An adaptive sequential wavelet-based algorithm developed for dynamic optimization problems. (2nd February 2019) - Santos, Lizandro de Sousa; Secchi, Argimiro Resende; Prata, Diego Martinez; Biscaia Jr., Evaristo Chalbaud
Highlights: Adaptive wavelet discretization is applied to solve dynamic optimization problems. A wavelet compression algorithm is developed to automatically compute the optimal compression threshold for optimizing the adaptive procedure. The proposed approach is compared with some heuristics wavelets compression procedures. We demonstrate the superiority of the wavelet adaptive algorithm over an equidistant discretization and heuristic approaches for ten examples. Abstract: In this paper we present an adaptive wavelet algorithm (WAA) tailored for dynamic optimization problems (DOP). The main feature of the WAA is the automatic computation of time-domain discretization, generating a self-adapting control parameterization, which depends on the nonlinear characteristics of the mathematical model. For this, the control variables are analyzed and treated at different wavelet levels. First, we have demonstrated the advantages of WAA over heuristic adaptive procedures, proposed in the last years. Second, the results of the proposed strategy are illustrated through the solution of ten case studies. According to the results, the computation cost could be reduced by about 56% on average. Besides, the average NLP size reduction was approximately 49.94%, showing that one of the most considerable advantages of the algorithm is the adaptive discretization without prior information of the control profile.