Leveraging Classical and Quantum Computing for Process Systems Engineering Applications: Decomposition Algorithm with Ising Solvers for Efficient Discrete Landscape Exploration
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.
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.
Computer-aided Molecular and Process Design (CAMPD) is an equation-oriented multi-scale decision making framework for designing both materials (molecules) and processes for separation, reaction, and reactive separation whenever material choice significantly impacts process performance. The inherent nonlinearity and nonconvexity in CAMPD optimization models, introduced through the property and process models, pose challenges to state-of-the-art solvers. Recently, quantum computing (QC) has shown promise for solving complex optimization problems, especially those involving discrete decisions. This motivates us to explore the potential usage of quantum optimization techniques for solving CAMPD problems. We have developed a technique for directly solving a class of mixed integer nonlinear programs using QC. Our approach represents both continuous and integer design decisions by a set of binary variables through encoding schemes. This transformation allows to reformulate certain types of CAMPD problems into Quadratic Unconstrained Binary Optimization (QUBO) models that can be directly solved using quantum annealing techniques. We illustrate this technique for the selection of optimal ionic liquids (IL) and the configuration of a reactor-separator process network. We also discuss several challenges that are associated with quantum optimization when solving large scale CAMPD problems.
Mixed-integer linear programming problems are extensively used in industry for a wide range of optimization tasks. However, as they get larger, they present computational challenges for classical solvers within practical time limits. Quantum annealers can, in principle, accelerate the solution of problems formulated as quadratic unconstrained binary optimization instances, but their limited scale currently prevents achieving practical speedups. Quantum-classical algorithms have been proposed to take advantage of both paradigms and to allow current quantum computers to be used in larger problems. In this work, a hardware-agnostic Benders' decomposition algorithm and a series of enhancements with the goal of taking the most advantage of quantum computing are presented. The decomposition consists of a master problem with integer variables, which is reformulated as a quadratic unconstrained binary optimization problem and solved with a quantum annealer, and a linear subproblem solved by a classical computer. The enhancements consist, among others, of different embedding processes that substantially reduce the pre-processing time of the embedding computation without compromising solution quality, a conservative handling of cut constraints, and a stopping criterion that accounts for the limited size of current quantum computers and their heuristic nature. The proposed algorithm is benchmarked against classical approaches using a D-Wave quantum annealer for a scalable family of transmission network expansion planning problems.
The optimization of front-end crude oil scheduling is a critical determinant of refinery profitability and operational stability. However, the coupling of discrete logistics events (e.g., vessel berthing) with continuous material flows (e.g., pipeline transfers) renders this problem an NP-hard Mixed-Integer Linear Programming (MILP) challenge, often intractable for classical solvers at industrial scales. This study proposes a novel hybrid quantum-classical framework to address these computational bottlenecks. We employ Benders Decomposition to decouple the monolithic model into a discrete Master Problem (MP) and a continuous Subproblem (SP). To exploit the search capabilities of quantum computing, the MP is reformulated as a Quadratic Unconstrained Binary Optimization (QUBO) model and solved via a hybrid quantum solver, while the SP enforces mass balance and quality constraints through iterative optimality and feasibility cuts. Extensive experiments on 15 multi-scale instances demonstrate that the proposed framework significantly outperforms traditional metaheuristics (e.g., Genetic Algorithms, Tabu Search), reducing total operating costs by approximately 73--80% and achieving computational speeds comparable to state-of-the-art commercial solvers (Gurobi). By effectively leveraging global optimality cuts, the method overcomes the tendency of heuristic approaches to trap in local optima, providing a robust and scalable solution for complex refinery logistics.
Efficient production planning is essential in modern manufacturing to improve performance indicators such as lead time and to reduce reliance on human intuition. While mathematical optimization approaches, formulated as job shop scheduling problems, have been applied to automate this process, solving large-scale production planning problems remains computationally demanding. Moreover, many practical scenarios involve conflicting objectives, making traditional scalarization techniques ineffective in finding diverse and useful Pareto-optimal solutions. To address these challenges, we developed a quantum-classical hybrid algorithm that decomposes the problem into two subproblems: resource allocation and task scheduling. Resource allocation is formulated as a quadratic unconstrained binary optimization problem and solved using annealing-based methods that efficiently explore complex solutions. Task scheduling is modeled as a mixed-integer linear programming problem and solved using conventional solvers to satisfy detailed scheduling constraints. We validated the proposed method using benchmark instances based on foundry production scenarios. Experimental results demonstrate that our hybrid approach achieves superior solution quality and computational efficiency compared to traditional monolithic methods. This work offers a promising direction for high-speed, multi-objective scheduling in industrial applications.
Optimization is a crucial challenge across various domains, including finance, resource allocation, and mobility. Quantum computing has the potential to redefine the way we handle complex problems by reducing computational complexity and enhancing solution quality. Optimization, particularly of objective functions, stands to benefit significantly from quantum solvers, which leverage principles of quantum mechanics like superposition, entanglement, and tunneling. The Ising and Quadratic Unconstrained Binary Optimization (QUBO) models are the most suitable formulations for these solvers, involving binary variables and constraints treated as penalties within the overall objective function. To harness quantum approaches for optimization, two primary strategies are employed: exploiting quantum annealers—special-purpose optimization devices—and designing algorithms based on quantum circuits. This review provides a comprehensive overview of quantum optimization methods, examining their advantages, challenges, and limitations. It demonstrates their application to real-world scenarios and outlines the steps to convert generic optimization problems into quantum-compliant models. Lastly, it discusses available tools and frameworks that facilitate the exploration of quantum solutions for optimization tasks.
For various optimization problems, the classical time to solution is super-polynomial and intractable to solve with classical bit-based computing hardware to date. Digital and quantum annealers have the potential to identify near-optimal solutions for such optimization problems using a quadratic unconstrained binary optimization (QUBO) problem formulation. This work benchmarks two use cases to evaluate the utility of QUBO solvers for combinatorial optimization problems, in order to determine if a QUBO formulation and annealing-based algorithms have an advantage over classical mixed-integer programming (MIP) and constraint programming (CP) solvers. Various QUBO and solver metrics such as problem mapping, quantitative interconnectivity, penalty structure, solver minimum cost (obtained optimal value) and solver time to solution have been applied to evaluate different QUBO problems. Constrained and unconstrained QUBO solvers are compared including the Fujitsu digital annealer (DA), various D-Wave hybrid quantum annealing solvers (QA, HQA), and the classical MIP/CP solvers HiGHS, Gurobi, SCIP, and CP-SAT. The two industrially relevant use cases are reaction network pathway analysis and mRNA codon selection. For reaction pathway analysis, classical MIP/CP solvers (especially Gurobi and CP-SAT) are observed to solve the problem to optimality in reasonable time frames. For mRNA codon selection, Gurobi outperformed all other solvers in time to solution for all problem sizes, followed by CP-SAT and the D-Wave Nonlinear (NL) HQA solver.