**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