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

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List of Publications Some of the work in this thesis has also appeared in the following publications: Mitchell, T. J., and Pipe, A. G. (2005) Convergence Synthesis of Dynamic Frequency Modulation Tones Using an Evolution Strategy. Applications on Evolutionary Computing: EvoWorkshops. 533-538. Mitchell, T. J. and Sullivan, C. W. (2005) Frequency Modulation Tone Matching Using a Fuzzy Clustering Evolution Strategy. In: Proceedings of the 118th Convention of the Audio Engineering Society. Barcelona. Mitchell, T. and Pipe, A. (2006) A Comparison of Evolution Strategy-based Methods for Frequency Modulated Musical Tone Timbre Matching. In: Proceedings of the 7th International Conference in Adaptive Computing in Design and Manufacture. Bristol. pp. 167-175. Mitchel, T.J. and Creasey, D.P. (2007) Evolutionary Sound Matching: A Test Methodology and Comparative Study. Proceedings of The Sixth International Conference on Machine Learning and Applications (ICMLA'07). ii
Abstract With the ever-increasing complexity of sound synthesisers, there is a growing demand for automated parameter estimation and sound space navigation techniques. This thesis explores the potential for evolutionary computation to automatically map known sound qualities onto the parameters of frequency modulation synthesis. Within this exploration are original contributions in the domain of synthesis parameter estimation and, within the developed system, evolutionary computation, in the form of the evolutionary algorithms that drive the underlying optimisation process. Based upon the requirement for the parameter estimation system to deliver multiple search space solutions, existing evolutionary algorithmic architectures are augmented to enable niching, while maintaining the strengths of the original algorithms. Two novel evolutionary algorithms are proposed in which cluster analysis is used to identify and maintain species within the evolving populations. A conventional evolution strategy and cooperative coevolution strategy are defined, with cluster-orientated operators that enable the simultaneous optimisation of multiple search space solutions at distinct optima. A test methodology is developed that enables components of the synthesis matching problem to be identified and isolated, enabling the performance of different optimisation techniques to be compared quantitatively. A system is consequently developed that evolves sound matches using conventional frequency modulation synthesis models, and the effectiveness of different evolutionary algorithms is assessed and compared in application to both static and time- varying sound matching problems. Performance of the system is then evaluated by interview with expert listeners. The thesis is closed with a reflection on the algorithms and systems which have been developed, discussing possibilities for the future of automated synthesis parameter estimation techniques, and how they might be employed. iii
Page 1 and 2: Mitchell, T. J. (2010) An explorati
Page 3: Acknowledgments With so many people
Page 7 and 8: 4 A Clustering-Based Niching Evolut
Page 9 and 10: 7.7.1.3 Contrived Matching with Tim
Page 11 and 12: 5.10: Mean and 95% confidence inter
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
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Species 1 Genus Figure 3.2: Meta-ES
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diffusion model, on the other hand,
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fitness Niche Centre Figure 3.4: Ni
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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
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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
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Hanagandi, V. and Nikolaou, M. (199
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Huband, S., Hingston, P., While L.
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Lim, S. M. and B. T. G. Tan. (1999)
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Miller, B. L., and Goldberg, D. E.
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Popovici, E. and De Jong, K. (2005)
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Rudolph, G (1991) Global Optimizati
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Tan, B. T. G. and S. M. Lim, (1996)
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Wiegand, R. P., and Sarma, J. (2004
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Appendix 1 - Listening Test 1 - Res
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