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satellite-placement

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Group satellites into constellations such that their average observation coverage is maximized

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# Satellite Placement

Suppose you have a set of `N` satellites and `k` targets on Earth that you want
to observe. Each of your satellites has varying capabilities for Earth
observation; in particular, the amount of ground that they can observe for a set
amount of time is different. Since there are `k` targets, you would like to have
`k` constellations to monitor said targets. How do you group your satellites
into `k` constellations such that the coverage of each constellation is
maximized? This is the question that we will be addressing in this demo!

There are two versions available. The first version has `N=12` and `k=4`.
The larger version has `N=39` and `k=13`.

Note: in this demo we are assuming that `N` is a multiple of `k`.

## Usage

To run the smaller demo, using D-Wave's Simulated Annealing package (Neal),
run the command:

```bash
python satellite.py small.json sa
```

To run the larger demo, using D-Wave's Hybrid Solver Service (HSS),
run the command:

```bash
python satellite.py large.json hss
```

It will print out a set of satellite constellations and create an image to
visualize the scores for each constellation, as shown below. Satellites closer
to the center (grey star) have a higher score.

![Example Output](https://raw.githubusercontent.com/dwave-examples/satellite-placement/master/readme_imgs/constellations.png)

Note: the larger demo is memory-intensive. It may use more than 10 GB of RAM.

## Code Overview

The idea is to consider all possible combinations of satellites, eliminate
constellations with particularly low coverage, and encourage the following type
of solutions:

* Constellations that have better coverage
* Satellites to only join *one* constellation
* A specific number of constellations in our final solution (i.e. encourage the
  solution to have `k` constellations)

## Code Specifics

We add weights to each constellation such that we are favoring constellations
with a high coverage (aka high score). This is done with
`bqm.add_variable(frozenset(constellation), -score)`.  Note that `frozenset` is
used to convey the concept that each variable in the model is a set of
individual satellites, and the ordering does not matter.  Incidentally, the code
that defines the variables iterates over only the combinations (not the
permutations), so defining the variables as tuples would work just as well
(however, `set` cannot be used because the variables must be immutable).

## References

G. Bass, C. Tomlin, V. Kumar, P. Rihaczek, J. Dulny III. Heterogeneous Quantum
Computing for Satellite Constellation Optimization: Solving the Weighted
K-Clique Problem. 2018 Quantum Sci. Technol. 3 024010.
https://arxiv.org/abs/1709.05381

## License

Released under the Apache License 2.0. See [LICENSE](./LICENSE) file.

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