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

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.

References:

1. Amaran, S., et al., Simulation optimization: a review of algorithms and applications. Annals of Operations Research, 2016. 240(1): p. 351-380.
2. Boukouvala, F., R. Misener, and C.A. Floudas, Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO. European Journal of Operational Research, 2016. 252(3): p. 701-727.
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