Reliability Optimization With The Lagrange-Multiplier and Branch-And-Bound Technique

IEEE Transactions on Reliability

Volumn R-36, Issue 5, 1987, Pages 624-630

  Kuo, Way ^a   Lin, Hsin Hui ^a   Xu, Zhongkai ^a   Zhang, Weixing ^a  

^a IOWA STATE UNIVERSITY   (United States)

Author keywords

Branch and bound; Integer programming; Kuhn Tucker conditions; Lagrange multiplier method; Mixed integer programming; Newton's method; Reliability optimization

Indexed keywords

MATHEMATICAL PROGRAMMING, NONLINEAR; REDUNDANCY; RELIABILITY - OPTIMIZATION;

BRANCH-AND-BOUND; CONSTRAINED RELIABILITY OPTIMIZATION; INTEGER PROGRAMMING; LAGRANGE MULTIPLIER METHOD; MIXED INTEGER PROGRAMMING;

RELIABILITY THEORY;

EID: 0023596164     PISSN: 00189529     EISSN: 15581721     Source Type: Journal    
DOI: 10.1109/TR.1987.5222487     Document Type: Article

References (16)

1. K.K. Aggarwal, J.S. Gupta, K.B. Misra, “A new heuristic criterion for solving a redundancy optimization problem”, IEEE Trans. Reliability, vol. R-24, 1975 Jan, pp. 86–87.
2. R.L. Burden, J.D. Faires, A.C. Reynolds, Numerical Analysis, Prindle, Weber and Schmidt, 2nd edition, 1981.
3. R.S. Garfinkel, G.L. Nemhause, Integer Programming, John Wiley & Sons, 1972.
4. O.K. Gupta, A. Ravindran, “Branch-and-bound experiments in convex nonlinear programming”, Management Science, Vol. 31, 1985 Dec, pp. 1533–1546.
5. R. Hooke, T.A. Jeeves, “Direct search solution of numerical and statistical problems”, J. ACM, Vol. 8, 1961, pp. 212–224.
6. N.W. Kuhn, A.W. Tucker, “Nonlinear programming”, in Proc. Second Berkeley Symp. Mathematical Statistics and Probability, Berkeley, California, 1951, pp. 481–492.
7. S. Kumar, “Sequential evaluation of terminal pair reliability in a reliability network”, Microelectronics and Reliability, Vol. 22, no 2, 1982, pp. 115–182.
8. H.H. Lin, Way Kuo, “A comparative study of the heuristic reliability optimization method”, Proc. 1987 Intern. Industrial Engineering Conf. Washington, DC 1987 May.
9. K.B. Misra, M.D. Ljubojevic, “Optimal reliability design of a system: A new look”, IEEE Trans. Reliability, vol. R-22, 1973 Oct, pp. 255–258.
10. K.B. Misra, “Reliability optimization of a series-parallel system”, IEEE Trans. Reliability, Vol. R-21, 1972 Oct, pp. 230–238.
11. Y. Nakagawa, K. Nakashima, Y. Hattori, “Optimal reliability allocation by branch-and-bound technique”, IEEE Trans. Reliability, vol. R-27, 1978 Apr, pp. 31–38.
12. F.A. Tillman, C.L. Hwang, Way Kuo, Optimization of Systems Reliability, Marcel Dekker, 1985.
13. F.A. Tillman, C.L. Hwang, Way Kuo, “Determining component reliability and redundancy for optimum system reliability”, IEEE Trans. Reliability, vol. R-26, no 3, 1977 Aug, pp. 162–165.
14. P. Wolfe, “The secant method for simultaneous non-linear equations”, Commun. ACM, vol. 12, 1959, pp. 12–13.
15. IMSL Library Reference Manual, International Mathematical and Statistical Libraries, Inc. Houston, Texas, 1984.
16. PORT Mathematical Subroutine Library, AT&T Bell Laboratories, Inc., Murray Hill, New Jersey, 1984.