A minimal-state processing search algorithm for satisfiability problems

The Vertex Coloring Problem and its generalizations

“…This ratio always refers to the best results reported, for the corresponding instance, in the associated paper (i.e. k for Impasse [92], HCA [51] and PC-RPC [15], bestk for MIPS-CLR [50]) and the best solution value found by the Tabu Search algorithm, the Evolutionary algorithm and algorithm MMT. Since Morgenstern [92], Galinier and Hao [51] and Blöchliger and Zufferey [15] did not consider the entire set of instances, in Table 2.7 we compare our results with those of the other algorithms on the common subset of instances.…”

“…If the algorithm is not able to solve the problem with k init colors, it dynamically modifies this target value. In the first 4 columns we report the results obtained giving the target value k init as external input, the best value (bestk) found over the 5 runs, the average solution value (avgk) and the average running time approximately scaled w.r.t the benchmark problem (we run the benchmark problem on a machine similar to the one used in [50], which spent 17 seconds user time to solve the benchmark problem). In the following 4 columns we report the results obtained by setting the target value k init equal to the cardinality of a maximal clique in the graph, computed during the initialization of the algorithm: the best value (bestk) found over the 5 runs, the average value of k (avgk) and the average running time approximately scaled w.r.t the benchmark problem.…”

“…• The MIPS-CLR (MInimal-state Processing Search algorithm for the graph CoLoRing problem) by Funabiki and Higashino [50]. This algorithm works in optimization version but requires as input the target value k init for the coloring, together with some other parameters whose values are tuned for hard instances.…”

“…They are mainly based on simulated annealing (Johnson, Aragon, McGeoch and Schevon [72] compared different neighborhoods and presented extensive computational results on random graphs; Morgenstern [92] proposed a very effective neighborhood search) or Tabu Search (Hertz and De Werra [62]; Dorne and Hao [43]; Caramia and Dell'Olmo [25] proposed a local search with priorities rules, inspired from Tabu Search techniques). Funabiki and Higashino [50] proposed one of the most effective algorithms for the problem, which combines a Tabu Search technique with different heuristic procedures, color fixing and solution recombination in the attempt to expand a feasible partial coloring to a complete coloring. Hybrid algorithms integrating local search and diversification via crossover operators were proposed (Fleurent and Ferland [49]; Galinier and Hao [51] proposed to combine an effective crossover operator with Tabu Search), showing that diversification is able to improve the performance of local search.…”

Heuristic algorithms and learning techniques: applications to the graph coloring problem

“…MIPS-MInimal-state Processing Search, a descent algorithm with hill-climbing capabilities combined with maximum clique heuristics and greedy construction stage [Funabiki and Higashino, 2000]; ILS-Iterated Local Search [Chiarandini and Stützle, 2002;Paquete and Stützle, 2002]), research work investigating two local search architectures with different perturbation operators; VNS-Variable Neighborhood Search , an algorithm employing a local search and several different neighborhoods operators that are alternated so as to take the search process out of local minima; ALS-Adaptive Local Search [Devarenne et al, 2006], a local search using a large neighborhood exploration technique with loop detection mechanisms and with a new type of Tabu list; PCOL-Partial Coloring Tabu search (also called PartialCol) [Blöchliger and Zufferey, 2008], a reactive Tabu search that encodes potential solutions as partial (incomplete) legal colorings; VSS-Variable Search Space , an algorithm in which the search process switches iteratively between several search spaces, each with its own encoding, objective function and neighborhood structures;…”