General swap-based multiple neighborhood tabu search for the maximum independent set problem

A review on algorithms for maximum clique problems

“…From Table 4 as well as the results reported by the original papers, one first observes that the newest heuristic SBTS (Jin & Hao, 2015) is the only method able to attain the best-known clique size for these 9 graphs (in fact this remains true for all DIMACS and BHOSLIB instances) while the other heuristics miss at least one best-known result. Secondly, algorithms based on the vertex penalty mechanism such as DLS (Pullan & Hoos, 2006), PLS (Pullan, 2006), CLS (Pullan, Mascia, & Brunato, 2011) perform very well on the brock instances, but have troubles to find an optimal (or best known) solution for the large MANN instances.…”

“…These instances are supposed to be hard theoretically for exact algorithms and only few exact algorithms (see for instance McCreesh & Prosser (2013)) report results on these instances. On the other hand, several recent heuristic algorithms can attain the known optimal solutions for these instances with no particular difficulty (Benlic & Hao, 2013; ACCEPTED MANUSCRIPT A C C E P T E D M A N U S C R I P T Cai, Su, & Chen, 2010;Cai, Su, & Sattar, 2011;Grosso, Locatelli & Pullan, 2008;Jin & Hao, 2015;Pullan, Mascia, & Brunato, 2011;Richter, Helmert, & Gretton, 2007;Wu, Hao, & Glover, 2012).…”

“…2 summarizes this classification which is also used in this review to guide our presentation of local search algorithms. (Fleurent & Ferland (1996b)), b (Friden, Hertz, & Werra (1989)), c (Wu & Hao (2011)), d (Battiti & Protasi (2001)), e (Gendreau, Soriano, & Salvail (1993)), f (Katayama, Hamamoto, & Narihisa (2005)), g (Pullan (2006)), h (Pullan & Hoos (2006)), i (Pullan, Mascia, & Brunato (2011)), j (Benlic & Hao (2013)), k (Jin & Hao (2015)), l (Hansen, Mladenović, & Uroševié (2004)), m (Wu, Hao, & Glover (2012)). …”

“…Most local search methods using the legal strategy jointly rely on two or three of these move operators. For instance, methods that employ the add and drop moves include the tabu search algorithms (Gendreau, Soriano, & Salvail, 1993), the RLS algorithm (Battiti & Protasi, 2001) and the KLS algorithm (Katayama, Hamamoto, & Narihisa, 2005) while examples of using all three moves (add, drop and swap) are the VNS algorithm (Hansen, Mladenović, & Uroševié, 2004), the family of PLS (Pullan, 2006), DLS (Pullan & Hoos, 2006), CLS (Pullan, Mascia, & Brunato, 2011) algorithms, the MN/TS algorithm (Wu, Hao, & Glover, 2012), the BLS algorithm (Benlic & Hao, 2013) and the SBTS algorithm (Jin & Hao, 2015). Notice that in some rare cases, more general swap(a, b) could be also useful allowing to exchange a and b vertices between C and V \ C.…”

“…Very recently, a general swap-based tabu search (SBTS) algorithm (Jin & Hao, 2015) is introduced for the equivalent MIS. Each iteration of SBTS corresponds to either an intensification step or a diversification step by applying a general (k, 1)-swap (k ≥ 0) operator.…”