, which is used to generate initial solutions in the hybrid search algorithm for the minimum sum coloring problem (see Chapter 4). Given a graph G, the MIS aims to determine a subset S ? V of maximum cardinality such that no two vertices of S are adjacent. SBTS integrates distinguished features including a general and unified (k, 1)-swap operator, four constrained neighborhoods and specific rules for neighborhood exploration. Extensive evaluations on two popular benchmarks (DIMACS and BHOSLIB) of 120 instances show that SBTS attains the best-known results for all the instances with very different structures and topologies. The best-known results are also attained on an additional set of 11 real instances from code theory, SBTS: Swap-Based Tabu Search for maximum independent set This Appendix presents a general swap-based tabu search (SBTS) heuristic for the maximum independent set problem (MIS), 2015.
, 2.5 (k, 1)-swap, neighborhoods and exploration of neighborhoods
, 3.3 Computational results of SBTS on DIMACS, BHOSLIB and CODE instances
, ) 161.77 50(49.56) 1074.17 50(49.45) 117149.15) 214.58 50(49.08) 1037.68 50(49.16) 1041.40 50(49.24) 2.61 52.03) 240.36 53(52.04) 2306.74 53(52.06) 1707, vol.114, pp.39-53
,
, 5 that except SBTS, each reference algorithm fails to find the best-known results for at least two instances (entries in italic). Indeed, given that these instances have very different characteristics and structures, it is known that it is very difficult for a single heuristic to perform well on all the instances
, SBTS has a slightly better average result of 74.21 against 74.18 of PLS which is the best among the reference algorithms (except NuMVC whose average is an optimistic upper bound since its results are missing for six instances)
, C", and "keller" with a high success rate except for C2000.9 which is among the most difficult instance. For this instance, MN/TS and BLS achieve the best-known result (80) with an average of 78.37 and 78.60 respectively while PLS fails to find solutions larger than 78. For the group "MANN", MN/TS, BLS and PLS cannot reach the best-known results for MANN_a45 (345) and MANN_a81 (1100). The largest solutions they find have a size of 340, 342, and 344 for MANN_a45, and a size of 1090, 1094, and 1098 for MANN_a81 respectively. Generally, List of figures 1.1 An illustrative example for the MSCP, which are maximum clique or maximum independent set algorithms) reach the best reported results for the groups "brock
, 38 3.2 N 1 : An illustrative example with two partial colorings (c and c ? are restricted here to two V i and V j color classes)
, An illustrative example of the DGX crossover
, An illustrative example of the GGX crossover
, An illustration for the IDTS procedure
, Comparisons of HSA and four reference algorithms for the lower bounds, p.63
, Comparisons of HSA and four reference algorithms for the upper bounds, p.66
, An illustrative example of the construction phase with forward checking, p.77
,
,
, Main characteristics of the MSCP benchmark (94 instances)
, Main heuristic and metaheuristic approaches for the BCP and the, p.29
, Main characteristics of the BCP and the BMCP benchmark (66 instances), p.31
, 42 3.2 Detailed computational results of MASC on the set of 39 COLOR 2002-2004 instances (upper part) and 24 DIMACS instances (bottom part)
, Comparisons of MASC with five state-of-the-art sum coloring algorithms, p.45
, MASC vs. five state-of-the-art sum coloring algorithms
, Results of MASC on 17 large graphs with at least 500 vertices
,
, Comparative results of the tabu search improvement method according to the neighborhood employed
,
, 58 4.2 Detailed computational results of HSA on the set of 58 COLOR 2002-2004 instances and 36 DIMACS instances
, Comparisons of HSA with four state-of-the-art sum coloring algorithms for the lower bounds of the MSCP on 94 graphs, p.61
, Comparisons of HSA with four state-of-the-art sum coloring algorithms for the upper bounds of the MSCP on 94 graphs
, Comparisons on 20 selected graphs for the upper and lower bounds of the MSCP, p.66
, FDC analysis on 20 selected graphs for the lower and upper bounds of the MSCP, p.67
,
, Comparisons with four state-of-the-art algorithms on BCP instances, p.82
, Detailed computational results of LHS on the set of 33 BMCP instances, p.84
, Comparisons of LHS with five state-of-the-art algorithms on the set of 33 BMCP instances 85
, Assessment of the learning-based guiding function
, 100 7.2 Detailed computational results of SBTS on the set of 80 DIMACS instances. Each instance is solved 100 times and each run is limited to a maximum of 10 8 iterations, p.106
, Detailed computational results of SBTS on the set of 40 BHOSLIB instances. Each instance is solved 100 times and each run is limited to a maximum of 10 8 iterations, p.108
, Detailed computational results of SBTS on the set of 11 CODE instances. Each instance is solved 100 times and each run is limited to a maximum of 10 8 iterations, p.109
, Comparisons of SBTS with five reference algorithms on 45 most difficult DIMACS and
, , 2012.
