Leveraging Classical and Quantum Methods for Process Systems Engineering Applications

Yirang Park, David E. Bernal Neira

Keywords: quantum computing, process optimization, process design, quantum annealing

Abstract: Mixed-integer nonlinear programming (MINLP) is a modeling paradigm that combines discrete and continuous variables to model and solve a wide range of optimization problems. Its flexibility is especially useful for many real-world decision problems in engineering, operations, and finance, as these problems often involve discrete decisions and nonlinear system behaviors. Despite the ease of modeling, MINLP problems are challenging to solve as monolithic problems due to the combinatorial complexity of discrete variables and nonlinearities; however, they can be made manageable by adopting a decomposition strategy. Additionally, recent advances in computational hardware create opportunities for addressing different parts of the problem more efficiently. Discrete subproblems can benefit from potentially quantum Ising solvers, while simulators and nonlinear solvers offer powerful tools for handling nonlinearities. To fully exploit these emerging computational capabilities, we propose an integrated approach that decomposes MINLP problems into discrete and continuous components and solves each subproblem using the most suitable computational method. In this work, two case studies are presented: an illustrative example involving the selection of an ionic liquid and its process design, and a more complex problem of drug substance manufacturing process optimization. The discrete subproblem in each case is formulated as an integer programming problem and solved using a commercial classical optimization solver, Gurobi. For comparative analysis, the same problem is reformulated as a quadratic unconstrained binary optimization and solved with simulated annealing, quantum annealing (QA), and entropy quantum computing (EQC). For the quantum methods, two different computing systems are used: D-Wave's specialized quantum annealer for QA, and Quantum Computing Incorporated (QCI)'s Dirac-1 quantum computer for EQC. The continuous subproblem is solved using Gurobi and a simulator-based optimization approach, respectively. In both examples, in terms of computational efficiency, Gurobi achieved the shortest runtime, whereas EQC took the longest, followed by QA and SA, in reaching feasible and optimal solutions. The heuristic methods demonstrated advantages in solution diversity compared to Gurobi's global search approach, identifying all or most of the feasible solutions in a single run and better capturing a broad solution space in a single run, while Gurobi provides global optimality guarantee and speed. This comparative analysis highlights the distinct strengths of each method and underscores the potential of this heterogeneous computing approach, which enables the use of different methods to address practical optimization problems.

Submission Number: 3