A compact row storage scheme for Cholesky factors using elimination trees
ACM Transactions on Mathematical Software (TOMS)
A fast algorithm for reordering sparse matrices for parallel factorization
SIAM Journal on Scientific and Statistical Computing
Parallel algorithms for sparse linear systems
SIAM Review
Adaptation in natural and artificial systems
Adaptation in natural and artificial systems
Modification of the minimum-degree algorithm by multiple elimination
ACM Transactions on Mathematical Software (TOMS)
An introduction to genetic algorithms
An introduction to genetic algorithms
A New Implementation of Sparse Gaussian Elimination
ACM Transactions on Mathematical Software (TOMS)
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Multiple Vehicle Routing with Time and Capacity Constraints Using Genetic Algorithms
Proceedings of the 5th International Conference on Genetic Algorithms
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In the direct solution of sparse symmetric and positive definite linear systems, finding an ordering of the matrix to minimize the height of the elimination tree (an indication of the number of parallel elimination steps) is crucial for effectively computing the Cholesky factor in parallel. This problem is known to be NP-hard. Though many effective heuristics have been proposed, the problems of how good these heuristics are near optimal and how to further reduce the height of the elimination tree remain unanswered. This paper is an effort for this investigation. We introduce a genetic algorithm tailored to this parallel ordering problem, which is characterized by two novel genetic operators, adaptive merge crossover and tree rotate mutation. Experiments showed that our approach is cost effective in the number of generations evolved to reach a better solution in reducing the height of the elimination tree.