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Improving Performance of Heuristic Algorithms by Lebesgue Spectrum Filter
Mikio HASEGAWA
Publication
IEICE TRANSACTIONS on Communications
Vol.E99B
No.11
pp.22562262 Publication Date: 2016/11/01
Online ISSN: 17451345
DOI: 10.1587/transcom.2016NEI0002
Type of Manuscript: INVITED PAPER (Special Section on Deepening and Expanding of Information Network Science) Category: Keyword: chaos, combinatorial optimization, lebesgue spectrum filter, CDMA, traveling salesman problema, quadratic assignment problems,
Full Text: FreePDF(687.2KB)
Summary:
The previous researches on the chaotic CDMA have theoretically derived the chaotic sequences having the minimum asynchronous crosscorrelation. To minimize the asynchronous crosscorrelation, autocorrelation of each sequence have to be C(τ)≈C×r^{τ}, r=2+√3, dumped oscillation with increase of the lag τ. There are several methods to generate such sequences, using a chaotic map, using the Lebesgue spectrum filter (LSF) and so on. In this paper, such lowest crosscorrelation found in the chaotic CDMA researches is applied to solution search algorithms for combinatorial optimization problems. In combinatorial optimization, effectiveness of the chaotic search has already been clarified. First, an importance of chaos and autocorrelation with dumped oscillation for combinatorial optimization is shown. Next, in order to realize ideal solution search, the LSF is applied to the HopfieldTank neural network, the 2opt method and the 2exchange method. Effectiveness of the LSF is clarified even for the large problems for the traveling salesman problems and the quadratic assignment problems.