,
,
, Models and solution techniques for frequency assignment problems, Annals of Operations Research, vol.153, issue.1, pp.79-129, 2007.
, Two hybrid ant algorithms for the general T-colouring problem, International Journal of Bio-Inspired Computation, vol.2, issue.5, pp.353-362, 2010.
, Generation of lower bounds for minimum span frequency assignment, Discrete Applied Mathematics, vol.119, issue.1, pp.59-78, 2002.
, Fast local search for the maximum independent set problem, Journal of Heuristics, vol.18, issue.4, pp.525-547, 2012.
DOI : 10.1007/978-3-540-68552-4_17
, Minimum color sum of bipartite graphs, Journal of Algorithms, vol.28, issue.2, p.19, 1998.
DOI : 10.1006/jagm.1998.0938
, Reactive local search for the maximum clique problem, Algorithmica, vol.29, issue.4, p.96, 2001.
, A study of breakout local search for the minimum sum coloring problem. Simulated Evolution and Learning, vol.20, p.55, 2012.
, Breakout local search for maximum clique problems, Computers & Operations Research, vol.40, issue.1, pp.192-206, 2013.
DOI : 10.1016/j.cor.2012.06.002
URL : http://www.info.univ-angers.fr/pub/hao/papers/CORBenlicHao2012.pdf
, An application of reinforcement learning for efficient spectrum usage in next-generation mobile cellular networks, IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews, vol.40, issue.4, pp.477-484, 2010.
, The maximum clique problem. Handbook of Combinatorial Optimization, p.96, 1999.
DOI : 10.1007/978-1-4757-3023-4_1
, Minimum sum set coloring of trees and line graphs of trees, Discrete Applied Mathematics, vol.159, issue.5, p.19, 2011.
, A tabu search approach for the sum coloring problem, Electronic Notes in Discrete Mathematics, vol.36, p.20, 2010.
, New methods to color the vertices of a graph, Communications of the ACM, vol.22, issue.4, pp.251-256, 1979.
, R-evo: a reactive evolutionary algorithm for the maximum clique problem, IEEE Transactions on Evolutionary Computation, vol.15, issue.6, p.96, 2011.
, An agent-based algorithm for generalized graph colorings, Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, vol.29, pp.19-26, 2006.
DOI : 10.1145/1143997.1144001
URL : http://www.cs.york.ac.uk/rts/docs/GECCO_2006/docs/p19.pdf
, Estimating the size of correcting codes using extremal graph problems. Optimization, p.111, 2009.
, Numvc: An efficient local search algorithm for minimum vertex cover, vol.109, 2014.
DOI : 10.1613/jair.3907
URL : http://arxiv.org/pdf/1402.0584
, An exact algorithm for the maximum clique problem, Operations Research Letters, vol.9, issue.6, p.96, 1990.
DOI : 10.1016/0167-6377(90)90057-c
, A tabu search algorithm for frequency assignment, Annals of Operations Research, vol.63, issue.2, pp.301-319, 1996.
DOI : 10.1007/bf02125459
, Stochastic local search algorithms for graph set T-colouring and frequency assignment, Constraints, vol.12, issue.3, pp.371-403, 2007.
DOI : 10.1007/s10601-007-9023-y
, On the use of some known methods for T-colorings of graphs, Annals of Operations Research, vol.41, issue.4, pp.343-358, 1993.
, Neighborhood portfolio approach for local search applied to timetabling problems, Journal of Mathematical Modelling and Algorithms, vol.5, issue.1, pp.65-89, 2006.
, Ant algorithms for discrete optimization, Artificial Life, vol.5, issue.2, p.28, 1999.
DOI : 10.1162/106454699568728
, An evolutionary approach for frequency assignment in cellular radio networks, IEEE International Conference on Evolutionary Computation, vol.2, pp.539-544, 1995.
, Tabu search for graph coloring, T-colorings and set T-colorings, Meta-Heuristics, pp.77-92, 1999.
DOI : 10.1007/978-1-4615-5775-3_6
, New algorithm for the sum coloring problem, International Journal of Contemporary Mathematical Sciences, vol.6, issue.10, pp.453-463, 2011.
