The solution of repeated fixed-horizon trajectory optimization problems of processes that are either too difficult or too complex to be described by physics-based models can pose formidable challenges. Very often, soft-computing methods e.g. black-box modeling and evolutionary optimization are used. These approaches are ineffective or even computationally intractable for searching high-dimensional parameter spaces. In this paper, a structured iterative process is described for addressing such problems: the starting point is a simple parameterization of the trajectory starting with a reduced number of parameters; after selection of values for these parameters so that this simpler problem is covered satisfactorily, a refinement procedure increases the number of parameters and the optimization is repeated. This continuous parameter refinement and optimization process can yield effective solutions after only a few iterations. To illustrate the applicability of the proposed approach we investigate the problem of dynamic optimization of the operation of HVAC (heating, ventilation, and air conditioning) systems, and illustrative simulation results are presented. Finally, the development of advanced communication and interoperability components is described, addressing the problem of how the proposed algorithm could be deployed in realistic contexts.
Modeling and Computing Methods for Solving Optimization Problems
