There are several optimization problems in physics, chemistry, finance, computer science, engineering and operations research in which the analytical expressions of the objective function and/or the constraints are unavailable. However, it is possible to obtain input-output data through simulations. These are black-box problems where the derivative information is often not available or too expensive to approximate numerically. Due to the absence of derivative information, it becomes challenging to optimize and guarantee optimality of the solution. In this presentation, methods and algorithms to address some of the challenges in blackbox optimization (BBO) will be presented. A top-down approach is taken by first addressing an easier class of black-box problems and then the difficulty and complexity of the problems is gradually increased. In the first part of the talk, a class of grey-box problems is considered for which the closed form of the objective and/or constraints are unknown, but it is possible to estimate a global upper bound on the diagonal Hessian elements. A novel underestimator is constructed based on these bounds. This lower bounding technique is implemented within a branch-and-bound framework with guaranteed convergence to -global optimality. The technique is applied for the deterministic global optimization of dynamic problems. In the second part of the presentation, box-constrained black-box problems are addressed for which only simulations can be performed, and no model insights are possible. A novel optimization method, UNIPOPT (Univariate Projection-based Optimization) based on the projection onto a univariate space will be presented. A special function is identified in this space that also contains the global minimum of the original function. Computational experiments suggest that UNIPOPT often have better space exploration features compared to other well-known approaches. The third part of the presentation addresses general black-box problems with constraints of both known and unknown algebraic forms. An efficient two-phase algorithm based on a trust-region framework is proposed for problems particularly involving high function evaluation cost. The performance of the approach is illustrated through computational experiments on numerical problems and dynamic process intensification case studies for which only input-output data are available.
Biography
Ishan Bajaj is currently a postdoctoral research associate in the research group of Prof. Christos Maravelias in the Department of Chemical and Biological Engineering at University of WisconsinMadison. He received a B.Tech in Chemical Engineering from Indian Institute of Technology, Bombay and Ph.D. in Chemical Engineering from Texas A&M University. His doctoral thesis, pursued under the supervision of Prof. Faruque Hasan, was on the development of efficient optimization methods and algorithms for computationally expensive black-box models. Due to his research contributions, he received a PSE Young Researcher Award from the CAST division of AIChE and Distinguished Graduate Research Award from the Department of Chemical Engineering at Texas A&M University. His research interests lie in the development of theory and methodologies for optimal design and operation of hybrid renewable energy systems, and synthesis of pathways for sustainable fuels and chemicals.