Simulation-Based Optimization over Discrete Spaces Using Projection to Continuous Latent Spaces

Simulation-based optimization of complex systems over discrete decision spaces is a challenging computational problem. Specifically, discrete decision spaces lead to a combinatorial explosion of possible alternatives, making it computationally prohibitive to perform simulations for all possible combinations. In this work, we present a new approach to handle these issues by transforming/projecting the discrete decision space into a continuous latent space using a probabilistic model known as Variational AutoEncoders. The transformation of the decision space facilitates the implementation of Bayesian optimization (BO), which is an efficient approach that strategically navigates the space to reduce the number of expensive simulations. Here, the key observation is that points in the latent space correspond to decisions in the original mixed-discrete space, but the latent space is much easier to navigate using BO. We illustrate the benefits of our approach through a couple of case studies that aim to design complex distillation systems: the recovery of caprylic acid from water by liquid-liquid extraction and the separation of an azeotropic mixture using a thermally couple column known as an extractive dividing wall column.