On implementation of computational algorithms for optimal design 1: Preliminary investigation

In this two part paper, the problem of implementation of computational algorithms for design optimization into a computer software is discussed. A recently developed algorithm that generates and incorporates approximate second order information about the problem is selected for detailed analyses and discussions. It is shown that numerical behaviour of the algorithm is influenced by variation of the key parameters and procedures. The concept of numerical experiments is introduced, and certain variations of the algorithm and parameters are selected and their influence on its performance is studied. It is shown that the numerical rate of convergence can be substantially improved with proper procedures and values of the parameters. The first part of the paper describes some preliminary analyses and investigations. The second part describes further numerical analyses and detailed procedures for evaluation of performance of various variations of an algorithm or different computer codes. The basic conclusion from the study is that robust and efficient implementation of algorithms requires expert knowledge and considerable numerical experimentation. A wide range of small scale and large scale problems of varying difficulty must be solved to evaluate performance of an algorithm. The study suggests development of knowledge-based systems for practical design optimization.

[1]  Edward J. Haug,et al.  Applied optimal design: Mechanical and structural systems , 1979 .

[2]  Jasbir S. Arora,et al.  A hybrid optimization method and its role in computer-aided design , 1986 .

[3]  J. Arora,et al.  An active set RQP algorithm for engineering design optimization , 1986 .

[4]  P. Gill,et al.  Methods for computing and modifying the $LDV$ factors of a matrix , 1975 .

[5]  Shih-Ping Han.  A globally convergent method for nonlinear programming , 1975 .

[6]  M. J. D. Powell,et al.  THE CONVERGENCE OF VARIABLE METRIC METHODS FOR NONLINEARLY CONSTRAINED OPTIMIZATION CALCULATIONS , 1978 .

[7]  Jasbir S. Arora,et al.  Interactive Design Optimization with Modern Database Management Concepts. , 1986 .

[8]  K. Schittkowski.  The nonlinear programming method of Wilson, Han, and Powell with an augmented Lagrangian type line search function , 1982 .

[9]  J S Arora,et al.  Uses of artificial intelligence in design optimization , 1986 .

[10]  P. B. Thanedar,et al.  Computational methods for optimum design of large complex systems , 1986 .

[11]  Klaus Schittkowski,et al.  More test examples for nonlinear programming codes , 1981 .

[12]  J. Arora,et al.  A recursive quadratic programming method with active set strategy for optimal design , 1984 .

[13]  M. J. D. Powell,et al.  A fast algorithm for nonlinearly constrained optimization calculations , 1978 .

[14]  Jasbir S. Arora,et al.  An Algorithm for Optimum Structural Design without Line Search , 1981 .

[15]  Ashok Dhondu Belegundu,et al.  A Study of Mathematical Programming Methods for Structural Optimization , 1985 .

[16]  J. Arora,et al.  Development of an Artificially Intelligent Nonlinear Optimization Expert System , 1986 .

[17]  J. Arora,et al.  Performance of some SQP algorithms on structural design problems , 1986 .