Automatically Generated Algorithms for the Vertex Coloring Problem
The vertex coloring problem is a classical problem in combinatorial optimization that consists of assigning a color to each vertex of a graph such that no adjacent vertices share the same color, minimizing the number of colors used. Despite the various practical applications that exist for this prob...
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| Published in | PloS one Vol. 8; no. 3; p. e58551 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
United States
Public Library of Science
13.03.2013
Public Library of Science (PLoS) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1932-6203 1932-6203 |
| DOI | 10.1371/journal.pone.0058551 |
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| Abstract | The vertex coloring problem is a classical problem in combinatorial optimization that consists of assigning a color to each vertex of a graph such that no adjacent vertices share the same color, minimizing the number of colors used. Despite the various practical applications that exist for this problem, its NP-hardness still represents a computational challenge. Some of the best computational results obtained for this problem are consequences of hybridizing the various known heuristics. Automatically revising the space constituted by combining these techniques to find the most adequate combination has received less attention. In this paper, we propose exploring the heuristics space for the vertex coloring problem using evolutionary algorithms. We automatically generate three new algorithms by combining elementary heuristics. To evaluate the new algorithms, a computational experiment was performed that allowed comparing them numerically with existing heuristics. The obtained algorithms present an average 29.97% relative error, while four other heuristics selected from the literature present a 59.73% error, considering 29 of the more difficult instances in the DIMACS benchmark. |
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| AbstractList | The vertex coloring problem is a classical problem in combinatorial optimization that consists of assigning a color to each vertex of a graph such that no adjacent vertices share the same color, minimizing the number of colors used. Despite the various practical applications that exist for this problem, its NP-hardness still represents a computational challenge. Some of the best computational results obtained for this problem are consequences of hybridizing the various known heuristics. Automatically revising the space constituted by combining these techniques to find the most adequate combination has received less attention. In this paper, we propose exploring the heuristics space for the vertex coloring problem using evolutionary algorithms. We automatically generate three new algorithms by combining elementary heuristics. To evaluate the new algorithms, a computational experiment was performed that allowed comparing them numerically with existing heuristics. The obtained algorithms present an average 29.97% relative error, while four other heuristics selected from the literature present a 59.73% error, considering 29 of the more difficult instances in the DIMACS benchmark. The vertex coloring problem is a classical problem in combinatorial optimization that consists of assigning a color to each vertex of a graph such that no adjacent vertices share the same color, minimizing the number of colors used. Despite the various practical applications that exist for this problem, its NP-hardness still represents a computational challenge. Some of the best computational results obtained for this problem are consequences of hybridizing the various known heuristics. Automatically revising the space constituted by combining these techniques to find the most adequate combination has received less attention. In this paper, we propose exploring the heuristics space for the vertex coloring problem using evolutionary algorithms. We automatically generate three new algorithms by combining elementary heuristics. To evaluate the new algorithms, a computational experiment was performed that allowed comparing them numerically with existing heuristics. The obtained algorithms present an average 29.97% relative error, while four other heuristics selected from the literature present a 59.73% error, considering 29 of the more difficult instances in the DIMACS benchmark.The vertex coloring problem is a classical problem in combinatorial optimization that consists of assigning a color to each vertex of a graph such that no adjacent vertices share the same color, minimizing the number of colors used. Despite the various practical applications that exist for this problem, its NP-hardness still represents a computational challenge. Some of the best computational results obtained for this problem are consequences of hybridizing the various known heuristics. Automatically revising the space constituted by combining these techniques to find the most adequate combination has received less attention. In this paper, we propose exploring the heuristics space for the vertex coloring problem using evolutionary algorithms. We automatically generate three new algorithms by combining elementary heuristics. To evaluate the new algorithms, a computational experiment was performed that allowed comparing them numerically with existing heuristics. The obtained algorithms present an average 29.97% relative error, while four other heuristics selected from the literature present a 59.73% error, considering 29 of the more difficult instances in the DIMACS benchmark. |
| Audience | Academic |
| Author | Parada, Víctor Contreras Bolton, Carlos Gatica, Gustavo |
| AuthorAffiliation | 2 Escuela de Informática, Universidad Andrés Bello, Santiago, Chile Albert Einstein College of Medicine, United States of America 1 Departamento de Ingeniería Informática, Universidad de Santiago de Chile, Santiago, Chile |
| AuthorAffiliation_xml | – name: 2 Escuela de Informática, Universidad Andrés Bello, Santiago, Chile – name: 1 Departamento de Ingeniería Informática, Universidad de Santiago de Chile, Santiago, Chile – name: Albert Einstein College of Medicine, United States of America |
| Author_xml | – sequence: 1 givenname: Carlos surname: Contreras Bolton fullname: Contreras Bolton, Carlos – sequence: 2 givenname: Gustavo surname: Gatica fullname: Gatica, Gustavo – sequence: 3 givenname: Víctor surname: Parada fullname: Parada, Víctor |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/23516506$$D View this record in MEDLINE/PubMed |
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| CitedBy_id | crossref_primary_10_1016_j_asoc_2023_110474 crossref_primary_10_1371_journal_pone_0137724 crossref_primary_10_1155_2016_1682925 crossref_primary_10_1080_23311916_2016_1255165 |
| Cites_doi | 10.1007/BF02239976 10.1007/11564751_54 10.1117/12.512613 10.6028/jres.084.024 10.1201/9781420011326 10.1145/359094.359101 10.1162/evco.2008.16.1.31 10.1090/dimacs/026/01 10.1111/j.1475-3995.2009.00696.x 10.1109/TSMC.1986.289288 10.1007/3-540-32444-5_2 10.1016/j.cor.2010.01.015 10.1016/j.dam.2006.07.010 10.1007/978-3-642-22000-5_57 10.1109/TEVC.2010.2041061 10.1016/B978-1-4832-3187-7.50015-5 10.1016/j.dam.2005.05.022 10.1137/1031001 10.1090/dimacs/026/13 10.1016/j.disopt.2010.12.001 10.1016/j.disopt.2010.07.005 10.1287/ijoc.1070.0245 |
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| Copyright | COPYRIGHT 2013 Public Library of Science 2013 Contreras Bolton et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License: https://creativecommons.org/licenses/by/4.0/ (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. 2013 Contreras Bolton et al 2013 Contreras Bolton et al |
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| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 Conceived and designed the experiments: CCB GG VP. Performed the experiments: CCB GG VP. Analyzed the data: CCB GG VP. Contributed reagents/materials/analysis tools: CCB GG VP. Wrote the paper: CCB GG VP. Competing Interests: The authors have declared that no competing interests exist. |
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| SubjectTerms | Algorithms Artificial intelligence Automation Calibration Color Coloring Combinatorial analysis Competition Computation Computer applications Computer Graphics Computer Science Engineering Evolutionary algorithms Feasibility Studies Genetic algorithms Graph coloring Graph theory Heuristic Hybridization Integer programming Mathematics Mechanical properties Methods Optimization Problem solving Problems Social and Behavioral Sciences |
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| Title | Automatically Generated Algorithms for the Vertex Coloring Problem |
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