A multi-criteria approach to dynamic optimization

The approach of approximating a differential algebraic optimization problem (DAOP) by a nonlinear program (NLP) and subsequently solving it is considered. In this context, the two distinct objectives to be minimized are: (i) the approximation error and (ii) the predicted cost functional. It is first shown that the minimization of the approximation error by adjusting the collocation points leads to constraining the input space, thereby increasing the minimum predicted cost. This is the main motivation to seek compromise solutions and hence the overall problem is approached from a multicriteria optimization viewpoint. Various preference structures (lexicographic, Pareto and value function) available in the multicriteria literature provide an unified framework for the analysis of existing techniques and the methods proposed here