Quantum-Driven Optimisation in Agent-Based Transport Models: Early Lessons from Applying QUBO to Freight Logistics

XXX-X-XXXX-XXXX-X/XX/$XX.00 ©20XX IEEE Quantum-Driven Optimisation in Agent-Based Transport Models: Early Lessons from Applying QUBO to Freight Logistics Siti Fariya School of Social Sciences Heriot-Watt University Edinburgh, United Kingdom [email protected] Dhanan Sarwo Utomo School of Social Sciences Heriot-Watt University Edinburgh, United Kingdom [email protected] Abstract— This paper presents a conceptual framework for integrating quantum-driven optimisation into agent-based transport models (ABMs) to address congestion management challenges in freight logistics. Focusing on a busy roll-on/roll-off (Ro-Ro) gateway in Southeast England, we formulate the traffic flow optimisation problem as a MaxCut Quadratic Unconstrained Binary Optimisation (QUBO) problem. Using ORCA Computing’s PT-Series photonic quantum hardware, we apply quantum solvers to predict congestion states across critical port zones. These QUBO outputs are then embedded into an ABM to dynamically adjust vehicle routing and zone capacities, creating a hybrid quantum-classical workflow. We share early lessons from this integration, including insights into problem formulation, solver interpretation, and system coupling. This work provides foundational understanding and practical guidance for applying quantum-inspired methods to real-world transport systems and outlines future directions toward scalable, real-time hybrid logistics optimisation. Keywords— Quantum optimisation, QUBO, MaxCut, agentbased modelling, freight logistics, traffic flow, quantum-classical integration, congestion management, photonic quantum computing, hybrid workflows I. INTRODUCTION The freight logistics sector is under increasing pressure to improve operational efficiency, minimise congestion, and meet ambitious decarbonisation targets. Roll-on/roll-off (RoRo) terminals in Southeast England play a pivotal role in UK-EU trade, handling vast flows of trucks, passenger vehicles, and ferries. However, their operations are highly sensitive to disruptions, particularly during peak periods when demand surges and infrastructure constraints collide. Traditional approaches to optimising port and terminal operations, such as heuristics, metaheuristics, and rule-based methods, have provided valuable insights but face limitations when confronted with the complex, dynamic, and highdimensional nature of real-world transport systems. This has led to rising interest in advanced computational paradigms that can address these challenges more effectively. Among these, quantum optimisation, specifically through Quadratic Unconstrained Binary Optimisation (QUBO) formulations, has appeared as a promising tool. By translating complex decision problems into a mathematical format that can be processed by quantum hardware, QUBO-based approaches open new possibilities for tackling combinatorial and dynamic problems that have traditionally been challenging. Building on insights from the Quantum Technology Access Programme (QTAP) Digital Catapult in United Kingdom, a 6-month innovation programme giving innovator and companies hands-on access to quantum hardware, simulators, and expert support to explore real-world use cases and assess the potential of quantum technologies. This paper focuses on integrating QUBO optimisation outputs into an agent-based transport model (ABM), resulting in a hybrid quantum-classical workflow tailored to Ro-Ro terminal operations in Southeast England. We apply QUBO-driven vehicle allocation strategies to reduce congestion and improve throughput. Our contributions: 1. We demonstrate the practical set in of QUBO-based quantum optimisation within detailed ABMs for freight logistics. 2. We provide early insights into scalability, model translation, and real-time integration challenges faced by hybrid workflows. This work offers foundational lessons for deploying quantum optimisation in real-world transport systems, placing the groundwork for future advancements in quantum-assisted logistics planning. II. LITERATURE REVIEW The evolution of global supply chains and the rise of containerisation have significantly increased the operational demands on ports and terminals [1]. In response, the field of operations research has developed a wide range of optimisation techniques, particularly for container terminals and RoRo operations, including heuristic and metaheuristic approaches [2]. While these methods have yielded notable improvements, they often fall short when addressing the intricate, stochastic, and large-scale nature of modern transport systems, especially under peak demand conditions. In recent years, there has been growing attention to quantum optimisation, which offers a fundamentally different computational paradigm. The QUBO formulation has become central, enabling the mapping of many NP-hard optimisation problems onto quantum hardware [3]. Solving NP-hard problems with traditional optimisation methods is often computationally intensive, as the