From an Optimal Point to an Optimal Region: A Novel Methodology for Optimization of Multimodal Constrained Problems and a Novel Constrained Sliding Particle Swarm Optimization Strategy - Carine M. Rebello; Márcio A. F. Martins; José M. Loureiro; Alírio E. Rodrigues; Ana M. Ribeiro; Idelfonso B. R. Nogueira (Mathematics, 2021)
The present work proposes a novel methodology for an optimization procedure extending the optimal point to an optimal area based on an uncertainty map of deterministic optimization. To do so, this work proposes the deductions of a likelihood-based test to draw confidence regions of population-based optimizations. A novel Constrained Sliding Particle Swarm Optimization algorithm is also proposed that can cope with the optimization procedures characterized by multi-local minima. There are two open issues in the optimization literature, uncertainty analysis of the deterministic optimization and application of meta-heuristic algorithms to solve multi-local minima problems. The proposed methodology was evaluated in a series of five benchmark tests. The results demonstrated that the methodology is able to identify all the local minima and the global one, if any. Moreover, it was able to draw the confidence regions of all minima found by the optimization algorithm, hence, extending the optimal point to an optimal region. Moreover, providing the set of decision variables that can give an optimal value, with statistical confidence. Finally, the methodology is evaluated to address a case study from chemical engineering; the optimization of a complex multifunctional process where separation and reaction are processed simultaneously, a true moving bed reactor. The method was able to efficiently identify the two possible optimal operating regions of this process. Therefore, proving the practical application of this methodology.