Abstract
We present high-level, decomposition-based algorithms for large-scale block-angular optimization problems containing integer variables, and demonstrate their effectiveness in the solution of large-scale graph partitioning problems. These algorithms combine the subproblem-coordination paradigm (and lower bounds) of price-directive decomposition methods with knapsack and genetic approaches to the utilization of “building blocks” of partial solutions. Even for graph partitioning problems requiring billions of variables in a standard 0–1 formulation, this approach produces high-quality solutions (as measured by deviations from an easily computed lower bound), and substantially outperforms widely-used graph partitioning techniques based on heuristics and spectral methods.
This research was partially supported by the Air Force Office of Scientific Research under grant F49620-94-1-0036, and by the NSF under grants CDA-9024618 and CCR-9306807.
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Christou, I.T., Martin, W., Meyer, R.R. (1999). Genetic Algorithms as Multi-Coordinators in Large-Scale Optimization. In: Davis, L.D., De Jong, K., Vose, M.D., Whitley, L.D. (eds) Evolutionary Algorithms. The IMA Volumes in Mathematics and its Applications, vol 111. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1542-4_1
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