An Analytical Hessian and Parallel-Computing Approach for Efficient Dynamic Optimization Based on Control-Variable Correlation Analysis

Abstract

The approach of combined multiple-shooting with collocation is efficient for solving large-scale dynamic optimization problems. The aim of this work was to further improve its computational performance by providing an analytical Hessian and realizing a parallel-computing scheme. First, we derived the formulas for computing the second-order sensitivities for the combined approach. Second, a correlation analysis of control variables was introduced to determine the necessity of employing the analytical Hessian to solve an optimization problem. Third, parallel computing was implemented thanks to the nature of the combined approach, because the solutions of model equations and evaluations of both first-order and second-order sensitivities for individual time intervals are decoupled. Because these computations are expensive, a high speedup factor was gained through the parallelization. The performance of the proposed analytical Hessian, correlation analysis, and parallel computing is demonstrated in this articl...