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Generalized Differential Evolution for Numerical and Evolutionary Optimization

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NEO 2015

Part of the book series: Studies in Computational Intelligence ((SCI,volume 663))

Abstract

This chapter is about Generalized Differential Evolution (GDE), which is a general purpose optimizer for global nonlinear optimization. It is based on Differential Evolution (DE), which has been gaining popularity because of its simplicity and good observed performance. GDE extends DE for problems with several objectives and constraints. The chapter concentrates on describing different development phases and performance of GDE but it also contains a brief listing of other multi-objective DE approaches. Ability to solve multi-objective problems is mainly discussed, but constraint handling and the effect of control parameters are also covered. It is found that the latest GDE version is effective and efficient for solving constrained multi-objective problems having different types of decision variables.

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Notes

  1. 1.

    We define that \(\mathbf {x}\) dominates \(\mathbf {y}\) with respect to constraints iff \(\forall k : g'_k(\mathbf {x}) \le g'_k(\mathbf {y}) \wedge \exists k : g'_k(\mathbf {x}) < g'_k(\mathbf {y}), \quad g'_k(\mathbf {z}) = \max \left( g_k(\mathbf {z}), 0\right) \).

  2. 2.

    The search is rotationally invariant if it is independent from the rotation of coordinate axis of the search space. Rotationally invariant search is preferable if the problem is not separable as it is the case with most practical problems [58, 78].

  3. 3.

    Preferring the trial vector in the case of equal objective values has importance if the objective landscape contains a plateau; preferring the old vector would cause the search to stagnate on the plateau.

  4. 4.

    ZDT4 has multiple equally spaced local Pareto fronts and \(F = 0.5\) advances moving from one local front to another [47, 50].

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Acknowledgments

The first author would like to acknowledge support of the South Savo Regional Fund of the Finnish Cultural Foundation (Suomen Kulttuurirahaston Etelä-Savon rahasto) and support of the Mexican Government thought the Foreign Ministry (Gobierno de México, a través de la Secretería de Relaciones Exteriores). The second author gratefully acknowledges support from CONACyT project no. 221551.

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Authors and Affiliations

  1. Centre of Computational Engineering and Integrated Design (CEID), Lappeenranta University of Technology, P.O. Box 20, 53851, Lappeenranta, Finland

    Saku Kukkonen

  2. Computer Science Department, CINVESTAV-IPN, Av. IPN No. 2508, San Pedro Zacatenco, 07300, Mexico City, DF, Mexico

    Carlos A. Coello Coello

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  1. Saku Kukkonen
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  2. Carlos A. Coello Coello
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Correspondence to Saku Kukkonen .

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  1. Departamento de Comput Cinvestav-IPN, Mexico, Mexico

    Oliver Schütze

  2. Posgrado en Ciencias de la Ingeniería, Instituto Tecnológico de Tijuana, Tijuana, Baja California, Mexico

    Leonardo Trujillo

  3. Université de Bordeaux, Bordeaux, France

    Pierrick Legrand

  4. Posgrado en Ciencias de la Ingeniería, Instituto Tecnológico de Tijuana, Tijuana, Mexico

    Yazmin Maldonado

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Kukkonen, S., Coello Coello, C.A. (2017). Generalized Differential Evolution for Numerical and Evolutionary Optimization. In: Schütze, O., Trujillo, L., Legrand, P., Maldonado, Y. (eds) NEO 2015. Studies in Computational Intelligence, vol 663. Springer, Cham. https://doi.org/10.1007/978-3-319-44003-3_11

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