, A new ant colony optimization algorithm for the lower bound of sum coloring problem, Journal of Mathematical Modelling and Algorithms, vol.11, issue.2, pp.181-192, 2012.
, Greedy and heuristic algorithms for codes and colorings, IEEE Transactions on Information Theory, vol.44, issue.1, p.111, 1998.
DOI : 10.1109/18.651069
, Greedy randomized adaptive search procedures, Journal of Global Optimization, vol.6, issue.2, pp.109-133, 1995.
, Genetic and hybrid algorithms for graph coloring, Annals of Operations Research, vol.63, issue.3, pp.437-461, 1996.
DOI : 10.1007/bf02125407
, Stabulus: A technique for finding stable sets in large graphs with tabu search, Computing, vol.42, issue.1, p.96, 1989.
, Hybrid evolutionary algorithms for graph coloring, Journal of Combinatorial Optimization, vol.3, issue.4, p.79, 1999.
, Some lower bounds for a class of frequency assignment problems, IEEE Transactions on Vehicular Technology, vol.35, issue.1, pp.8-14, 1986.
, Computers and intractability, WH Freeman, vol.29, 2002.
, A simple simulated annealing algorithm for the maximum clique problem, Information Sciences, vol.177, issue.22, p.96, 2007.
, Tabu search. Handbook of Combinatorial Optimization, vol.54, p.97, 1999.
URL : https://hal.archives-ouvertes.fr/hal-01389283
, Minimal coloring and strength of graphs, Discrete Mathematics, vol.215, issue.1, p.19, 2000.
, Frequency assignment: Theory and applications, Proceedings of the IEEE, vol.68, pp.1497-1514, 1980.
DOI : 10.1109/proc.1980.11899
, Scatter search for graph coloring, Artificial Evolution, p.37, 2002.
DOI : 10.1007/3-540-46033-0_14
, Variable neighborhood search for the maximum clique, Discrete Applied Mathematics, vol.145, issue.1, pp.117-125, 2004.
, Memetic algorithms in discrete optimization, Handbook of Memetic Algorithms, p.36, 2012.
DOI : 10.1007/978-3-642-23247-3_6
, Study of genetic search for the frequency assignment problem, Artificial Evolution, pp.333-344, 1996.
, Tabu search for frequency assignment in mobile radio networks, Journal of Heuristics, vol.4, issue.1, pp.47-62, 1998.
, Increasing tree search efficiency for constraint satisfaction problems, Artificial Intelligence, vol.14, issue.3, p.75, 1980.
, A local search heuristic for chromatic sum, Proceedings of the 9th Metaheuristics International Conference, vol.20, p.57, 2011.
, Using tabu search techniques for graph coloring, Computing, vol.39, issue.4, pp.345-351, 1987.
DOI : 10.1007/bf02239976
, Approximation results for the optimum cost chromatic partition problem, Journal of Algorithms, vol.34, issue.1, p.19, 2000.
DOI : 10.1007/3-540-63165-8_226
, Coloring of trees with minimum sum of colors. arXiv preprint math/9904140, p.19, 1999.
, Effective learning-based hybrid search for bandwidth coloring, Accepted to IEEE Transactions on Systems, Man, and Cybernetics: Systems Sept, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01392205
, General swap-based multiple neighborhood tabu search for the maximum independent set problem, Engineering Applications of Artificial Intelligence, vol.37, pp.20-33, 2015.
DOI : 10.1016/j.engappai.2014.08.007
, Hybrid search for upper and lower bounds of the minimum sum coloring problem, 2015.
, A memetic algorithm for the minimum sum coloring problem, Computers & Operations Research, vol.43, pp.318-327, 2014.
DOI : 10.1016/j.cor.2013.09.019
URL : http://arxiv.org/pdf/1304.2641
, Computers and intractability: A guide to the theory of NPcompleteness, p.96, 1979.
, Graph coloring and its generalizations, 2002.
, Special issue on computational methods for graph coloring and its generalizations, Discrete Applied Mathematics, vol.156, issue.2, pp.145-146, 2008.
DOI : 10.1016/j.dam.2007.10.007
URL : https://doi.org/10.1016/j.dam.2007.10.007
, Cliques, coloring, and satisfiability: second DIMACS implementation challenge, 1993.
, Fitness distance correlation as a measure of problem difficulty for genetic algorithms, ICGA, vol.95, pp.184-192, 1995.
, Reducibility among combinatorial problems, Complexity of Computer Computations, vol.96, pp.85-103, 1972.
