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 average 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.

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

python satellite.py small.json neal

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

python satellite.py large.json hss

It will print out a set of satellite constellations.

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

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)

• The score_threshold - used to determine bad constellations - was assigned an arbitrarily picked number

• In the code, we add weights to each constellation such that we are favoring constellations with a high average coverage (aka high score). This is done with bqm.add_variable(frozenset(constellation), -score). Observe that we are using frozenset(constellation) as the variable rather than simply constellation as

  1. We need our variable to be a set (i.e. the order of the satellites in a constellation should not matter, {a, b, c} == {c, a, b}). In addition, add_variable(..) needs its variables to be immutable, hence, we are using frozenset rather than simply set.
  2. Since are there are more ways to form the set {a, b, c} than the set {a, a, a} -> {a}, the set {'a', 'b', 'c'} will accumulate a more negative score and thus be more likely to get selected. This is desired as we do not want duplicate items within our constellation. (Note: by "more ways to form the set", I am referring to how (b, c, a) and (a, c, b) are tuples that would map to the same set, where as (a, a, a) would be the only 3-tuple that would map to the set {a}.)

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

Released under the Apache License 2.0. See LICENSE file.