Novel Methods and Computational Studies for Global Optimization

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CBET-0827907FloudasIntellectual Merit: The goal of this project is to develop novel theoretical, algorithmic and computational techniques for global optimization problems. The computational techniques will apply to a variety of chemical engineering process design, synthesis and operations problems. The PIs will investigate four sub-areas: (i) the development of a new class of tight convex underestimators for twice-continuously differentiable univariate functions which will enhance the piecewise quadratic perturbation-based aBB (Meyer and Floudas (2005)) approach and will form the theoretical basis for applications in a variety of phase equilibrium, design and synthesis problems; (ii ) the theoretical development of tight convex underestimators for multivariate twice continuously differentiable functions and study its algorithmic development for bivariate, multilinear and general multivariate functions; (iii) a new theoretical and algorithmic approach for deterministic global optimization via an Augmented Lagrangian framework; and (iv) the development of new, hybrid global optimization methods combining the beneficial elements of the tight convex underestimators of the enhanced aBB deterministic global optimization framework and the augmented Lagrangian approach with stochastic based approaches. The PIs will also study the distributed computing implementations and apply them to medium- and large-scale non-convex optimization problems that arise in standard, extended, and generalized pooling and blending applications.Through this research, the PIs expect to identify new theoretical, algorithmic, and computational results affecting global optimization and methodologies. The innovative features the PIs expect to derive are: (a) new tight convex underestimators for twice-continuously differentiable constrained nonlinear optimization models for both univariate and multivariate functions; (b) new methods for deterministic global optimization via an Augmented Lagrangian framework; (c) improved deterministic global optimization methods that embed the convex lower bounding advances and can address medium to large scale global optimization problems; (d) novel hybrid global optimization methods that combine the rigor of deterministic methods with the tight convex underestimators and computationally efficient stochastic approaches; and (e) sequential and distributed computational tools. This research focuses on improving medium- to large-scale global optimization applications by enhancing process synthesis, design and process operations. Broader Impact: This research will develop rigorous global optimization methods addressing important problems in process design, synthesis and process operations. By facilitating faster response to the market demands and enabling the more efficient use of the processing facilities, petrochemical, chemical, pharmaceutical, manufacturing, and services/software companies will benefit from these methods, and thereby, the research will directly impact the US economy. Additionally, the research will enhance educational activities. The PIs will incorporate the research results into an elective graduate course on Nonlinear Mixed Integer Optimization in the form of lectures and projects. The PIs will also use selective algorithmic tools as part of a capstone senior design course called Design, Synthesis and Optimization of Chemical Processes. The PIs will broaden the participation of underrepresented groups through recruiting undergraduate and graduate students for the project. The PIs will disseminate the research results through presentations at domestic and international meetings, scholarly refereed journal publications and through a web page.