1. NAME AND TITLE

DOPEX: Laminated Shield Weight Optimization Code SystemSteepest Descent Calculational Model.

2. CONTRIBUTOR

NASA Lewis Research Center, Cleveland, Ohio.

3. CODING LANGUAGE AND COMPUTER

FORTRAN IV; IBM 360/370 and TSS 360 (A) or UNIVAC 1108 (B).

4. NATURE OF PROBLEM SOLVED

Given an initial set of shield layer thicknesses and parameters defining the relationship between radiation dose and layer thicknesses, DOPEX seeks a minimum weight by altering layer thicknesses of a radiation shield with two- or three-dose rate constraints. Right circular cylindrical geometry is presently coded in DOPEX; a user-written subroutine WEIGHT would be required if a different geometry is required.

5. METHOD OF SOLUTION

The method of steepest descent utilized by OPEX and reinterpreted in the OPEX-II code for one-dimensional, one-constraint optimization problems has been extended to the multi-constraint, multidimensional problem and coded into DOPEX. Given an initial configuration and an empirical dose-thickness relationship, DOPEX uses the method of steepest descent to alter shield layer thicknesses to obtain a minimum weight while simultaneously satisfying dose rate constraints.

6. RESTRICTIONS OR LIMITATIONS

A. One-dose constraint and spherical geometry,

B. Two-dose constraints and right circular cylindrical geometry,

C. Three-dose constraints and right circular cylindrical geometry.

A maximum of 25 shield layers and 25 dose rate components are allowed, but these limits could be increased by expanding the dimensions of appropriate variables in the DOPEX code.

7. TYPICAL RUNNING TIME

DOPEX required less than 0.1 minute on the IBM 7094 to execute the sample problem, a seven-layer shield with three dose rate constraints, each with 12 dose rate components. RSIC noted 2 seconds running time for the sample problem on the IBM 360/91.

8. COMPUTER HARDWARE REQUIREMENTS

IBM 360, standard I-O, 62K core.

9. COMPUTER SOFTWARE REQUIREMENTS

An IBM 360/75/91 operating system, a FORTRAN H compiler, and standard I-O are required.

10. REFERENCES

a. Included in the documentation:

G. P. Lahti, "The DOPEX CodeAn Application of the Method of Steepest Descent to Laminated-Shield-Weight Optimization with Several Constraints," NASA TM X-2554 (April 1972).

G. P. Lahti, "Application of the Method of Steepest Descent to Laminated Shield Weight Optimization with Several ConstraintsTheory," NASA TM X-2435 (November 1971).

b. Background information:

R. L. Bernick, "Application of the Method of Steepest Descent to Laminated Shield Weight Optimization," NAA-SR-Memo-8181 (April 1963).

R. L. Bernick, "The OPEX Shield Optimization Code," NAA-SR-Memo-11516 (July 1965).

G. P. Lahti, "OPEX-II, A Radiation Shield Optimization Code," NASA TM X-1769 (March 1969).

11. CONTENTS OF CODE PACKAGE

Included are the referenced document and one (1.2MB) DOS diskette which contains source deck and sample problem input and output.

12. DATE OF ABSTRACT

December 1974; updated May 1975.

KEYWORDS: OPTIMIZATION; TWO-DIMENSIONS