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qualign: solving sequence alignment based on quadratic unconstrained binary optimisation

Yuki Matsumoto, Shota Nakamura

Published Mar 8, 2023• 2 citations
Publisher

Abstract

Bioinformatics has, among others, the issue of solving complex computational problems with vast amounts of sequencing data. Recently, a new computing architecture, the annealing machine, has emerged that applies to actual problems and is available for practical use. This novel architecture can solve discrete optimisation problems by replacing algorithms designed under the von Neumann architecture. To perform computations on the annealing machine, quadratic unconstrained binary optimisation (QUBO) formulations should be constructed and optimised according to the application. In this study, we developed an algorithm under the annealing machine architecture to solve sequence alignment problems, a known fundamental process widely used in genetic analysis, such as mutation detection and genome assembly. We constructed a QUBO formulation based on dynamic programming to solve a pairwise sequence alignment and derived its general form. We compared with conventional methods to solve 40 bp of pairwise alignment problem. Our implementation, named qualign, solved sequence alignment problems with accuracy comparable to that of conventional methods. Although a small pairwise alignment was solved owing to the limited memory size of this method, this is the first step of the application of annealing machines. We showed that our QUBO formulation solved the sequencing alignment problem. In the future, increasing the memory size of annealing machine will allow annealing machines to impact a wide range of bioinformatics applications positively.Availability: the source code of qualign is available at https://github.com/ymatsumoto/qualign

DOI
10.14806/ej.28.0.1020

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Alignment-based conformance checking is a central task in process mining, but computing optimal alignments is computationally hard. This paper studies whether the alignment problem can be expressed directly as a Quadratic Unconstrained Binary Optimization problem and explored with quantum annealing. We present a direct QUBO formulation for optimal alignments on safe Petri nets, with a proof-of-concept implementation supporting exact solving, simulated annealing, and a D-Wave Advantage2 quantum processing unit. The study is intentionally preliminary: rather than claiming a practical quantum advantage, we test whether the formulation is semantically correct and where current hardware helps or fails. On small representative benchmarks, the QUBO recovers correct optimal alignments, including concurrency, loops, silent transitions, and duplicate labels. On loop-heavy instances, the quantum annealer can outperform simulated annealing on success probability. Scalability, however, is strongly limited by hardware connectivity and embedding overhead. Overall, direct QUBO-based alignment finding is feasible in principle, but still far from practical large-scale use.
Quantum and quantum-inspired optimisation algorithms are designed to solve problems represented in binary, quadratic and unconstrained form. Combinatorial optimisation problems are therefore often formulated as Quadratic Unconstrained Binary Optimisation Problems (QUBO) to solve them with these algorithms. Moreover, these QUBO solvers are often implemented using specialised hardware to achieve enormous speedups, e.g. Fujitsu’s Digital Annealer (DA) and D-Wave’s Quantum Annealer. However, these are single-objective solvers, while many real-world problems feature multiple conflicting objectives. Thus, a common practice when using these QUBO solvers is to scalarise such multi-objective problems into a sequence of single-objective problems. Due to design trade-offs of these solvers, formulating each scalarisation may require more time than finding a local optimum.We present the first attempt to extend the algorithm supporting a commercial QUBO solver as a multi-objective solver that is not based on scalarisation. The proposed multi-objective DA algorithm is validated on the bi-objective Quadratic Assignment Problem. We observe that algorithm performance significantly depends on the archiving strategy adopted, and that combining DA with non-scalarisation methods to optimise multiple objectives outperforms the current scalarised version of the DA in terms of final solution quality.
The Steiner Tree Problem (STP) is a well-known NP-hard combinatorial optimization problem, which has wide applications in network design, integrated circuit layout, bioinformatics, and other fields. However, traditional algorithms often struggle to balance efficiency and solution quality when dealing with large-scale STP instances. In this paper, we propose a new quantum annealing-based algorithm for solving the STP: we first model the STP into a quadratic unconstrained binary optimization (QUBO) form suitable for quantum annealing, then design a corresponding encoding strategy, and finally verify the algorithm through experimental tests. The results show that our quantum annealing-based method can obtain high-quality solutions with relatively low computational overhead for moderate-scale STP instances, providing a new feasible path for handling this intractable combinatorial optimization problem.
Quantum and quantum-inspired optimisation algorithms are designed to solve problems represented in binary, quadratic and unconstrained form. Combinatorial optimisation problems are therefore often formulated as Quadratic Unconstrained Binary Optimisation Problems (QUBO) to solve them with these algorithms. Moreover, these QUBO solvers are often implemented using specialised hardware to achieve enormous speedups, e.g. Fujitsu's Digital Annealer (DA) and D-Wave's Quantum Annealer. However, these are single-objective solvers, while many real-world problems feature multiple conflicting objectives. Thus, a common practice when using these QUBO solvers is to scalarise such multi-objective problems into a sequence of single-objective problems. Due to design trade-offs of these solvers, formulating each scalarisation may require more time than finding a local optimum. We present the first attempt to extend the algorithm supporting a commercial QUBO solver as a multi-objective solver that is not based on scalarisation. The proposed multi-objective DA algorithm is validated on the bi-objective Quadratic Assignment Problem. We observe that algorithm performance significantly depends on the archiving strategy adopted, and that combining DA with non-scalarisation methods to optimise multiple objectives outperforms the current scalarised version of the DA in terms of final solution quality.
This paper investigates several Quadratic Unconstrained Binary optimisation (QUBO) formulations for the parallel machine scheduling problem P m | | C max with the goal of assessing their suitability for quantum annealing and related heuristic optimisation methods. Three QUBO models are constructed, ranging from formulations derived from classical integer and one-hot encodings to a more compact load-balancing based representation. Extensive computational experiments using Simulated Annealing (SA) and Quantum Annealing (QA) reveal substantial differences in scalability and solution quality among the formulations. The alternative load-balanced model consistently yields near-optimal makespans, typically within 1%–3% of the theoretical lower bound, highlighting its stability and effectiveness compared to the more penalty sensitive formulations, whose performance deteriorates for larger instances. Sensitivity analyses further reveal that the appropriate selection of penalty weights and problem-specific parameter tuning significantly influences both solution accuracy and computational effort in QUBO formulations. While current quantum hardware limitations restrict experimentation to small problem sizes, the findings illustrate how compact QUBO designs can better exploit quantum optimisation frameworks. The insights gained in this study provide practical modelling guidelines for future quantum scheduling research and lay the groundwork for extending QUBO-based approaches to more complex scheduling environments. • Three QUBO formulations are compared for identical parallel machine scheduling. • A compact load-balancing QUBO avoids auxiliary variables. • Load balancing yields makespans on average within 1–3%. • Both simulated and quantum annealing produce near-optimal schedules. • Penalty selection and encoding strongly affect scalability and solution quality.
Annealing machines specialized for combinatorial optimization problems have been developed, and some companies offer services to use those machines. Such specialized machines can only handle binary variables, and their input format is the quadratic unconstrained binary optimization (QUBO) formulation. Therefore, discretization is necessary to solve problems with continuous variables. However, there is a severe constraint on the number of binary variables with such machines. Although the simple binary expansion in the previous research requires many binary variables, we need to reduce the number of such variables in the QUBO formulation due to the constraint. We propose a discretization method that involves using correlations of continuous variables. We numerically show that the proposed method reduces the number of necessary binary variables in the QUBO formulation without a significant loss in prediction accuracy.