%E J. Gottlieb
%E G. Raidl
%K constraint satisfaction
%K graph colouring
%X We introduce a novel representation for the graph colouring problem, called the Integer Merge Model, which aims to reduce the time complexity of an algorithm. Moreover, our model provides useful information for guiding heuristics as well as a compact description for algorithms. To verify the potential of the model, we use it in dsatur, in an evolutionary algorithm, and in the same evolutionary algorithm extended with heuristics. An empiricial investigation is performed to show an increase in efficiency on two problem suites , a set of practical problem instances and a set of hard problem instances from the phase transition.
%B Springer Lecture Notes on Computer Science
%I Springer-Verlag
%P 123--134
%G eng
%9 inproceedings
%0 Journal Article
%J Journal of Software
%D 2006
%T Increasing the efficiency of graph colouring algorithms with a representation based on vector operations
%A Juhos, I.
%A van Hemert, J. I.
%K graph colouring
%X We introduce a novel representation for the graph colouring problem, called the Integer Merge Model, which aims to reduce the time complexity of graph colouring algorithms. Moreover, this model provides useful information to aid in the creation of heuristics that can make the colouring process even faster. It also serves as a compact definition for the description of graph colouring algorithms. To verify the potential of the model, we use it in the complete algorithm DSATUR, and in two version of an incomplete approximation algorithm; an evolutionary algorithm and the same evolutionary algorithm extended with guiding heuristics. Both theoretical and empirical results are provided investigation is performed to show an increase in the efficiency of solving graph colouring problems. Two problem suites were used for the empirical evidence: a set of practical problem instances and a set of hard problem instances from the phase transition.
%B Journal of Software
%V 1
%P 24--33
%G eng
%9 article
%0 Conference Paper
%B Springer Lecture Notes on Computer Science
%D 2005
%T Heuristic Colour Assignment Strategies for Merge Models in Graph Colouring
%A Juhos, I.
%A Tóth, A.
%A van Hemert, J. I.
%E G. Raidl
%E J. Gottlieb
%K constraint satisfaction
%K graph colouring
%X In this paper, we combine a powerful representation for graph colouring problems with different heuristic strategies for colour assignment. Our novel strategies employ heuristics that exploit information about the partial colouring in an aim to improve performance. An evolutionary algorithm is used to drive the search. We compare the different strategies to each other on several very hard benchmarks and on generated problem instances, and show where the novel strategies improve the efficiency.
%B Springer Lecture Notes on Computer Science
%I Springer-Verlag, Berlin
%P 132--143
%G eng
%9 inproceedings
%0 Conference Paper
%B Springer Lecture Notes on Computer Science
%D 2004
%T Binary Merge Model Representation of the Graph Colouring Problem
%A Juhos, I.
%A Tóth, A.
%A van Hemert, J. I.
%E J. Gottlieb
%E G. Raidl
%K constraint satisfaction
%K graph colouring
%X This paper describes a novel representation and ordering model that aided by an evolutionary algorithm, is used in solving the graph \emph{k}-colouring problem. Its strength lies in reducing the search space by breaking symmetry. An empirical comparison is made with two other algorithms on a standard suit of problem instances and on a suit of instances in the phase transition where it shows promising results.
%B Springer Lecture Notes on Computer Science
%I Springer-Verlag, Berlin
%P 124--134
%@ 3-540-21367-8
%G eng
%9 inproceedings
%0 Conference Paper
%B Kalmàr Workshop on Logic and Computer Science
%D 2003
%T A new permutation model for solving the graph k-coloring problem
%A Juhos, I.
%A Tóth, A.
%A Tezuka, M.
%A Tann, P.
%A van Hemert, J. I.
%K constraint satisfaction
%K graph colouring
%X This paper describes a novel representation and ordering model, that is aided by an evolutionary algorithm, is used in solving the graph k-coloring. A comparison is made between the new representation and an improved version of the traditional graph coloring technique DSATUR on an extensive list of graph k-coloring problem instances with different properties. The results show that our model outperforms the improved DSATUR on most of the problem instances.
%B Kalmàr Workshop on Logic and Computer Science
%P 189--199
%G eng
%9 inproceedings
%0 Journal Article
%J Journal of Heuristics
%D 1998
%T Graph Coloring with Adaptive Evolutionary Algorithms
%A Eiben, A. E.
%A van der Hauw, J. K.
%A van Hemert, J. I.
%K constraint satisfaction
%K graph colouring
%X This paper presents the results of an experimental investigation on solving graph coloring problems with Evolutionary Algorithms (EA). After testing different algorithm variants we conclude that the best option is an asexual EA using order-based representation and an adaptation mechanism that periodically changes the fitness function during the evolution. This adaptive EA is general, using no domain specific knowledge, except, of course, from the decoder (fitness function). We compare this adaptive EA to a powerful traditional graph coloring technique DSatur and the Grouping GA on a wide range of problem instances with different size, topology and edge density. The results show that the adaptive EA is superior to the Grouping GA and outperforms DSatur on the hardest problem instances. Furthermore, it scales up better with the problem size than the other two algorithms and indicates a linear computational complexity.
%B Journal of Heuristics
%I Kluwer Academic Publishers
%V 4
%P 25--46
%G eng
%9 article