Improving Performance of Heuristic Algorithms by Lebesgue Spectrum Filter

Abstract

SUMMARYThe previous researches on the chaotic CDMA have theoretically derived the chaotic sequences having the minimum asynchronous cross-correlation. To minimize the asynchronous cross-correlation, 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 cross-correlation 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 Hopfield-Tank neural network, the 2-opt method and the 2-exchange method. Effectiveness of the LSF is clarified even for the large problems for the traveling salesman problems and the quadratic assignment problems.

Analysis on Effectiveness of Surrogate Data‐Based Laser Chaos Decision Maker

“…Indeed, the effectiveness of chaotic time series with negative autocorrelation has been demonstrated in previous studies, for example, on code division multiple access (CDMA) in wireless communications by Kohda and Fujisaki [11] and Hasegawa [12]. It has been theoretically shown that the negative autocorrelation in each chaotic spreading sequence minimizes cross-correlation among those sequences.…”

Theory of Acceleration of Decision‐Making by Correlated Time Sequences

“…In addition, ref. [19] clarifies that the negative autocorrelation that minimizes cross-correlation accelerates the performance of solution search algorithms for combinatorial optimization problems. An FIR filter to generate the optimal chaotic CDMA sequence was also proposed based on the negative autocorrelation analysis [20].…”

“…In the literature, the usefulness of negative autocorrelation in time series has been theoretically analyzed regarding code division multiple access (CDMA) [17][18][19]. To achieve high performance in CDMA, the cross-correlation between the spreading sequences must be small.…”