The area of optimization is a strong focus of the process systems engineering community. As a result, a plethora of models, algorithms, and software have been developed for algebraic nonlinear programs (NLPs) and mixed-integer nonlinear programs (MINLPs). These techniques have had and will continue to have an impact in process synthesis, design, and operations. Yet, the algebraic NLP/MINLP paradigm: o often requires modelers to make restrictive assumptions in order to make possible the solution of their models with current optimization software; o is inefficient when expensive simulations must be carried out for modeling complex systems via proprietary software; and o is not in line with engineering practice, where technological developments are almost always based on experimental measurements rather than algebraic models.
Experiments, in particular, provide measurements of the objective function to be optimized but no direct information on derivatives or any other information required by algebraic NLP/MINLP optimization. This project aims to develop optimization algorithms and software capable of optimizing without an explicit algebraic model. Towards this goal, the PS plans to: o complete a critical comparison of existing methods for this problem, especially in regard to their ability to find global solutions and improve starting points; o develop novel local and global optimization algorithms for optimizing systems described by any combination of algebraic, simulation, and experimental components; o use previously developed algorithms to optimize systems involving multiple scales, hidden constraints, and noisy objective functions; o develop and make available innovative software that relies on modern cyberinfrastruc- ture and implements the algorithms developed in this research.
Intellectual Merit
The project will lay the foundations of a new generation of optimization algorithms and software capable of solving complex problems for which algebraic NLPs and MINLPs are not available. Such problems abound in all scientific fields that rely on simulation or experiments for design and optimization. The task of optimizing algebraic NLPs and MINLPs is, in general, a very challenging one. Optimizing without explicit algebraic models can be even more challenging. This research addresses that challenge by capitalizing on recent progress in global optimization of algebraic NLPs and MINLPs to develop new, more efficient algorithms for algebraic-model-free optimization.
Broader Impacts
The project involves graduate student mentoring, integration of research results in course work, targeted minority student recruitment, and broad dissemination of the results through innovative cyber-enabled software implementing the results of the research. In addition, the research will have an immediate and wide impact on industrial practice as it specifically provides algorithms for experiment-based optimization and design.
Scientists and engineers have long used optimization algorithms to analyze, design, and optimize natural and manmade systems. To make the most of optimization algorithms and increase solvability of their models, users of optimization algorithms typically utilize algebraic models of their systems and processes. However, developing such models is often a rather laborious process and requires making restrictive assumptions about the system under study. Actual implementation of the results of such analysis is almost always based on experimental, rather than modeling, approaches. Optimization algorithms for the design and analysis of systems in the absence of models are much needed but largely underdeveloped in comparison to algebraic model-based optimization. This project began with a critical comparison of existing methods for optimization without an algebraic model, especially in regard to their ability to find good solutions and improve starting points based on a small number of simulations or experiments. As part of this comparison, we tested 22 computational implementations on over 500 test problems, which represents a scale of testing that had never been reached before for these algorithms. Our results were communicated with the authors of these codes and, in many cases, were used to improve the capabilities of their software. The main conclusion we drew from this comparison is that algorithms based on surrogate models of objectives, gradients or higher derivatives tend to have an edge over approaches based on (random) sampling for our collection of test problems. Using these insights, we proceeded to develop new surrogate model-based algorithms for local and global optimization. In parallel to algorithm testing and development, we worked on a number of applications of optimization without an explicit algebraic model. These applications included the optimization of crystallization processes, polymerase chain reactions, Lithium ion batteries, antenna design, prostate cancer treatment, and control of the spreading of influenza epidemics. In the course of investigating these problems, we demonstrated that the same surrogate-based algorithms are applicable with similarly high success rates in diverse application areas.
