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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 tex2html_wrap_inline330 is satisfied, it concludes to observe comet i at the time j and sets tex2html_wrap_inline336 as 1.

The value of energy is limited as tex2html_wrap304 .

At first, initialize tex2html_wrap_inline340 so that the better the condition is, the larger the energy of the time comes. Here tex2html_wrap_inline342 means the corrected magnitude of comet i at time j, tex2html_wrap_inline348 means the brightest corrected magnitude of comet i. First, define the square of comet i, tex2html_wrap_inline354 , as follows:

displaymath314

If the condition of the comet doesn't change all through a night, it has a smallest square tex2html_wrap_inline356 . Here, tex2html_wrap_inline358 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:

displaymath315

The definition of the difference of tex2html_wrap_inline364 at a step, tex2html_wrap_inline366 , is as follows. Here tex2html_wrap_inline368 means the corrected magnitude of comet i at the time j and tex2html_wrap_inline374 is the brightest value among the corrected magnitude of comet i. At first, it sets tex2html_wrap_inline378 as 0, then submits the following rules.

  • Increase
    • No time to observe the comet. tex2html_wrap305
      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.

      displaymath316

  • Decrease
    • More than 2 comets to observe at the time. tex2html_wrap306
      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.

      displaymath317

    • More than 2 time blocks to observe the comet. tex2html_wrap307
      The fainter the corrected magnitude is, which means the condition is worse, the more the energy decreases.

      displaymath318

  • Random
    To avoid falling into a local minimum, the system uses random. In 10% case, it adds 1 to tex2html_wrap_inline390 , in other 10% case, it subtracts 1 from tex2html_wrap_inline392 .

When tex2html_wrap308 is calculated,

displaymath319

displaymath320

and goes to next step.

The energy adjustment of each element is not a parallel process. The scheduler changes each tex2html_wrap_inline394 one by one from tex2html_wrap_inline396 to tex2html_wrap_inline398 . Therefore, when tex2html_wrap_inline400 is adjusted, all the other elements have been adjusted already and tex2html_wrap_inline402 is calculated with the new tex2html_wrap_inline404 and tex2html_wrap_inline406 .

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

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Copyright(C) Seiichi Yoshida (comet@aerith.net). All rights reserved.
Tue Apr 15 03:17:05 JST 1997