, 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.

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