Sensitivity-based adaptive mesh refinement collocation method for dynamic optimization of chemical and biochemical processes.

Collocation on finite element (CFE) is an effective simultaneous method of dynamic optimization to increase the profitability or productivity of industrial process. The approach needs to select an optimal mesh of time interval to balance the computational cost with desired solution. A new CFE approach with non-uniform refinement procedure based on the sensitivity analysis for dynamic optimization problems is, therefore, proposed, where a subinterval is further refined if the obtained control parameters have significant effect on the performance index. To improve the efficiency, the sensitivities of state parameters with respect to control parameters are derived from the solution of the discretized dynamic system. The proposed method is illustrated by testing two classic dynamic optimization problems from chemical and biochemical engineering. The detailed comparisons among the proposed method, the CFE with uniform mesh, and other reported methods are also carried out. The research results reveal the effectiveness of the proposed approach.