## Using a derivative-free optimization method for multiple solutions of inverse transport problems

## Abstract

Identifying unknown components of an object that emits radiation is an important problem for national and global security. Radiation signatures measured from an object of interest can be used to infer object parameter values that are not known. This problem is called an inverse transport problem. An inverse transport problem may have multiple solutions and the most widely used approach for its solution is an iterative optimization method. This paper proposes a stochastic derivative-free global optimization algorithm to find multiple solutions of inverse transport problems. The algorithm is an extension of a multilevel single linkage (MLSL) method where a mesh adaptive direct search (MADS) algorithm is incorporated into the local phase. Furthermore, numerical test cases using uncollided fluxes of discrete gamma-ray lines are presented to show the performance of this new algorithm.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1247138

- Report Number(s):
- LA-UR-14-29126

Journal ID: ISSN 1389-4420; PII: 9306

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Optimization and Engineering

- Additional Journal Information:
- Journal Volume: 17; Journal Issue: 1; Journal ID: ISSN 1389-4420

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; inverse transport problem; derivative-free optimization; stochastic global optimization; multilevel single linkage; mesh adaptive direct search

### Citation Formats

```
Armstrong, Jerawan C., and Favorite, Jeffrey A. Using a derivative-free optimization method for multiple solutions of inverse transport problems. United States: N. p., 2016.
Web. doi:10.1007/s11081-015-9306-x.
```

```
Armstrong, Jerawan C., & Favorite, Jeffrey A. Using a derivative-free optimization method for multiple solutions of inverse transport problems. United States. doi:10.1007/s11081-015-9306-x.
```

```
Armstrong, Jerawan C., and Favorite, Jeffrey A. Thu .
"Using a derivative-free optimization method for multiple solutions of inverse transport problems". United States. doi:10.1007/s11081-015-9306-x. https://www.osti.gov/servlets/purl/1247138.
```

```
@article{osti_1247138,
```

title = {Using a derivative-free optimization method for multiple solutions of inverse transport problems},

author = {Armstrong, Jerawan C. and Favorite, Jeffrey A.},

abstractNote = {Identifying unknown components of an object that emits radiation is an important problem for national and global security. Radiation signatures measured from an object of interest can be used to infer object parameter values that are not known. This problem is called an inverse transport problem. An inverse transport problem may have multiple solutions and the most widely used approach for its solution is an iterative optimization method. This paper proposes a stochastic derivative-free global optimization algorithm to find multiple solutions of inverse transport problems. The algorithm is an extension of a multilevel single linkage (MLSL) method where a mesh adaptive direct search (MADS) algorithm is incorporated into the local phase. Furthermore, numerical test cases using uncollided fluxes of discrete gamma-ray lines are presented to show the performance of this new algorithm.},

doi = {10.1007/s11081-015-9306-x},

journal = {Optimization and Engineering},

number = 1,

volume = 17,

place = {United States},

year = {2016},

month = {1}

}