Energy Function

Next: Conditions of Constraint Up: Neural Network Scheduler for Previous: Corrected Magnitude

Energy Function

The scheduler adjusts the energy U of each element depending on the surrounding environment. The stronger energy means that you should observe the comet at the time much more. Finally, if is satisfied, it concludes to observe comet i at the time j and sets as 1.
The value of energy is limited as .
At first, initialize so that the better the condition is, the larger the energy of the time comes. Here means the corrected magnitude of comet i at time j, means the brightest corrected magnitude of comet i. First, define the square of comet i, , as follows:

If the condition of the comet doesn't change all through a night, it has a smallest square . Here, is the number of times. In that case, the system gives least weight to each time j to observe comet i at the time, because the comet can be observed anytime. On the other hand, if the square is large, the system gives much weight to good condition times because the comet can be observed at only those times. Considering those points, the initial energy is defined as follows:

The definition of the difference of at a step, , is as follows. Here means the corrected magnitude of comet i at the time j and is the brightest value among the corrected magnitude of comet i. At first, it sets as 0, then submits the following rules.

Increase

No time to observe the comet.
If no other comets should be observed at time j, increases the energy. The brighter the corrected magnitude is, which means the condition is better, the more the energy increases. When a comet has already occupy the time, it does not increase the energy. But if you prefer to brighter comets and the corrected magnitude of comet i is brighter, the system increases the energy.

Decrease

More than 2 comets to observe at the time.
The more observable time blocks the comet has, the more the energy decreases. If you prefer to brighter comets and one of the comets which should be observed at the same time is brighter than comet i, decrease 2 moreover.

More than 2 time blocks to observe the comet.
The fainter the corrected magnitude is, which means the condition is worse, the more the energy decreases.

Random
To avoid falling into a local minimum, the system uses random. In 10% case, it adds 1 to , in other 10% case, it subtracts 1 from .

When is calculated,

and goes to next step.
The energy adjustment of each element is not a parallel process. The scheduler changes each one by one from to . Therefore, when is adjusted, all the other elements have been adjusted already and is calculated with the new and .