solution space grows exponentially with problem size. This leads to long computation times or the need for heuristic approaches, which may only deliver approximate solutions. Early studies have shown promising applications in logistics and transport contexts. For example, Neukart et al. [4] applied quantum 2 annealers to optimise traffic flow, highlighting potential advantages over classical approaches. Ajagekar et al. [5] developed hybrid quantum-classical approaches for largescale discrete–continuous problems in chemical engineering, demonstrating the versatility of quantum methods across domains. Venturelli et al. [6] explored spin-glass models using quantum optimisation, providing valuable insights into algorithmic scalability and performance on complex combinatorial problems. Using the QUBO formulation, quantum approaches can explore large solution spaces in parallel and escape local minima more effectively, offering potential advantages over classical methods for tackling NPhard problems. Despite these advances, little research has explored how quantum optimisation can be meaningfully embedded within simulation frameworks such as agent-based models (ABMs). ABMs are powerful tools for simulating the behaviours of heterogeneous agents, such as vehicles, operators, and infrastructure and for capturing emergent system-level dynamics. Integrating QUBO-optimised decisions into ABMs offers potential for real-time, adaptive logistics management, yet this intersection remains largely unexplored. To address this gap, the present study proposes a conceptual and computational framework for embedding QUBO-based optimisation within an agent-based transport model of RoRo terminal operations. In doing so, it contributes to the emerging field of hybrid quantum-classical workflows for freight logistics, offering practical insights for researchers and practitioners aiming to apply quantum technologies in transport systems. III. METHODOLOGY This work presents a conceptual framework for integrating quantum-driven optimisation into transport ABMs to explore congestion management strategies in freight logistics. The approach combines a QUBO formulation of the traffic flow problem, quantum solver execution, and integration of solver outputs into an agentbased simulation. A. Graph-Based System Representation We represent the Ro-Ro terminal as a graph, where nodes correspond to key operational zones (e.g., buffer area, UK border control, random checks, check-in points, freight queue, tourist queue) and edges represent the direct connections between zones. This graph structure captures the spatial and functional relationships between system components and serves as the basis for defining congestion interactions. Figure 1. Graph representation of the Ro-Ro terminal system. In Figure 1. nodes represent key operational zones, and edges represent physical or operational connections between them. This graph forms the basis for defining the QUBO congestion minimisation problem. B. QUBO Formulation The objective is to minimise congestion and improve throughput across key port zones, including buffer areas, inspection points, and check-in gates. We define binary decision variables xi for each zone i, where xi=1 indicates congestion and xi = 0 indicates smooth flow. The QUBO objective function seeks to partition the graph to minimise congestion propagation, with the general form: min ∑₍ᵢ,ⱼ₎∈𝐸 𝑤ᵢⱼ 𝑥ᵢ𝑥ⱼ + ∑ᵢ 𝑏ᵢ𝑥ᵢ, (1) Where xᵢ is a binary decision variable (1 if node i is predicted congested, 0 otherwise), wᵢⱼ is the interaction weight between connected nodes i and j, and bᵢ is the node-specific bias or penalty term. We implemented the QUBO formulation in Python, using libraries such as networkx and numpy to build the adjacency matrix and define interaction terms. C. Quantum Solver Execution We prepared The QUBO problem was submitted to ORCA Computing’s PT-Series photonic quantum hardware, using their Binary Bosonic Solver. The PT-Series is a type of quantum computer that uses photons (particles of light) for computation; it’s ORCA Computing’s branded platform designed to tackle optimisation and machine learning problems. The Binary Bosonic Solver (BBS) is an algorithm developed by ORCA Computing to solve binary optimisation problems, especially those formulated as QUBO (Quadratic Unconstrained Binary Optimisation) problems, using their photonic quantum hardware. The solver returns binary solutions representing predicted congestion patterns across the terminal network. To address variability inherent in current near-term quantum devices, multiple solver runs were performed, and the solution landscape was analysed across different configurations. Figure 2 shows the convergence behaviour of four solver configurations (config1 - config4) over 80 updates. The y-axis represents the objective function value, while the x-axis shows the update steps. Figure 2. Objective function evolution across quantum solver configurations. This illustrates variability between runs and highlights the importance of multi-run analysis to identify stable, highquality solutions. 