Recent hardware developments in quantum technologies have inspired a myriad of special-purpose hardware devices tasked to solve optimization problems. In this paper, we explore the application of Fujitsu's quantum-inspired CMOS-based Digital Annealer (DA) in solving constrained routing problems arising in transportation and logistics. More precisely in this paper, we study the vehicle sharing problem and show that the DA as a QUBO solver can potentially fill the gap between two common methods: exact solvers like Cplex and heuristics. We benchmark the scalability and quality of solutions obtained by DA with Cplex and with a greedy heuristic. Our results show that the DA is a general QUBO solver that is more robust than heuristics, and more scalable than Cplex. Our methodology and framework which focus on QUBO problems is also applicable to other quantum-inspired and fully quantum devices that are undergoing development.
Recent hardware developments in quantum technologies have inspired a myriad of special-purpose hardware devices tasked to solve optimization problems. In this paper, we explore the application of Fujitsu's quantum-inspired CMOS-based Digital Annealer (DA) in solving constrained routing problems arising in transportation and logistics. More precisely in this paper, we study the vehicle sharing problem and show that the DA as a QUBO solver can potentially fill the gap between two common methods: exact solvers like Cplex and heuristics. We benchmark the scalability and quality of solutions obtained by DA with Cplex and with a greedy heuristic. Our results show that the DA is a general QUBO solver that is more robust than heuristics, and more scalable than Cplex. Our methodology and framework which focus on QUBO problems is also applicable to other quantum-inspired and fully quantum devices that are undergoing development.
The Vehicle Routing Problem (VRP) is an NP-Hard optimization problem that has been widely studied over the last decades due to its wide practical applications. The goal of the VRP is to design efficient routes for vehicles performing service functions such as the distribution of goods from one or more central locations. There exist many variants to the VRP. These variations arise due to application-specific constraints such as vehicle capacities, delivery time windows, split deliveries, and many more. Due to the complexity of the problem, solvers are usually designed for specific variants and do not generally scale well to larger problem instances. As we approach the physical scaling limits of Moore's law, different novel special-purpose hardware are being designed for solving combinatorial optimization problems such as quantum and quantum-inspired devices. However, these devices are able to solve problems up to fixed variable sizes. In this work, we carry out experiments on the Fujitsu Digital Annealer (DA), quantum-inspired hardware, and show that we are able to get near-optimal results for instances of the Capacitated VRP (CVRP) that can be directly solved on the DA. We further develop a hybrid method for solving large-scale VRP instances. In order to achieve this, we develop a novel candidate route generation method, whose core solves a multi-objective clustering problem on the DA. Once a set of candidate routes has been selected, we then solve a Set Partitioning Problem on the DA to get a final solution. We apply our method to the CVRP and the CVRP with Time-Windows and show that we are able to get near-optimal solutions for problem instances significantly larger the base solvers could solve directly, within the same amount of computation time.
Combinatorial optimization problems are ubiquitous in various disciplines and applications. Many heuristic algorithms have been devoted to solve these types of problems. In order to increase the efficiency for finding the optimal solutions, an application-specific hardware, called digital annealer (DA) has been developed for solving combinatorial optimization problems using quadratic unconstrained binary optimization (QUBO) formulations. In this study, we formulated the number partitioning problem and the graph partitioning problem into QUBO forms and solved such problems with the DA developed by Fujitsu Ltd. The QUBO formulation of the number partitioning problem is fully connected. The DA found the overall runtime for the optimal solution to be less than 30 seconds for 6500 binary variables. For the graph partitioning problem, we adopted modularity as the metric for determining the quality of the partitions. For Zachary's Karate Club graph, the modularity obtained was 0.445, a 6% increase against D-wave Quantum Annealer and Simulated Annealing. Moreover, to explore the DA's potential applications to real-world problems, we used the search for communities or virtual microgrids in a power distribution network as an example. The problem was formulated into graph partitioning. It is shown that the DA effectively identified community structures in the IEEE 33-bus and IEEE 118-bus network.
