(598f) Optimization of Data-Dependent Mixed-Integer Nonlinear Problems

Kim, S. H., Georgia Institute of Technology
Boukouvala, F., Georgia Institute of Technology
Many engineering problems involve complex computer simulations to describe phenomena that cannot be explicitly captured by physics-based algebraic equations. In order to optimize such systems, one needs to rely on black/grey-box, or derivative-free optimization methods [1, 2]. Due to the increased interest in optimization with data, several exciting developments can be found in the literature, ranging from methods which are purely sample-driven, to methods that employ a combination of sampling, fitting of surrogate models and derivative-based optimization [2]. A lot of the developments in the area of derivative-free optimization focus on nonlinear constrained optimization problems, in which all of the variables are continuous, while the objective function and at least a subset of the constraints rely on a black-box simulation. However, many chemical process systems problems, such as flowsheet superstructure optimization (synthesis), contain discrete or binary variables [3]. While many algorithms exist to solve equation-based MINLPs, solving a black-box-MINLP (bb-MINLP) is very challenging since integrality constraints cannot be relaxed due to lack of algebraic equations and the inability to collect simulation samples at non-integral values.

Existing bb-MINLP solvers can be divided into two broad categories. The first category is based on local trust-region search, in which the pattern or mesh-guided search is used for optimization of both continuous and discrete variables [4, 5]. The second approach employs the concept of surrogate functions for optimization. In this case, the surrogate models are constructed for the objective and constraints as a function of continuous and discrete variables by assuming continuity of all variables, while after a solution is obtained for in the continuous space, the discrete variables are fixed to the nearest discrete value [6, 7]. Despite the above recent advances, current methods have only been tested on relatively low dimensional problems. In this work, we will present several approaches for solving bb-MINLP problems by employing various sampling strategies, surrogate models, decomposition strategies, machine-learning driven heuristics, and high-performance computing. Results will be presented for a set of benchmarking problems as well as process synthesis optimization case studies.


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