3 D. Postprocessing Following quantum solver execution, a postprocessing phase translates the binary output vector into actionable system parameters for the transport ABMs. This involves mapping binary variables (e.g., congestion/no-congestion per zone) into routing priorities, lane capacities, or operational adjustments. The agent-based model (ABM) simulates individual agents, such as freight vehicles, passenger cars, and control infrastructure, each with defined objectives, for example, minimising travel time, following optimal routes, or managing traffic flow. This step is essential to bridge the quantum solution layer with the micro-level ABM environment, ensuring that agents operate within realistic, interpretable system states. E. Agent-Based Model Integration The ABMs simulates the detailed, micro-level behaviours of individual vehicle agents, including freight trucks, passenger cars, and ferries, operating within the Ro-Ro terminal system. The ABM captures how agents make decisions about lane choice, queueing, and processing at checkpoints, while interacting dynamically with both the physical infrastructure and other agents. Figure 3. Conceptual workflow for integrating QUBO-based quantum optimisation into an agent-based transport model. The integration of the QUBO-derived congestion outputs into the ABM is designed as a conceptual coupling layer where optimisation results influence both agent behaviours and system-level parameters. Specifically, the integration operates across three interconnected pathways: • Informing agent routing decisions. The QUBO solver provides binary predictions of congestion states across the network, where each node (e.g., buffer zone, check-in, inspection point) is marked as congested or free-flowing. In the ABM, these congestion signals are used to bias agent decision-making, steering vehicles away from predicted bottlenecks when alternative routes or lanes are available. For example, trucks approaching a congested buffer lane may be probabilistically reassigned to neighbouring, less congested lanes, or cars may be rerouted toward underused check-in booths. • Adjusting system-level parameters Beyond individual agent decisions, the QUBO outputs also inform macro-level system adjustments, such as processing capacities at certain checkpoints can be dynamically reduced if the solver predicts a congestion buildup, reflecting realistic slowdowns under heavy load. Alternatively, additional resources (e.g., activating backup lanes, opening extra booths) can be simulated when congestion hotspots are detected, modelling operational responses. These adjustments allow the ABM to explore how quantum-optimised interventions affect system performance at multiple scales. • Exploring emergent system dynamics. Through running comparative ABM simulations under baseline (no quantum input) and quantuminformed scenarios, the framework enables conceptual exploration of how quantum-guided interventions reshape traffic patterns and queue distributions. Specifically, it examines whether congestion is effectively mitigated system-wide or merely shifted to other zones, and how local quantum-informed decisions propagate through the network to influence aggregate performance indicators, such as average waiting times, throughput, and queue lengths. The primary aim is not to compare the computational speed of quantum versus classical solvers, but rather to assess the quality and optimality of the solutions in improving system performance. F. Feedback Loop After the ABM simulation, system performance is evaluated using key indicators such as throughput, waiting times, and queue lengths. This analysis helps identify areas where the QUBO-derived solutions were too rigid or lacked detail. Insights from these results are then used to refine the QUBO formulation, adjust problem variables, or introduce additional objectives, creating an iterative process that improves solution quality and system performance. The most advanced hybrid workflow operates as a continuous QUBO - ABM – QUBO - ABM loop, where quantum optimisation and agent-based simulation repeatedly inform and improve each other. This integration serves as an early-stage proof of concept for hybrid quantum-classical workflows in transport logistics, providing methodological insights into coupling static quantum outputs with dynamic agent-based simulations. While currently exploratory, the approach offers a pathway for future research into real-time, scalable, and generalisable quantum-assisted transport management systems. Figure 3 summarises this hybrid workflow, illustrating the end-to-end pipeline from system representation, QUBO formulation, and quantum solver execution, through to postprocessing and integration within the ABM simulation. IV. EARLY LESSONS AND LEARNING EXPERIENCE The integration of quantum-driven optimisation into an transport ABMs offers valuable early insights into the design 4 and potential of hybrid quantum-classical workflows for freight logistics. While this work is conceptual, several important lessons