Optimal tolerance allotment using a genetic algorithm and truncated Monte Carlo simulation

As is typical of stochastic-optimization problems, the multivariate integration of the probability-density function is the most difficult task in the optimal allotment of tolerances. In this paper, a truncated Monte Carlo simulation and a genetic algorithm are used as analysis (i.e. multivariate-integration) and synthesis (i.e. optimization) tools, respectively. The new method has performed robustly in limited experiments, and was able to provide a significant reduction in optimal cost when compared with results published in a previous study.

[1]  Elijah Polak,et al.  Computational methods in optimization , 1971 .

[2]  Charles W. Carroll The Created Response Surface Technique for Optimizing Nonlinear, Restrained Systems , 1961 .

[3]  Øyvind Bjørke,et al.  Computer Aided Tolerancing , 1989 .

[4]  John L. Brown On the expansion of the bivariate Gaussian probability density using results of nonlinear theory (Corresp.) , 1968, IEEE Trans. Inf. Theory.

[5]  Anthony V. Fiacco,et al.  Nonlinear programming;: Sequential unconstrained minimization techniques , 1968 .

[6]  Mokhtar S. Bazaraa,et al.  Nonlinear Programming: Theory and Algorithms , 1993 .

[7]  István Deák,et al.  Multidimensional Integration and Stochastic Programming , 1988 .

[8]  A. Ruszczynski,et al.  Stochastic approximation method with gradient averaging for unconstrained problems , 1983 .

[9]  Krzysztof C. Kiwiel,et al.  An aggregate subgradient method for nonsmooth convex minimization , 1983, Math. Program..

[10]  K. Dejong,et al.  An analysis of the behavior of a class of genetic adaptive systems , 1975 .

[11]  T. Donnelly,et al.  Algorithm 462: bivariate normal distribution , 1973 .

[12]  T. C. Woo,et al.  Tolerances: Their Analysis and Synthesis , 1990 .

[13]  Roger J.-B. Wets,et al.  Stochastic Programming: Solution Techniques and Approximation Schemes , 1982, ISMP.

[14]  J. Hammersley,et al.  Monte Carlo Methods , 1965 .

[15]  Jinkoo Lee,et al.  Tolerance optimization using genetic algorithm and approximated simulation. , 1992 .

[16]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[17]  Zvi Drezner,et al.  Computation of the bivariate normal integral , 1978 .

[18]  Douglass J. Wilde,et al.  Minimum Exponential Cost Allocation of Sure-Fit Tolerances , 1975 .

[19]  I. J. Goo,et al.  The centroid method of numerical integration , 1971 .

[20]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[21]  Kenneth Alan De Jong,et al.  An analysis of the behavior of a class of genetic adaptive systems. , 1975 .

[22]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[23]  G. Hachtel The simplicial approximation approach to design centering , 1977 .