List-Based Optimisers: Experiments and Open Questions

List-Based Optimisers: Experiments and Open Questions

Maurice Clerc (Independent Consultant, Groisy, France)
Copyright: © 2013 |Pages: 16
DOI: 10.4018/ijsir.2013100102
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For any iterative stochastic optimisation algorithm, it is possible to replace the Random Number Generator (RNG) by a predefined short list of numbers, used cyclically. The author presents here some experiments to check this approach. The results show that it may indeed be interesting, for the same list can be used for variants of a given problem, and even for different problems. However, there are still some important open questions, in particular about the possible methods for building the lists, which are, for the moment, quite empirical.
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List-Based Optimisers

Most stochastic optimisers make use of a coded random number generator (RNG), like KISS ( Marsaglia & Zaman, 1993 ), or Mersenne-Twister ( Matsumoto & Nishimura, 1998 ), or those that are embedded in a language like C. As these are not based on a hardware system, they are in fact deterministic, at least if we always use the same seed. They generate a long list of pseudo-random numbers (typically in ijsir.2013100102.m01), whose length is ideally far bigger than what is needed to solve a problem, even if the algorithm is executed several times. In such a case all runs are different, in the hope that it improves the probability of finding a good solution.

So, we can, in fact, assume that we have a predefined list of numbers in ijsir.2013100102.m02, say ijsir.2013100102.m03. During the optimisation process, whenever we need a “random” number, we pick it up sequentially and cyclically in ijsir.2013100102.m04, i.e., for the ijsir.2013100102.m05-th random number we pick ijsir.2013100102.m06. In order to avoid any confusion with true random numbers, from now on we will call these l-random numbers. The idea here is to reduce the length of the list ijsir.2013100102.m07 as much as possible, and simultaneously, to improve the performance. So, we will speak of a List-Based Optimiser (LBO) only when L is relatively small (typically at most one hundred l-random numbers for a 30D problem).

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