# Heuristic approach to Satellite Range Scheduling with Bounds using Lagrangian Relaxation

## Abstract

Here, this paper focuses on scheduling antennas to track satellites using a novel heuristic method. The objectives pursued in developing a schedule are two-fold: (1) minimize the priority weighted number of time periods that satellites are not tracked; and (2) equalize the percent of time each satellite is uncovered. The heuristic method is a population-based local search tailored to the unique characteristics of this problem. In order to validate the performance of the heuristic, bounds are developed using Lagrangian relaxation. The heuristic method and the bounds are applied to several test problems. In all cases, the heuristic identifies a solution that is better than the upper bound and is generally quite close (but obviously larger) than the lower bound with about an order of magnitude reduction in computation time. Lastly, a comparison with CPLEX 12.7 is provided.

- Authors:

- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Cornell Univ., Ithaca, NY (United States)

- Publication Date:

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

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

- OSTI Identifier:
- 1429667

- Alternate Identifier(s):
- OSTI ID: 1478221

- Report Number(s):
- SAND-2017-11574J; SAND-2017-2553J

Journal ID: ISSN 1932-8184; 658158

- Grant/Contract Number:
- AC04-94AL85000; NA0003525

- Resource Type:
- Accepted Manuscript

- Journal Name:
- IEEE Systems Journal

- Additional Journal Information:
- Journal Volume: 12; Journal Issue: 4; Journal ID: ISSN 1932-8184

- Publisher:
- IEEE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; satellites; heuristic algorithms; decision support systems; optimal scheduling; integer linear programming

### Citation Formats

```
Brown, Nathanael J. K., Arguello, Bryan, Nozick, Linda Karen, and Xu, Ningxiong. Heuristic approach to Satellite Range Scheduling with Bounds using Lagrangian Relaxation. United States: N. p., 2018.
Web. doi:10.1109/jsyst.2018.2821094.
```

```
Brown, Nathanael J. K., Arguello, Bryan, Nozick, Linda Karen, & Xu, Ningxiong. Heuristic approach to Satellite Range Scheduling with Bounds using Lagrangian Relaxation. United States. doi:10.1109/jsyst.2018.2821094.
```

```
Brown, Nathanael J. K., Arguello, Bryan, Nozick, Linda Karen, and Xu, Ningxiong. Mon .
"Heuristic approach to Satellite Range Scheduling with Bounds using Lagrangian Relaxation". United States. doi:10.1109/jsyst.2018.2821094. https://www.osti.gov/servlets/purl/1429667.
```

```
@article{osti_1429667,
```

title = {Heuristic approach to Satellite Range Scheduling with Bounds using Lagrangian Relaxation},

author = {Brown, Nathanael J. K. and Arguello, Bryan and Nozick, Linda Karen and Xu, Ningxiong},

abstractNote = {Here, this paper focuses on scheduling antennas to track satellites using a novel heuristic method. The objectives pursued in developing a schedule are two-fold: (1) minimize the priority weighted number of time periods that satellites are not tracked; and (2) equalize the percent of time each satellite is uncovered. The heuristic method is a population-based local search tailored to the unique characteristics of this problem. In order to validate the performance of the heuristic, bounds are developed using Lagrangian relaxation. The heuristic method and the bounds are applied to several test problems. In all cases, the heuristic identifies a solution that is better than the upper bound and is generally quite close (but obviously larger) than the lower bound with about an order of magnitude reduction in computation time. Lastly, a comparison with CPLEX 12.7 is provided.},

doi = {10.1109/jsyst.2018.2821094},

journal = {IEEE Systems Journal},

number = 4,

volume = 12,

place = {United States},

year = {2018},

month = {4}

}

#### Figures / Tables:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*