The line balancing problem consits in assigning tasks to stations in orderto respect precedence constraints and cycle time constraints. In thispaper, the cycle time is fixed and the objective is to minimize the numberof stations. We propose to use metaheuristics based on simulated annealingby exploiting the link between the line balancing problem and the binpacking problem. The principle of the method lies in the combinationbetween a metaheuristic and a bin packing heuristic. Two representationsof a solution and two neighboring systems are proposed and the methods arecompared with results from the literature. They are better or similar totabu search based algorithm.


The notion of treewidth is of considerable interest in relation to NP-hard problems.Indeed, several studies have shown that the tree-decomposition method can be used to solve many basic optimization problems in polynomialtime when treewidth is bounded, even if, for arbitrary graphs, computingthe treewidth is NP-hard.Several papers present heuristics with computational experiments.For many graphs the discrepancy between the heuristic resultsand the best lower bounds is still very large. The aim of this paper is to propose two new methodsfor computing the treewidth of graphs: a heuristic and a metaheuristic.The heuristic returns good results in a short computation time,whereas the metaheuristic (a Tabu search method)returns the best results known to have been obtained so far for all the DIMACS vertex coloring / treewidth benchmarks (a well-known collection of graphs used for both vertex coloring and treewidth problems.) Our results actually improve on the previous best results for treewidth problems in 53% of the cases. Moreover, we identify properties of the triangulation processto optimize the computing time of our method.