[Paper Review] Finding Optimal Pathways in Chemical Reaction Networks Using Ising Machines

Yuta Mizuno, Tamiki Komatsuzaki|arXiv (Cornell University)|Aug 8, 2023

Machine Learning in Materials ScienceMaterials Science49 references3 citations

TL;DR

This paper presents the first application of Ising machines—specifically D-Wave's quantum annealer and classical simulated annealing—for solving optimal pathway-finding problems in chemical reaction networks (CRNs). By formulating the constrained combinatorial optimization problem as an Ising model with structured penalty terms, and using Bayesian optimization with problem-aware grouping to tune penalty strengths, the method achieves feasible approximate solutions despite challenges in finding exact optima, especially for larger networks.

ABSTRACT

Finding optimal pathways in chemical reaction networks is essential for elucidating and designing chemical processes, with significant applications such as synthesis planning and metabolic pathway analysis. Such a chemical pathway-finding problem can be formulated as a constrained combinatorial optimization problem, aiming to find an optimal combination of chemical reactions connecting starting materials to target materials in a given network. Due to combinatorial explosion, the computation time required to find an optimal pathway increases exponentially with the network size. Ising machines, including quantum and simulated annealing devices, are promising novel computers dedicated to such hard combinatorial optimization. However, to the best of our knowledge, there has yet to be an attempt to apply Ising machines to chemical pathway-finding problems. In this article, we present the first Ising/quantum computing application for chemical pathway-finding problems. The Ising model, translated from a chemical pathway-finding problem, involves several types of penalty terms for violating constraints. It is not obvious how to set appropriate penalty strengths of different types. To address this challenge, we employ Bayesian optimization for parameter tuning. Furthermore, we introduce a novel technique that enhances tuning performance by grouping penalty terms according to the underlying problem structure. The performance evaluation and analysis of the proposed algorithm were conducted using a D-Wave Advantage system and simulated annealing. The benchmark results reveal challenges in finding exact optimal pathways. Concurrently, the results indicate the feasibility of finding approximate optimal pathways, provided that a certain degree of relative error in cost value is acceptable.

Motivation & Objective

• To address the NP-hard challenge of finding optimal pathways in large chemical reaction networks (CRNs), which suffer from combinatorial explosion and growing data sizes.
• To explore the feasibility of applying Ising machines—quantum and classical annealing devices—for solving CRN pathway-finding as a constrained combinatorial optimization problem.
• To overcome the difficulty of setting appropriate penalty strengths in the Ising model formulation by introducing a novel grouping strategy based on problem structure.
• To improve solution quality through postprocessing techniques such as steepest descent and inflow/outflow adjustment.
• To evaluate performance using both D-Wave Advantage and simulated annealing, benchmarking convergence and solution quality under varying problem sizes.

Proposed method

• The chemical pathway-finding problem is mapped to an Ising model with spin variables representing reaction choices, using unary or order encoding to represent integer variables.
• The Ising Hamiltonian includes multiple penalty terms for constraints such as mass balance, reaction feasibility, and target species formation, each with adjustable penalty strengths.
• A novel grouping strategy is introduced to cluster penalty terms based on the underlying network structure (e.g., by reaction depth or species category), improving tuning efficiency.
• Bayesian optimization with the tree-structured Parzen estimator (TPE) is used to tune penalty strengths, minimizing a score function that reflects constraint violations and cost.
• Postprocessing steps—steepest descent and inflow/outflow adjustment—are applied to refine raw Ising machine solutions into valid chemical pathways.
• Performance is evaluated on synthetic CRN benchmarks using both D-Wave Advantage and simulated annealing, with convergence and score improvement tracked across multiple tuning runs.

Figure 1 : An example of a chemical reaction network and a pathway: the Solvay process.

Experimental results

Research questions

• RQ1 Can Ising machines effectively solve optimal pathway-finding problems in chemical reaction networks, given their combinatorial complexity?
• RQ2 How do different encoding schemes (unary vs. order) and grouping strategies impact the performance of penalty strength tuning in Ising-based pathway optimization?
• RQ3 Does Bayesian optimization outperform random search in tuning penalty parameters for Ising models in CRN pathway problems?
• RQ4 To what extent do postprocessing techniques improve the quality of solutions generated by Ising machines?
• RQ5 How do penalty strength values scale with network size, particularly for mass balance constraints of target species?

Key findings

• Bayesian optimization with problem-aware grouping significantly outperformed random search in tuning penalty strengths, especially for larger problems, as shown by faster convergence and lower score values.
• Postprocessing via steepest descent and inflow/outflow adjustment improved the solution quality by several orders of magnitude on the D-Wave Advantage system, with the latter being particularly effective.
• For simulated annealing, inflow/outflow adjustment improved solution quality, but steepest descent did not, indicating method-specific effectiveness of postprocessing.
• Optimized penalty strengths for mass balance constraints of target species were consistently higher than for other constraints and showed strong linear correlation with the number of integer variables, with R² values up to 0.92 across different encoding and grouping methods.
• Despite challenges in finding exact optimal pathways, the method successfully identified approximate optimal pathways with acceptable relative error in cost, demonstrating feasibility for real-world CRN applications.
• The study revealed that penalty strength scaling is predictable and follows a linear trend with network size, enabling informed parameter initialization for future applications.

Figure 2 : The overview of the proposed algorithm for finding pathways in chemical reaction networks using Ising machines.