# Next-generation Algorithms for Assessing Infrastructure Vulnerability and Optimizing System Resilience

## Abstract

This report summarizes the work performed under the project project Next-Generation Algo- rithms for Assessing Infrastructure Vulnerability and Optimizing System Resilience. The goal of the project was to improve mathematical programming-based optimization technology for in- frastructure protection. In general, the owner of a network wishes to design a network a network that can perform well when certain transportation channels are inhibited (e.g. destroyed) by an adversary. These are typically bi-level problems where the owner designs a system, an adversary optimally attacks it, and then the owner can recover by optimally using the remaining network. This project funded three years of Deon Burchett's graduate research. Deon's graduate advisor, Professor Jean-Philippe Richard, and his Sandia advisors, Richard Chen and Cynthia Phillips, supported Deon on other funds or volunteer time. This report is, therefore. essentially a replication of the Ph.D. dissertation it funded [12] in a format required for project documentation. The thesis had some general polyhedral research. This is the study of the structure of the feasi- ble region of mathematical programs, such as integer programs. For example, an integer program optimizes a linear objective function subject to linear constraints, and (nonlinear) integrality con- straints on the variables. The feasible region withoutmore »

- Authors:

- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1183056

- Report Number(s):
- SAND2015-4059

584043

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Burchett, Deon L., Chen, Richard Li-Yang, Phillips, Cynthia A., and Richard, Jean-Philippe.
```*Next-generation Algorithms for Assessing Infrastructure Vulnerability and Optimizing System Resilience*. United States: N. p., 2015.
Web. doi:10.2172/1183056.

```
Burchett, Deon L., Chen, Richard Li-Yang, Phillips, Cynthia A., & Richard, Jean-Philippe.
```*Next-generation Algorithms for Assessing Infrastructure Vulnerability and Optimizing System Resilience*. United States. doi:10.2172/1183056.

```
Burchett, Deon L., Chen, Richard Li-Yang, Phillips, Cynthia A., and Richard, Jean-Philippe. Fri .
"Next-generation Algorithms for Assessing Infrastructure Vulnerability and Optimizing System Resilience". United States. doi:10.2172/1183056. https://www.osti.gov/servlets/purl/1183056.
```

```
@article{osti_1183056,
```

title = {Next-generation Algorithms for Assessing Infrastructure Vulnerability and Optimizing System Resilience},

author = {Burchett, Deon L. and Chen, Richard Li-Yang and Phillips, Cynthia A. and Richard, Jean-Philippe},

abstractNote = {This report summarizes the work performed under the project project Next-Generation Algo- rithms for Assessing Infrastructure Vulnerability and Optimizing System Resilience. The goal of the project was to improve mathematical programming-based optimization technology for in- frastructure protection. In general, the owner of a network wishes to design a network a network that can perform well when certain transportation channels are inhibited (e.g. destroyed) by an adversary. These are typically bi-level problems where the owner designs a system, an adversary optimally attacks it, and then the owner can recover by optimally using the remaining network. This project funded three years of Deon Burchett's graduate research. Deon's graduate advisor, Professor Jean-Philippe Richard, and his Sandia advisors, Richard Chen and Cynthia Phillips, supported Deon on other funds or volunteer time. This report is, therefore. essentially a replication of the Ph.D. dissertation it funded [12] in a format required for project documentation. The thesis had some general polyhedral research. This is the study of the structure of the feasi- ble region of mathematical programs, such as integer programs. For example, an integer program optimizes a linear objective function subject to linear constraints, and (nonlinear) integrality con- straints on the variables. The feasible region without the integrality constraints is a convex polygon. Careful study of additional valid constraints can significantly improve computational performance. Here is the abstract from the dissertation: We perform a polyhedral study of a multi-commodity generalization of variable upper bound flow models. In particular, we establish some relations between facets of single- and multi- commodity models. We then introduce a new family of inequalities, which generalizes traditional flow cover inequalities to the multi-commodity context. We present encouraging numerical results. We also consider the directed edge-failure resilient network design problem (DRNDP). This problem entails the design of a directed multi-commodity flow network that is capable of fulfilling a specified percentage of demands in the event that any G arcs are destroyed, where G is a constant parameter. We present a formulation of DRNDP and solve it in a branch-column-cut framework. We present computational results.},

doi = {10.2172/1183056},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2015},

month = {5}

}