were identified during the process. A. Postprocessing of Quantum Outputs One of the key lessons is the importance of meaningful postprocessing of the raw outputs from the quantum solver. The QUBO solution provides binary values for each node, indicating predicted congestion states. However, these outputs are not immediately usable by the ABM. They must be translated into operational signals, such as adjusting zone capacities, modifying agent routing preferences, or activating alternative lanes. Without careful postprocessing, the integration risks either overreacting to noisy quantum outputs or underutilising their insights. B. Hybrid Workflow Complexity Coupling a static optimisation layer (quantum solver) with a dynamic, time-evolving agent-based simulation introduces methodological complexity. For example: • The QUBO formulation reflects a snapshot of the system but does not account for temporal dynamics. • The ABM must decide how frequently to update its parameters based on quantum outputs and how to reconcile possible mismatches between the quantum model and the simulation scale. • This hybrid design requires thoughtful interfacing between the two components to ensure consistent and interpretable outcomes. C. Variability and Stability Current near-term quantum devices, such as photonic quantum processors, are inherently stochastic and sensitive to problem scaling. • Multiple solver runs are often needed to stabilise the outputs and identify consistent congestion patterns. • This raises questions about how to design robust aggregation strategies or post selection methods to filter meaningful signals from noisy quantum solutions. D. Conceptual Opportunities Despite these challenges, the study reveals promising opportunities: • Quantum outputs can serve as an additional decision layer, complementing traditional agent heuristics with global system-level optimisation insights. • Hybrid workflows enable experimentation with new forms of adaptive, data-informed control in transport systems. • The approach has the potential to generalise beyond a single port setting, offering insights for airports, intermodal hubs, and urban traffic networks. E. Limitations This work is exploratory and conceptual; it does not yet provide quantitative performance benchmarks or claim operational advantages over classical optimisation methods. Scalability, real-time integration, and generalisability remain open research challenges that future work must address. V. CONCLUSION AND FUTURE WORKS This study offers one of the first conceptual explorations of integrating quantum optimisation, specifically MaxCutbased QUBO formulations, into transport ABMs for freight logistics. The hybrid quantum-classical approach introduces a promising new paradigm, combining global system-level optimisation insights from quantum solvers with micro-level behavioural detail from ABMs. One key takeaway is that quantum outputs alone are not sufficient; meaningful integration requires careful design of interfaces between the quantum and classical layers. Translating binary congestion predictions into actionable simulation adjustments involves both postprocessing and domain knowledge. Moreover, the QUBO formulation necessarily simplifies real-world system dynamics to fit current quantum hardware limits, meaning some operational nuances are abstracted away. The stochastic nature of near-term quantum devices, such as the photonic quantum processor used in this work, raises questions about solution variability and robustness. While repeated runs and post selection strategies can mitigate noise, they also increase workflow complexity. Finally, the approach raises broader methodological questions: • How frequently should static quantum optimisations be recomputed to inform dynamic systems? • How do we reconcile mismatches in timescales, resolutions, and model assumptions across the quantum and classical layers? • How scalable is the approach when moving from small system representations to real-world, highresolution transport networks? The key contribution of this work is methodological: providing early insights and design principles for coupling quantum optimisation with dynamic simulation models in logistics. While this study does not claim computational advantage or report performance benchmarks, it offers foundational lessons for future quantum-assisted transport applications. Future work will focus on several critical directions: • Scaling the QUBO formulations to larger, more complex networks. • Exploring real-time or near-real-time integration between quantum solvers and ABMs. • Investigating generalisability across different transport domains, such as urban traffic management or intermodal logistics hubs. • Incorporating richer agent behaviours and operational constraints into the hybrid modelling framework. • Exploring how ABM outputs (e.g., congestion patterns or agent interactions) can serve as adaptive inputs to update the QUBO formulation, enabling a continuous closed-loop optimisation system. 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