This is Fig. 2 from the 1990 GENOPT paper: David Bushnell, "GENOPT - A program that writes user-friendly optimization code", International Journal of Solids and Structures, Vol. 26. No. 9/10, pp. 1173-1210, 1990, called "1990 GENOPT paper" in some of the other slides. (The ABSTRACT is shown on the first slide of this slide show.)
Shown here is a schematic of the evolution of a design with only one set of design iterations and only two decision variables, X(1) and X(2). With each iteration the gradient-based optimizer, ADS, establishes a “window” of permitted excursion of the decision variables.
In GENOPT this “window” shrinks by a factor of 0.8 with each design iteration. Upon re-execution of OPTIMIZE the “window” is re-expanded to its original size, which depends upon lower and upper bounds supplied by the end user in DECIDE and upon certain strategies used by the optimizer installed with GENOPT.
This optimizer, called "ADS", was written many years ago by Garrett Vanderplaats and colleagues. GENOPT uses ADS "hardwired" in a gradient-based option: "modified method of steepest descent".
Vanderplaats, G. N., "ADS--a FORTRAN program for automated design synthesis, Version 2.01", Engineering Design Optimization, Inc, Santa Barbara, CA, January, 1987
Vanderplaats, G. N. and Sugimoto, H., "A general-purpose optimization program for engineering design", Computers and Structures, Vol. 24, pp 13-21, 1986
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