## Asynchronously parallel optimization solver for finding multiple minima

## Abstract

This paper proposes and analyzes an asynchronously parallel optimization algorithm for finding multiple, high-quality minima of nonlinear optimization problems. Our multistart algorithm considers all previously evaluated points when determining where to start or continue a local optimization run. Theoretical results show that, under certain assumptions, the algorithm almost surely starts a finite number of local optimization runs and identifies, or has a single local optimization run converging to, every minimum. The algorithm is applicable to general optimization settings, but our numerical results focus on the case when derivatives are unavailable. In numerical tests, a PYTHON implementation of the algorithm is shown to yield good approximations of many minima (including a global minimum), and this ability scales well with additional resources. Our implementation’s time to solution is shown also to scale well even when the time to evaluate the function evaluation is highly variable.

- Authors:

- Argonne National Lab. (ANL), Lemont, IL (United States)

- Publication Date:

- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1466333

- Grant/Contract Number:
- AC02-06CH11357

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Mathematical Programming Computation

- Additional Journal Information:
- Journal Volume: 10; Journal Issue: 3; Journal ID: ISSN 1867-2949

- Publisher:
- Springer

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; Concurrent Function Evaluations; Derivative-Free Optimization; Global Optimization; Multistart; Parallel Optimization Algorithms

### Citation Formats

```
Larson, Jeffrey, and Wild, Stefan M. Asynchronously parallel optimization solver for finding multiple minima. United States: N. p., 2018.
Web. doi:10.1007/s12532-017-0131-4.
```

```
Larson, Jeffrey, & Wild, Stefan M. Asynchronously parallel optimization solver for finding multiple minima. United States. doi:10.1007/s12532-017-0131-4.
```

```
Larson, Jeffrey, and Wild, Stefan M. Fri .
"Asynchronously parallel optimization solver for finding multiple minima". United States. doi:10.1007/s12532-017-0131-4. https://www.osti.gov/servlets/purl/1466333.
```

```
@article{osti_1466333,
```

title = {Asynchronously parallel optimization solver for finding multiple minima},

author = {Larson, Jeffrey and Wild, Stefan M.},

abstractNote = {This paper proposes and analyzes an asynchronously parallel optimization algorithm for finding multiple, high-quality minima of nonlinear optimization problems. Our multistart algorithm considers all previously evaluated points when determining where to start or continue a local optimization run. Theoretical results show that, under certain assumptions, the algorithm almost surely starts a finite number of local optimization runs and identifies, or has a single local optimization run converging to, every minimum. The algorithm is applicable to general optimization settings, but our numerical results focus on the case when derivatives are unavailable. In numerical tests, a PYTHON implementation of the algorithm is shown to yield good approximations of many minima (including a global minimum), and this ability scales well with additional resources. Our implementation’s time to solution is shown also to scale well even when the time to evaluate the function evaluation is highly variable.},

doi = {10.1007/s12532-017-0131-4},

journal = {Mathematical Programming Computation},

number = 3,

volume = 10,

place = {United States},

year = {2018},

month = {2}

}