As Moore’s Law slows, alternative computing paradigms are essential for tackling complex combinatorial optimization problems. This paper introduces DigiQUBO, a high-performance digital Quadratic Unconstrained Binary Optimization (QUBO) solver designed for quantum-inspired optimization. DigiQUBO leverages a advanced Digital Annealing (DA) approach to efficiently solve large-scale QUBO problems, offering a competitive alternative to traditional annealing methods. To evaluate its effectiveness, DigiQUBO is applied to the Traveling Salesman Problem (TSP), a well-known NP-hard problem with applications in logistics, network design, and computational biology. In solving a 40-city Traveling Salesman Problem (TSP), DigiQUBO achieved an average route distance improvement of 13% compared to Simulated Annealing (SA), and a reduction of 37% compared to D-Wave’s LeapHybridSampler, while maintaining comparable runtime to Fujitsu DA3. DigiQUBO significantly enhances solution quality and computational efficiency by integrating two key advanced techniques: two-way one-hot group encoding for improved constraint satisfaction and Bayesian Optimization for automated annealing parameter tuning. Performance comparisons against Simulated Annealing (SA), Fujitsu DA3, and D-Wave’s LeapHybridSampler demonstrate superior results in balancing accuracy and execution time. The results highlight DigiQUBO as a promising digital annealing technology that bridges the gap between classical and quantum optimization, offering a practical and efficient solution in the post-Moore’s Law era.
Large-scale combinatorial scheduling problems -- job-shop scheduling, flow-shop scheduling, and vehicle routing among them -- remain NP-hard at practically relevant scale, and quantum computing has entered this space along two related tracks: genuinely quantum solvers, principally quantum annealers and gate-based devices running the quantum approximate optimization algorithm (QAOA), and quantum-inspired classical solvers, such as coherent Ising machines and digital annealers, that borrow the same Ising/QUBO problem structure without requiring quantum hardware. This article synthesizes both tracks as applied specifically to scheduling. We trace the theoretical foundations from quantum and simulated annealing through the QUBO formulation techniques that make scheduling problems solver-ready, then review direct applications to job-shop, flow-shop, and vehicle-routing problems, reporting the concrete, verified numbers the underlying studies provide. The consistent finding is that quantum hardware remains constrained by qubit connectivity, embedding overhead, and shallow achievable circuit depth to small benchmark instances, while quantum-inspired classical solvers, unconstrained by qubit count, already reach scheduling-relevant problem sizes with reported performance competitive with or exceeding classical heuristics. We close by identifying benchmarking rigor, hardware connectivity, and the near-total absence of work on dynamic, online scheduling as the field's clearest open problems.
We present a comprehensive case study comparing the performance of D-Waves' quantum-classical hybrid framework, Fujitsu's quantum-inspired digital annealer, and Gurobi's state-of-the-art classical solver in solving a transport robot scheduling problem. This problem originates from an industrially relevant real-world scenario. We provide three different models for our problem following different design philosophies. In our benchmark, we focus on the solution quality and end-to-end runtime of different model and solver combinations. We find promising results for the digital annealer and some opportunities for the hybrid quantum annealer in direct comparison with Gurobi. Our study provides insights into the workflow for solving an application-oriented optimization problem with different strategies, and can be useful for evaluating the strengths and weaknesses of different approaches.
Quadratic unconstrained binary optimization (QUBO) models have garnered growing interests as a strong alternative modelling framework for solving combinatorial optimization problems. A wide variety of optimization problems that are usually studied using conventional Operations Research approaches can be formulated as QUBO problems. However, QUBO solvers do not guarantee optimality when solving optimization problems. Instead, obtaining high quality solutions using QUBO solvers entails tuning of multiple parameters. Here in our work, we conjecture that the initial states adjustment method used in QUBO solvers can be improved, where careful tuning will yield overall better results. We propose a data-driven multi-start algorithm that complements the QUBO solver (namely Fujitsu Digital Annealer) in solving constrained optimization problems. We implemented our algorithm on a variety of capacitated vehicle routing problem instances, and empirical results show that different initial state adjustment methods do make a difference in the quality of solutions obtained by the QUBO solver.