A local search method for costly black-box problems and its application to CSP plant start-up optimization refinement
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A local search method for costly black‑box problems and its application to CSP plant start‑up optimization refinement Andrea Manno1,2 · Edoardo Amaldi2 · Francesco Casella2 · Emanuele Martelli3 Received: 1 February 2019 / Revised: 24 January 2020 / Accepted: 24 January 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract A variety of engineering applications are tackled as black-box optimization problems where a computationally expensive and possibly noisy function is optimized over a continuous domain. In this paper we present a derivative-free local method which is well-suited for such problems, and we describe its application to the optimization of the start-up phase of an innovative Concentrated Solar Power (CSP) plant. The method, referred to as rqlif, exploits a regularized quadratic model and a linear implicit filtering strategy so as to be parsimonious in terms of function evaluations. After assessing the performance of rqlif on a set of analytical test problems in comparison with three well-known local algorithms, we apply it in conjunction with a global algorithm based on RBFs interpolation to the start-up optimization of the CSP plant developed in the PreFlexMS H2020 project. For the test problems, rqlif provides good quality solutions in a limited number of function evaluations. For the application, the global–local strategy yields a substantial improvement with respect to the reference solution and significantly reduces the thermo-mechanical stress suffered by the plant components. Keywords Derivative-free optimization · Costly black-box optimization · Local optimization · Start-up optimization · Solar power · Engineering application * Andrea Manno [email protected] Edoardo Amaldi [email protected] Francesco Casella [email protected] Emanuele Martelli [email protected] 1
Centro di Eccellenza DEWS, Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica, Università degli Studi dell’Aquila, Via Vetoio, 67100 L’Aquila, Italy
2
Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Via Ponzio 34/5, 20133 Milan, Italy
3
Dipartimento di Energia, Politecnico di Milano, Via Lambruschini 4, 20156 Milan, Italy
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1 Introduction Many decision making problems arising in engineering and economy (e.g., Audet and Kokkolaras 2016; Costa et al. 2015; Hellstrom and Holmström 1999; Campana et al. 2009) must be formulated as black-box optimization problems since the evaluation of the objective function and/or constraints is performed by a simulation code. Typically, such simulation codes solve complex models using ad-hoc convergence algorithms. Examples of such complex models are finite element models in mechanical engineering (Le Besnerais et al. 2011; Meo and Zumpano 2008), CFD models in fluid dynamics (Madsen and Langthjem 2001; Olivero et al. 2014), flowsheet models in process engineering (Martelli and Amaldi 2014), and systems of DAEs in control engineering (Peeters
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