A Three-section Algorithm of Dynamic Programming Based on Three-stage Decomposition System Model for Grade Transition Trajectory Optimization Problems

Abstract

This paper introduces a practical solving scheme of gradetransition trajectory optimization (GTTO) problems under typical certificate-checking–updating framework. Due to complicated kinetics of polymerization, differential/algebraic equations (DAEs) always cause great computational burden and system non-linearity usually makes GTTO non-convex bearing multiple optima. Therefore, coupled with the three-stage decomposition model, a three-section algorithm of dynamic programming (TSDP) is proposed based on the general iteration mechanism of iterative programming (IDP) and incorporated with adaptivegrid allocation scheme and heuristic modifications. The algorithm iteratively performs dynamic programming with heuristic modifications under constant calculation loads and adaptively allocates the valued computational resources to the regions that can further improve the optimality under the guidance of local error estimates. TSDP is finally compared with IDP and interior point method (IP) to verify its efficiency of computation.