Mitchell, T. J. (2010) An exploration of evolutionary computation ...

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List of figures 1.1: Simple FM Model ………………………………………………………………………………………... 4 1.2: FM spectrum plots with increasing modulation index, adapted from Chowning (1973) ………………... 5 1.3: Bessel functions of the first kind and order n ……………………………………………………………. 6 2.1: The evolutionary model ………………………………………………………………………………….. 12 2.2: Canonical GA pseudocode .………………………………………………………………………………. 15 2.3: Multi-membered ES pseudocode ..……………………………………………………………………….. 18 2.4: Two-dimensional probability isolines of (a) isotropic, (b) ellipsoidal and (c) rotated ellipsoidal mutation ………………………………………………………………………………………………….. 3.1: Island model ……………………………………………………………………………………………… 40 3.2: Meta-ES ………………………………………………………………………………………………….. 42 3.3: Fine-grained architecture ………………………………………………………………………………… 43 3.4: Niche identification technique …………………………………………………………………………… 46 3.5: Cooperative coevolution architecture ……………………………………………………………………. 49 4.1: FCES pseudocode …….………………………………………………………………………………….. 52 4.2: Pseudocode for the fuzzy centroid optimisation procedure ….…………………………………………... 54 4.3: Hard cluster centroid optimisation procedure ……………………………………………………………. 58 4.4: Multimodal landscape and contour plot ………………………………………………………………….. 66 4.5: Results from experiments with the multimodal function .….…………………………………………….. 67 4.6: Langermans Function with contour plot …………………………………………………………………. 69 4.7: Results from experiments with Langermann‘s function …………………………………………………. 70 4.8: Maximum of two quadratics function with contour plot ………………………………………………… 72 4.9: Results from experiments with Maximum of Two Quadratics function ………………………………… 73 4.10: Multimodal function convergence dynamics …………………………………………………………….. 76 4.11: Langermann's function convergence dynamics ………………………………………………………….. 76 4.12: Maximum of Two Quadratics function convergence dynamics …………………………………………. 77 4.13: Himmelblau's function landscape and contour plot ……………………………………………………… 79 4.14: Mean and 95% confidence intervals for Optima and MPR results on Himmelblau's function ………….. 80 4.15: Mean and 95% confidence intervals for Optima and MPR results on the multimodal function ………… 82 4.16: Waves function landscape and contour plot ……………………………………………………………... 83 4.17: Mean and 95% confidence intervals for Optima and MPR results on the waves function ……………… 83 4.18: Two-dimentional sine function landscape and contour plot ……………………………………………... 85 4.19: Mean and 95% confidence intervals for Optima and MPR results on the n-dimensional sine function ………………………………………………………………………………………………….. 4.20: Mean and 95% confidence intervals for Optima and Best solution results on the multimodal function ………………………………………………………………………………………………….. 5.1: Two population NCCEA ………………………………………………………………………………… 99 5.2: NCCEA showing different linkage arrangement ………………………………………………………… 101 5.3: NCCEA with common linkage …………………………………………………………………………... 102 5.4: NCCEA pseudocode …..…………………………………………………………………………………. 103 5.5: Mean and 95% confidence intervals for Total results on Himmelblau‘s function ……………………….. 107 5.6: Best response curves for the Himmelblau function ……………………………………………………… 108 5.7: Maximum fitness curve for x dimension of Himmelblau‘s function ......………………………………… 110 5.8: Mean and 95% confidence intervals for Total results on Himmelblau‘s function ………………………. 111 5.9: Mean and 95% confidence intervals for Optima results on the multimodal function …………………… 113 22 86 87 viii
5.10: Mean and 95% confidence intervals for Sum results on the multimodal function ………………………. 113 5.11: Contour plot of the multimodal function indicating final CCCES solutions …………………………….. 114 5.12: Mean and 95% confidence intervals for Optima and Sum results on the multimodal function ………… 115 5.13: Convergence trajectories for all algorithms when applied to the MTQ function with discrete recombination ……………………………………………………………………………………………. 6.1: Control to synthesis mapping via intermediate representation …………………………………………... 123 6.2: Parallel Simple FM model ……………………………………………………………………………….. 126 6.3: Simple FM landscapes with contrived target at fc = 1760Hz, fm = 1760Hz, I = 4.0 and A = 1.0 produced by the Zero Crossing fitness function (a), and Centroid function (b) …………………………. 6.4: Relative spectral error landscape with contrived target at fc = 1760Hz, fm = 1760Hz, I = 4.0 and A = 1.0 ……………………………………………………………………………………………………. 6.5: Frequency spectra of three FM tones …………………………………………………………………….. 136 6.6: Equivalent windowed relative squared error landscape with contrived target at fc = 1760Hz, fm = 1760Hz, I = 4.0 and A = 1. 0 …………………………………………………………………………….. 7.1: (a) single, (b) double and (c) triple parallel simple FM arrangements …………………………………... 142 7.2: (a) single, (b) double and (c) triple parallel time-varying simple FM arrangements …………………….. 143 7.3: adsr envelope generator ………………………………………………………………………………….. 144 7.4: Evolutionary sound matching model …………………………………………………………………….. 146 7.5: Mean and 95% confidence intervals for Average and Remaining error results when matching Single Simple FM contrived tones ………………………………………………………………………………. 7.6: Convergence plot for the CCCES and CES ……………………………………………………………… 157 7.7: Mean and 95% confidence intervals for Average and Remaining error results when matching Double Simple FM contrived tones ………………………………………………………………………............. 7.8: Mean and 95% confidence intervals for Average and Remaining error results when matching Triple Simple FM contrived tones ………………………………………………………………………………. 7.9: Static triple FM target (top) and corresponding CES match (bottom) …………………………………... 161 7.10: Static triple FM target and corresponding CES match with log amplitude scale ………………………... 