IEEE Transactions on Signal Processing
COLING '10 Proceedings of the 23rd International Conference on Computational Linguistics: Posters
Improving a Lagrangian decomposition for the unconstrained binary quadratic programming problem
Computers and Operations Research
Rigorous Enclosures of Ellipsoids and Directed Cholesky Factorizations
SIAM Journal on Matrix Analysis and Applications
An SDP approach to multi-level crossing minimization
Journal of Experimental Algorithmics (JEA)
A hybridization between memetic algorithm and semidefinite relaxation for the max-cut problem
Proceedings of the 14th annual conference on Genetic and evolutionary computation
Linkage neighbors, optimal mixing and forced improvements in genetic algorithms
Proceedings of the 14th annual conference on Genetic and evolutionary computation
Memetic search for the max-bisection problem
Computers and Operations Research
A memetic approach for the max-cut problem
PPSN'12 Proceedings of the 12th international conference on Parallel Problem Solving from Nature - Volume Part II
Better bounds for graph bisection
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
On measures to build linkage trees in LTGA
PPSN'12 Proceedings of the 12th international conference on Parallel Problem Solving from Nature - Volume Part I
More concise and robust linkage learning by filtering and combining linkage hierarchies
Proceedings of the 15th annual conference on Genetic and evolutionary computation
Max-k-Cut by the Discrete Dynamic Convexized Method
INFORMS Journal on Computing
A computational study and survey of methods for the single-row facility layout problem
Computational Optimization and Applications
Application of a MAX-CUT Heuristic to the Contig Orientation Problem in Genome Assembly
Proceedings of the International Conference on Bioinformatics, Computational Biology and Biomedical Informatics
Solving large scale Max Cut problems via tabu search
Journal of Heuristics
Exact Approaches to Multilevel Vertical Orderings
INFORMS Journal on Computing
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We present a method for finding exact solutions of Max-Cut, the problem of finding a cut of maximum weight in a weighted graph. We use a Branch-and-Bound setting that applies a dynamic version of the bundle method as bounding procedure. This approach uses Lagrangian duality to obtain a “nearly optimal” solution of the basic semidefinite Max-Cut relaxation, strengthened by triangle inequalities. The expensive part of our bounding procedure is solving the basic semidefinite relaxation of the Max-Cut problem, which has to be done several times during the bounding process. We review other solution approaches and compare the numerical results with our method. We also extend our experiments to instances of unconstrained quadratic 0–1 optimization and to instances of the graph equipartition problem. The experiments show that our method nearly always outperforms all other approaches. In particular, for dense graphs, where linear programming-based methods fail, our method performs very well. Exact solutions are obtained in a reasonable time for any instance of size up to n = 100, independent of the density. For some problems of special structure we can solve even larger problem classes. We could prove optimality for several problems of the literature where, to the best of our knowledge, no other method is able to do so.