In this paper, an exact algorithm was proposed for optimal redundancy in a series system with multiple component choices. A reformulation of the nonseparable reliability function was approximated by a separable intege...In this paper, an exact algorithm was proposed for optimal redundancy in a series system with multiple component choices. A reformulation of the nonseparable reliability function was approximated by a separable integer programming problem. The resulting separable nonlinear integer programming problem is used to compute upper bounds by Lagrangian relaxation and dual search. A special partition scheme was derived to reduce the duality gap in a branch-and-bound process, thus ensure the convergence of the algorithm. Computational results show that the algorithm is efficient for solving this class of reliability optimization problems.展开更多
Based on the calculation results of pair correlation energy contributions of the various electron pairs in Na2 and H2NNH2 systems and the application of the scaling ionic partition scheme for symmetrical A2 type syste...Based on the calculation results of pair correlation energy contributions of the various electron pairs in Na2 and H2NNH2 systems and the application of the scaling ionic partition scheme for symmetrical A2 type systems, the to-tal correlation energies of Na2 and H2NNH2 have been reproduced by using this simple scheme. The two results show that the absolute deviations are within an acceptable range of error, however, in this way, more than 90% of computational work can be saved. The most attractive result in present paper is that, in these two molecules the co-efficients c1 and c2 in the estimation equation can be obtained by the proportion of correlation energy of A- to that of A+ singlet system. Therefore, it is believed that the proposed ionic partition scheme for symmetrical A2 mole-cules would be very useful to estimate the correlation energies of large symmetrical molecules.展开更多
文摘In this paper, an exact algorithm was proposed for optimal redundancy in a series system with multiple component choices. A reformulation of the nonseparable reliability function was approximated by a separable integer programming problem. The resulting separable nonlinear integer programming problem is used to compute upper bounds by Lagrangian relaxation and dual search. A special partition scheme was derived to reduce the duality gap in a branch-and-bound process, thus ensure the convergence of the algorithm. Computational results show that the algorithm is efficient for solving this class of reliability optimization problems.
文摘Based on the calculation results of pair correlation energy contributions of the various electron pairs in Na2 and H2NNH2 systems and the application of the scaling ionic partition scheme for symmetrical A2 type systems, the to-tal correlation energies of Na2 and H2NNH2 have been reproduced by using this simple scheme. The two results show that the absolute deviations are within an acceptable range of error, however, in this way, more than 90% of computational work can be saved. The most attractive result in present paper is that, in these two molecules the co-efficients c1 and c2 in the estimation equation can be obtained by the proportion of correlation energy of A- to that of A+ singlet system. Therefore, it is believed that the proposed ionic partition scheme for symmetrical A2 mole-cules would be very useful to estimate the correlation energies of large symmetrical molecules.
