Heliostats are arrays of mirrors that together focus sunlight on a small target. Such solar concentrators are typically used to drive heat exchangers in solar-thermal power plants. Sometimes, heliostats are also used for daylighting, and in very high temperature solar furnaces.
To be efficient, heliostat systems must maximize solar energy reflected by each mirror. So they track the sun's changing position intra-day, and over seasons. A bit of straightforward spherical geometry solves the tracking problem, but another, much harder problem emerges, literally from the shadows.
As the sun moves around, individual mirrors partially block each other, and cast shadows onto each other. This causes a drop in collection efficiency, and also makes it hard to conserve real estate, as we can't pack mirrors densely. The trick is to simultaneously avoid shadowing, and decrease real-estate usage.
Traditional optimization techniques optimize overall heliostat densities and placement patterns. Yet, we found further efficiencies, by choosing to optimize individual mirror positions. This is a more complex optimization problem, given the non-convex, non-smooth nature of the search space.