The.Algorithm.Design.Manual.Springer-Verlag.1998

War Story: Annealing Arrays
optimal, it couldn't really tell how good our solution was. We tweaked and tweaked until our program
stopped improving.
Our final solution refined the initial array by applying the following random moves:
● swap - swap a prefix/suffix on the array with one that isn't.
● add - add a random prefix/suffix to the array.
● delete - delete a random prefix/suffix from the array.
● useful add - add the prefix/suffix with the highest usefulness to the array.
● useful delete - delete the prefix/suffix with the lowest usefulness from the array.
● string add - randomly select a string not on the array, and add the most useful prefix and/or suffix
that covers this string (additional preference is given to a prefix/suffix whose corresponding
suffix/prefix is already on the array).
A standard annealing schedule was used, with an exponentially decreasing temperature (dependent upon
the problem size) and a temperature-dependent Boltzmann criterion for accepting states that have higher
costs. Our final cost function was defined as
where max is the size of the maximum chip dimension, min is the size of the minimum chip dimension, ,
and is the number of strings in S currently on the chip.
Careful analysis of successful moves over the course of the annealing process suggested a second phase
of annealing to speed convergence. Once the temperature reaches a predetermined cutoff point, the
temperature schedule was changed to force the temperature to decrease more rapidly, and the probability
distribution for choosing moves was altered to include only swap, add, and delete, with preference given
to swap moves. This modification sped up late convergence, which had been slower than it was in the
early stages of the annealing process.
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