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Derivative-Free Augmented Lagrangian for Global Optimization: Cost Minimization in a Simplified Activated Sludge System Model

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Journal of Mathematical Modelling and Algorithms in Operations Research

Abstract

A methodology for finding the optimal values of the decision variables from an efficient simplified mathematical model of an activated sludge system is addressed in this paper. The work herein presented arises in a wastewater treatment plant design context, where investment and operational costs are to be minimized and computational effort is to be reduced. To achieve the best design, a non-linear optimization solution method based on an augmented Lagrangian approach is proposed. At each iteration, a subproblem is globally solved by a derivative-free recursive branching technique, known as the multilevel coordinate search algorithm of Huyer and Neumaier [20]. The presented technique has been shown to work quite well when solving the herein proposed non-convex and non-smooth constrained optimization model. The numerical results show the reliability of the obtained solutions at a reduced computational cost.

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Authors and Affiliations

  1. Algoritmi Research Centre, University of Minho, Campus de Gualtar, 4710-057, Braga, Portugal

    Isabel Espirito Santo, Roman Denysiuk & Edite M.G.P. Fernandes

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  1. Isabel Espirito Santo
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  2. Roman Denysiuk
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  3. Edite M.G.P. Fernandes
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Correspondence to Isabel Espirito Santo.

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Espirito Santo, I., Denysiuk, R. & Fernandes, E.M. Derivative-Free Augmented Lagrangian for Global Optimization: Cost Minimization in a Simplified Activated Sludge System Model. J Math Model Algor 14, 35–53 (2015). https://doi.org/10.1007/s10852-014-9256-x

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