On The Global Dynamic Optimization of Highly Nonlinear Systems

We address the relationship between nonlinear behavior and the determination of globally optimal solutions in dynamic systems. Specifically, in determination of optimal transition trajectories between steady state operating points, we analyze the impact of output multiplicities in obtaining global optima around regions featuring severe nonlinearities. In order to quantify the presence or multiple local optima we propose an empirical indicator able to predict the potential for the emergence of unique global solutions. Although the presence of output multiplicities does not seem to be strictly necessary to detect multiple optima, we find that unique global solutions are likely to emerge for transitions around nonlinear regions. Moreover, for dynamic optimization, we found that current global optimization solvers tend to demand large computational effort when compared against local optimization solvers. Therefore, with appropriate variable bounds, good initialization strategies and, if necessary, multiple restart strategies, local optimization solvers seem to be competitive, in terms of CPU time, when faced with the decision of finding global optimal solutions.