Leveraging Classical and Quantum Computing for Process Systems Engineering Applications: Decomposition Algorithm with Ising Solvers for Efficient Discrete Landscape Exploration

Abstract

Conceptual process design is a crucial aspect of chemical engineering that involves process synthesis. Mixed-integer nonlinear programming is a powerful framework for modeling such design problems by combining discrete and continuous variables; however, the combinatorial complexity of discrete choices, coupled with nonlinearities, presents challenging monolithic problems. Using decomposition, discrete subproblems can potentially benefit from Ising solvers, while simulators and nonlinear solvers offer powerful tools for handling nonlinearities. This work aims to: evaluate use of Ising-based solvers for discrete optimization and holistic process optimization through two case studies: an ionic liquid selection and its process design, and a more complex problem of drug manufacturing process optimization. The discrete subproblem is formulated as an integer program or quadratic unconstrained binary optimization and solved using a commercial classical or Ising solvers such as simulated annealing (SA), quantum annealing (QA), and entropy computing (EC) respectively. The commercial classical solver had the shortest runtime, whereas EC took the longest, followed by QA and SA, in reaching feasible and optimal solutions. The heuristics identified all or most feasible solutions in a single run, demonstrating advantages in solution diversity and efficient and broad exploration of the solution space over the classical solver, while the classical solver provides an optimality guarantee and rapid convergence speed. In process design, where insights of alternative designs and cost comparisons are more valuable than an optimal solution, heuristics offer a better-suited decision-making strategy. The comparative analysis highlights the strengths of each method and underscores the potential of this heterogeneous computing approach that leverages different methods to address practical optimization problems.