161 7.11: Unfiltered additive synthesis tone ………………………………………………………………………... 163 7.12: Additive-subtractive target tone synthesis model ………………………………………………………... 164 7.13: Additive-subtractive target tone spectra …………………………………………………………………. 165 7.14: Mean and 95% confidence intervals for error when matching additive-subtractive target tones ............... 166 7.15: Acoustic target spectra …………………………………………………………………………………… 168 7.16: Mean and 95% confidence intervals for error when matching acoustic target tones ……………............. 169 7.17: Muted trumpet tone (top), and corresponding match (bottom) ………………………………………….. 170 7.18: Muted trumpet tone and corresponding match with log amplitude ……………………………………… 170 7.19: Mean and 95% confidence intervals for Average and Remaining error results when matching time- varying single simple FM contrived sounds ……………………………………………………………... 7.20: Mean and 95% confidence intervals for Average and Remaining error results when matching time- varying double simple FM contrived sounds …………………………………………………………….. 7.21: Mean and 95% confidence intervals for Average and Remaining error results when matching time- varying triple simple FM contrived sounds ……………………………………………………………… 7.22: Contrived time-varying triple simple FM target and CCES evolved match ……………………………... 178 7.23: Mean and 95% confidence intervals for error when matching acoustic time-varying sounds …………... 180 7.24: Mean and 95% confidence intervals for error when matching an acoustic time-varying oboe sound …... 182 7.25: Oboe target sound and time-varying triple simple FM match evolved by CCCES ……………………… 183 7.26: 3D- Spectrogram of oboe target sound and CCCES evolved match …………………………………….. 184 119 134 136 138 154 158 160 173 175 176 ix
Page 1 and 2: Mitchell, T. J. (2010) An explorati
Page 3 and 4: Acknowledgments With so many people
Page 5 and 6: Abstract With the ever-increasing c
Page 7 and 8: 4 A Clustering-Based Niching Evolut
Page 9: 7.7.1.3 Contrived Matching with Tim
Page 13 and 14: List of Tables 4.1: MTQ function pa
Page 15 and 16: To experimental musicians lacking t
Page 17 and 18: 1.1.2 Frequency Modulation Audio Sy
Page 19 and 20: The Bessel functions for are shown
Page 21 and 22: 1.3 Contributions In satisfying the
Page 23 and 24: Chapter 2 Background: Evolutionary
Page 25 and 26: Figure 2.1: The evolutionary model
Page 27 and 28: 2.3 Canonical Evolutionary Algorith
Page 29 and 30: it position (locus) may be absent o
Page 31 and 32: t = 0; initialise P μ(t); loop beg
Page 33 and 34: When The benefit of (intermediate)
Page 35 and 36: sphere, or hypersphere, dependent u
Page 37 and 38: the rule may only be applied when a
Page 39 and 40: Firstly, there is no guarantee that
Page 41 and 42: As the research field of evolutiona
Page 43 and 44: five of this thesis are based. The
Page 45 and 46: sparsely throughout the search spac
Page 47 and 48: Selection Pressure - The rate at wh
Page 49 and 50: enable the formation of species, it
Page 51 and 52: 3.4.1.2 Restricted Tournament selec
Page 53 and 54: over the landscape, and the dilutin
Page 55 and 56: Species 1 Genus Figure 3.2: Meta-ES
Page 57 and 58: diffusion model, on the other hand,
Page 59 and 60: fitness Niche Centre Figure 3.4: Ni
Page 61 and 62:
also applied within each subpopulat
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outperformed by a simple GA. A seco
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4.1 The Fuzzy Clustering Evolution
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membership to each cluster. In prac
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Fuzzy Intermediate Recombination -
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Parents are subsequently merged and
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4.2.3 New Recombination Operators T
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Global - the ability of the algorit
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period in which all sub-populations
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4.3.2.1 Experiments on the Multimod
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Discussion The canonical ES variant
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Results (20+140) / CES / discrete /
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function. The parameters for the fi
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Discussion The results acquired fro
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these experiments as the quantity o
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Performance Criteria In assessing t
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discrete recombination is employed;
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Figure 4.15: Mean and 95% confidenc
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Discussion These results corroborat
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Figure 4.19: Mean and 95% confidenc
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partitioned into five clusters, the
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However, the question arises as to
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The most consistent finding of Wieg
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Wiegand demonstrated that a pseudo-
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accurate approximation of an interv
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cooperating subpopulation into mult
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5.3.1.1 Collaboration One notable d
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If one representative is selected f
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The CCCES algorithm begins by initi
