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.

Figures (6)

• Figure 1: An illustrative workflow of the proposed approach. In step (1), we construct a single flowsheet of a superstructure that encapsulates the set of all feasible alternative process structures. Denoting critical flow paths and nodes, the process design and optimization is cast as a mathematical program, consisting of discrete (configuration) and continuous (operational) variables. Step (2), we decompose the problem into discrete and continuous parts, where the discrete subproblem is formulated as an integer program using approximation and logical statements. The integer program can further be reformulated into a quadratic unconstrained binary optimization to take advantage of Ising solvers. The solutions from the discrete subproblem fix the discrete variables in the continuous subproblem, where powerful nonlinear solvers and simulators can be leveraged. The bottom image illustrates the procedure used in the case studies presented in this work. The red box on the left represents discrete optimization at the configurational level, and the blue box on the right represents the continuous subproblem, which is handled by a classical solver or a simulator to optimize the process at the operational level.
• Figure 2: A superstructure of a drug substance manufacturing process (top) and a representative flow diagram for the main problem (bottom); dotted and solid lines indicate batch and continuous feed, respectively.
• Figure 3: A plot of energy or probability of solutions found through various methods in the IL case study. The vertical line indicates the optimal solution of the discrete subproblem found by Gurobi. Infeasible solutions are not shown in this plot.
• Figure 4: A plot of energy or probability of feasible solutions found through annealing methods. The vertical line indicates the optimal solution of the discrete subproblem, indicated by the first result of Gurobi. Infeasible solutions are not shown in this plot.
• Figure 5: Simulation objective function values ranked according to discrete subproblem solution by IP iterations (x-axis). Red dots indicate the objective function value of the corresponding simulation, and the blue line shows the best objective function value found with each iteration.