DOI : 10.1007/978-3-540-68279-0_8
, An effective local search for the maximum clique problem, Information Processing Letters, vol.95, issue.5, p.96, 2005.
, On sum coloring of graphs with parallel genetic algorithms, Adaptive and Natural Computing Algorithms, vol.22, pp.211-219, 2007.
, The optimal cost chromatic partition problem for trees and interval graphs, Graph-Theoretic Concepts in Computer Science, pp.279-292, 1997.
, The chromatic sum of a graph, vol.17, 1989.
, The chromatic sum of a graph: History and recent developments, International Journal of Mathematics and Mathematical Sciences, issue.30, p.18, 2004.
, Polynomial algorithm for finding chromatic sum for unicyclic and outerplanar graphs, Ars Combinatoria, vol.76, 2005.
, Approximation algorithms for the chromatic sum, Computing in the 90's, p.19, 1991.
, An introduction to chromatic sums, Proceedings of the 17th Conference on ACM Annual Computer Science Conference, pp.39-45, 1989.
DOI : 10.1145/75427.75430
, Multistart iterated tabu search for bandwidth coloring problem, Computers & Operations Research, vol.40, issue.5, p.83, 2013.
DOI : 10.1016/j.cor.2012.09.003
, Path relinking for bandwidth coloring problem, vol.29, p.83, 2014.
DOI : 10.1016/j.engappai.2016.02.008
URL : https://hal.archives-ouvertes.fr/hal-01412522
, A graph coloring algorithm for large scheduling problems, Journal of Research of the National Bureau of Standards, vol.84, issue.6, p.19, 1979.
, Combining graph structure exploitation and propositional reasoning for the maximum clique problem, IEEE International Conference on Tools with Artificial Intelligence (ICTAI), vol.1, p.96, 2010.
, Greedy algorithms for the minimum sum coloring problem, Logistique et Transports, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00451266
, Heuristic methods for graph coloring problems, Proceedings of the 2005 ACM Symposium on Applied Computing, vol.27, p.29, 2005.
DOI : 10.1145/1066677.1066892
, Iterated local search. arXiv preprint math/0102188, p.97, 2001.
, A memetic algorithm for graph coloring, European Journal of Operational Research, vol.203, issue.1, pp.241-250, 2010.
, Neighborhood analysis: a case study on curriculum-based course timetabling, Journal of Heuristics, vol.17, issue.2, pp.97-118, 2011.
, Sum coloring of graphs, Graph Colorings, vol.352, pp.55-65, 2004.
, The vertex coloring problem and its generalizations, vol.4, p.26, 2009.
, A metaheuristic approach for the vertex coloring problem, INFORMS Journal on Computing, vol.20, issue.2, p.36, 2008.
, An evolutionary approach for bandwidth multicoloring problems, European Journal of Operational Research, vol.189, issue.3, p.83, 2008.
DOI : 10.1016/j.ejor.2006.09.095
, A survey on vertex coloring problems, International Transactions in Operational Research, vol.17, issue.1, p.27, 2010.
DOI : 10.1111/j.1475-3995.2009.00696.x
URL : https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1475-3995.2009.00696.x
, Heuristics for the bandwidth colouring problem, International Journal of Metaheuristics, vol.1, issue.1, pp.11-29, 2010.
DOI : 10.1504/ijmheur.2010.033121
, Multi-threading a state-of-the-art maximum clique algorithm, Algorithms, vol.6, issue.4, p.105, 2013.
, A gentle introduction to memetic algorithms, Handbook of Metaheuristics, vol.50, pp.105-144, 2003.
DOI : 10.1007/0-306-48056-5_5
URL : http://www.lcc.uma.es/~ccottap/papers/handbook03memetic.pdf
, Lower bounds for the minimal sum coloring problem, Electronic Notes in Discrete Mathematics, vol.36, p.57, 2010.
DOI : 10.1016/j.endm.2010.05.084
, Upper and lower bounds for the minimum sum coloring problem, mscp. (Cited on pages 17, vol.21, p.60, 2013.
DOI : 10.1016/j.endm.2010.05.084
, Handbook of memetic algorithms, vol.379, 2012.
, A fast algorithm for the maximum clique problem, Discrete Applied Mathematics, vol.120, issue.1, p.96, 2002.
, An evolutionary approach with diversity guarantee and well-informed grouping recombination for graph coloring, Computers & Operations Research, vol.37, issue.10, p.41, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00453545
, Coloration neighbourhood search with forward checking, Annals of Mathematics and Artificial Intelligence, vol.34, issue.4, pp.327-340, 2002.