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For the subsequent experiments, the
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Discussion The results shown in tab
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Figure 5.7: Maximum-fitness curve f
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dimensional multimodal function wit
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From the results shown in Table 5.3
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that, as the dimensionality of the
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only a moderate increase in fitness
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It is interesting that the results
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Niching - it is desirable that mult
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6.2 Synthesiser Choice Since the fo
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Modulating Oscillators Carrier Osci
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6.4 Sound Synthesis Applications of
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with results again presented using
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employed by commercial synthesis ma
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While these metrics are able to suc
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Unlike the metrics considered in se
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Figure 6.6 provides a plot of the l
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6.5 Summary of this Chapter In this
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constant spectral form as static to
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Figure 7.2a represents the most fun
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7.3 Evolutionary Matching Synthesis
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If the frame size is assigned a pow
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an exhaustive search yields no bett
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CCES, in which each dimension of th
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7.6.1.1 Contrived Matching with Sin
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elative spectral error ranged from
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the second, where the parameters fo
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Discussion Figure 7.8: Mean and 95%
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and relative spectrum error is exam
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The flat spectrum produced by the a
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Matching Model Single Simple FM Dou
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Acoustic Target Matching Results Fi
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Figure 7.17: Muted trumpet tone (to
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Performance Criteria As before, res
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indicated the discreet recombinatio
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7.7.1.3 Contrived Matching with Tim
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(a): Target sound time waveform (b)
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Matching Model Single Simple FM Dou
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Algorithmic Parameters Oboe Target
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The frequency spectrograms are plot
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Frequency (Hz) Frequency (Hz) Frequ
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Amplitude (dB) Amplitude (dB) Figur
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Chapter 8 Listening Tests Despite t
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Amplitude (dB) Amplitude (dB) Ampli
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Listening Test One - Similarity Ran
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frequency harmonics well but the mi
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Listening Test Two - General Sound
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Figure 8.6c: Listening test two ins
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The FM sound produced by the matchi
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Frequency (Hz) Amplitude four descr
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Frequency (Hz) Amplitude (a) Violin
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capabilities of the triple simple F
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Chapter 9 Conclusions and Further W
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environments. It was shown that the
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Also included in chapter seven, was
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matching algorithm to probe the und
Page 231 and 232:
The author hopes that this work goe
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Bäck, T., and Schutz, M. (1996) In
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Chowning, J. M. (1973) The synthesi
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Eshelman, L. J. (1990) The CHC Adap
Page 239 and 240:
Hanagandi, V. and Nikolaou, M. (199
Page 241 and 242:
Huband, S., Hingston, P., While L.
Page 243 and 244:
Lim, S. M. and B. T. G. Tan. (1999)
Page 245 and 246:
Miller, B. L., and Goldberg, D. E.
Page 247 and 248:
Popovici, E. and De Jong, K. (2005)
Page 249 and 250:
Rudolph, G (1991) Global Optimizati
Page 251 and 252:
Tan, B. T. G. and S. M. Lim, (1996)
Page 253 and 254:
Wiegand, R. P., and Sarma, J. (2004
Page 255:
Appendix 1 - Listening Test 1 - Res
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