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Design of sound phase diffusers by means of multiobjective optimization approach using ev-MOGA evolutionary algorithm

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Abstract

In this paper a new approach to design sound phase diffusers is presented. The acoustic properties of such diffusers are usually increased by using single objective optimization methods. Here we propose the use of a multiobjective (MO) approach to design them in order to take into account several conflicting characteristic simultaneously. Three different MO problems are posed to consider various scenarios where fundamentally the objective is to maximize the normalized diffusion coefficient (following the corresponding Audio Engineering Society standard) for the so-called medium frequencies. This single objective could be divided into other several objectives to adjust performances to designer preferences. A multi-objective evolutionary algorithm (called ev-MOGA) is used to characterize the Pareto front in a smart way. ev-MOGA is modified, by using integer codification and tuning some of its genetic operators, to adapt it to the new requirements. Special interest is posed in selecting the diffusers codification properly to eliminate duplicities that would produce a multimodal problem. Precision in the manufacturing process is taking into account in the diffuser codification causing, that the number of different diffusers are quantified. Robust considerations related with the precision manufacturing process are considered in the decision making process. Finally, an optimal diffuser is selected considering designer preferences.

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Notes

  1. We do not use an aggregate objective function, to merge the different objectives. So we will avoid to weight the different objectives a priori.

  2. Available for MatlabⒸ at http://www.mathworks.com/matlabcentral/fileexchange/31080-ev-moga-multiobjective-evolutionary-algorithm.

  3. Maximizing an objective can be transformed in a minimization problem, since maxJ i = − min(−J i ).

  4. Notice that \(\mathbf {\Theta }_{P}^{\ast }\) is not unique.

  5. This codification is equivalent to characterize the diffusers as a vector of 6 increments. We do not codify the diffusers with increments since it is more difficult to manage the searching space and to implement genetic operators in the MOEA.

  6. \(\boldsymbol {\Theta }_{t}(a,L)\simeq \frac {\boldsymbol {\Theta }(a,L)}{2}\) when a>10 for L = 7.

  7. Based in the analyses of the Pareto front of Fig. 6a.

  8. The subsets corresponding to the extreme of the Pareto front (represented by blue ’x’ in Fig. 9a) are not represented in Fig. 9 since they are less interesting for the decision making.

  9. The subsets corresponding to the extreme of the Pareto front (represented by blue ’x’ in Fig. 12a) are not represented.

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Acknowledgments

Partially supported by EVO-CONTROL project (ref. PROMETEO/2012/028, Generalitat Valenciana - Spain) and MEC (Spanish goverment) under grant N∘ MTM2012-36740-C02-02.

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Authors and Affiliations

  1. Instituto Universitario de Automática e Informática Industrial, ai2, Valencia, Spain

    J. M. Herrero & X. Blasco

  2. Centro de Tecnologías Físicas: Acústica, Materiales y Astrofísica, Valencia, Spain

    J. V. Sánchez-Pérez

  3. Instituto para la Gestión Integrada de las zonas Costeras, Valencia, Spain

    J. Redondo

  4. Universitat Politècnica de València, Camino de Vera s/n, 46022, Valencia, Spain

    J. M. Herrero, X. Blasco, J. V. Sánchez-Pérez & J. Redondo

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  1. J. M. Herrero
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  2. X. Blasco
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Correspondence to J. M. Herrero.

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Herrero, J.M., Blasco, X., Sánchez-Pérez, J.V. et al. Design of sound phase diffusers by means of multiobjective optimization approach using ev-MOGA evolutionary algorithm. Struct Multidisc Optim 53, 861–879 (2016). https://doi.org/10.1007/s00158-015-1367-0

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