, Generalised graph colouring by a hybrid of local search and constraint programming, Discrete Applied Mathematics, vol.156, issue.2, p.83, 2008.
, Phased local search for the maximum clique problem, Journal of Combinatorial Optimization, vol.12, issue.3, pp.303-323, 2006.
DOI : 10.1007/s10878-006-9635-y
, Approximating the maximum vertex/edge weighted clique using local search, Journal of Heuristics, vol.14, issue.2, pp.117-134, 2008.
DOI : 10.1007/s10732-007-9026-2
, Cooperating local search for the maximum clique problem, Journal of Heuristics, vol.17, issue.2, pp.181-199, 2011.
DOI : 10.1007/s10732-010-9131-5
, A stochastic local search approach to vertex cover, Advances in Artificial Intelligence, vol.109, pp.412-426, 2007.
DOI : 10.1007/978-3-540-74565-5_31
URL : http://rsise.anu.edu.au/~charlesg/vc.pdf
, T-colorings of graphs: recent results and open problems, Discrete Mathematics, vol.93, issue.2, pp.229-245, 1991.
, On sum coloring of graphs, Discrete Applied Mathematics, vol.127, issue.3, pp.477-488, 2003.
, A hybrid hopfield networksimulated annealing approach for frequency assignment in satellite communications systems, IEEE Transactions on Systems, Man, and Cybernetics, vol.34, issue.2, pp.1108-1116, 2004.
, An exact bit-parallel algorithm for the maximum clique problem, Computers & Operations Research, vol.38, issue.2, p.96, 2011.
, Record breaking optimization results using the ruin and recreate principle, Journal of Computational Physics, vol.159, issue.2, p.97, 2000.
, On a graph partition problem with application to vlsi layout, Information Processing Letters, vol.43, issue.2, pp.87-94, 1992.
, Challenge problems: Independent sets in graphs, p.108, 2000.
, MA|PM: Memetic algorithms with population management. Computers & Operations Research, vol.33, pp.1214-1225, 2006.
, Finding a maximum planar subset of a set of nets in a channel, IEEE Transactions on Computer-aided Design of Integrated Circuits and Systems, vol.17, pp.93-94, 1987.
, T-colorings, list T-colorings, and set T-colorings of graphs, 1989.
, Tight bounds on the chromatic sum of a connected graph, Journal of Graph Theory, vol.13, issue.3, p.22, 1989.
, An efficient branch-and-bound algorithm for finding a maximum clique with computational experiments, Journal of Global Optimization, vol.37, issue.1, p.96, 2007.
, Feasible cellular frequency assignment using constraint programming abstractions, Proceedings of the Workshop on Constraint Programming Applications, in conjunction with the Second International Conference on Principles and Practice of Constraint Programming (CP96), 1996.
, Noisy chaotic neural networks with variable thresholds for the frequency assignment problem in satellite communications, IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews, vol.38, issue.2, pp.209-217, 2008.
, Solving the minimum sum coloring problem via binary quadratic programming, 2013.
, An effective heuristic algorithm for sum coloring of graphs, Computers & Operations Research, vol.39, issue.7, p.63, 2012.
DOI : 10.1016/j.cor.2011.09.010
, An adaptive multistart tabu search approach to solve the maximum clique problem, Journal of Combinatorial Optimization, vol.26, issue.1, pp.86-108, 2013.
DOI : 10.1007/s10878-011-9437-8
, Improved lower bounds for sum coloring via clique decomposition, vol.23, p.57, 2013.
, A review on algorithms for maximum clique problems, European Journal of Operational Research, vol.242, issue.3, pp.693-709, 2015.
DOI : 10.1016/j.ejor.2014.09.064
, Multi-neighborhood tabu search for the maximum weight clique problem, Annals of Operations Research, vol.196, issue.1, pp.611-634, 2012.
DOI : 10.1007/s10479-012-1124-3
URL : https://hal.archives-ouvertes.fr/hal-01389283
, A simple model to generate hard satisfiable instances, p.105, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00396466
, An evolutionary algorithm with guided mutation for the maximum clique problem, IEEE Transactions on Evolutionary Computation, vol.9, issue.2, p.96, 2005.
DOI : 10.1109/tevc.2004.840835
, A breakthrough in spectrum conserving frequency assignment technology, IEEE Transactions on Electromagnetic Compatibility, vol.19, issue.3, pp.313-319, 1977.