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Balázs Kulcsár

Publications and source records attributed to Balázs Kulcsár.

At least 19 recordsLinked to original sources
arXiv2026

GREAT: A Graph Edge Attention Network for the Electric Vehicle Routing Problem with Asymmetric Costs

Due to the ongoing electrification of transportation systems, energy-based routing problems such as the Electric Vehicle Routing Problem (EVRP) are becoming increasingly important. Unlike Euclidean routing problems, the EVRP involves asymmetric energy costs caused by road topology. Existing learning-based routing approaches are based on graph neural networks (GNNs) or transformer architectures operating on Euclidean node coordinates, making them poorly suited for asymmetric, non-Euclidean edge-based metrics such as energy consumption. To address this, we propose the Graph Edge Attention Network (GREAT), a novel GNN-related architecture that operates purely in edge space rather than on node coordinates, making it naturally compatible with asymmetric routing costs. Integrated into an end-to-end reinforcement learning framework, GREAT jointly optimizes routing and charging decisions for the EVRP. We train the model using real-world energy consumption data from San Francisco, derived from physical road networks enriched with topological features, and evaluate generalization on datasets from San Francisco, Vienna, and Gothenburg. Across diverse battery sizes (15-40 kWh) and customer demand distributions, GREAT outperforms a strong HGS-based EVRP heuristic in most tested settings, achieving energy reductions of up to 8.78% while reducing runtime by a factor of 60. Moreover, we benchmark against a custom adaptive large neighborhood search (ALNS) that jointly optimizes routing and charging. GREAT achieves competitive performance at a faster runtime, and we show that the ALNS can profit from a warm start with the GREAT solution. We further evaluate GREAT on standard (asymmetric) routing problems, including Traveling Salesman Problem, Capacitated Vehicle Routing Problem, and Orienteering Problem, where it achieves state-of-the-art performance among neural methods for non-Euclidean settings.

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arXiv2026

GREAT-ESDD: Graph Edge Attention Network for Effectively Steered Delivery Decisions

Online, same-day delivery requires operators to constantly update their routes, and the routing cost for deliveries increases with the number of customers. Out-of-home (OOH) delivery options can help companies handle increasing customer numbers while keeping delivery costs low. We develop a dynamic pricing-and-routing framework for this online ordering scenario with home and OOH delivery options. First, we develop a neural solver for the capacitated vehicle routing problem (CVRP) based on the Graph-Edge-Attention-Network (GREAT). We train it to solve CVRP with varying instance sizes and starting conditions, allowing it to reoptimize partially executed routes under changing conditions. It is fast while achieving solution quality competitive with traditional baselines. Our solver processes several CVRP instances in parallel in batches and we use it to solve the candidate routing problems that arise from an incoming customer's choice of home or OOH delivery. This provides an estimate of the delivery cost increase per option, which we use to set dynamic prices. Further, it directly provides the updated route once the customer decides. We trade off delivery fees against routing costs and steer customers toward OOH delivery when home delivery would be costly. However, effective steering requires us to know the customer preferences. To learn those online, we use Thompson sampling with a Laplace-approximated posterior. We call the resulting framework GREAT-ESDD (GREAT for Effectively Steered Delivery Decisions). Compared to a traditional routing solver, it increases profit by around 11% under a similar pricing decision time budget. Moreover, we show that we can estimate customer preferences successfully, outperforming a static pricing strategy after only 5 days of simulated operations.

cs.AI↗
arXiv2026

Two-Stage Learned Decomposition for Scalable Routing on Multigraphs

Most neural methods for Vehicle Routing Problems (VRPs) are limited to Euclidean settings or simple graphs. In this work, we instead consider multigraphs, where parallel edges represent distinct travel options with varying trade-offs (e.g., distance vs. time). Multigraphs are highly relevant in practice, yet few neural methods are designed for them, and those that do exist face major scalability issues. We address these scalability issues with Node-Edge Policy Factorization (NEPF), which splits the routing policy into a node permutation stage and an edge selection stage. To enable the decomposition, we introduce a pre-encoding edge aggregation scheme and a non-autoregressive architecture for the edge stage, as well as a hierarchical reinforcement learning method to train the stages jointly. Our experiments across six VRP variants demonstrate that NEPF trains and runs up to orders of magnitude faster than prior neural multigraph methods and scales to considerably larger instances, while matching or improving on their solution quality.

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arXiv2026

Assortment Control Unlocks the Value of Dynamic Pricing in Mixed Last-Mile Delivery

The growth of e-commerce has intensified the need for last-mile delivery systems that can jointly manage customer choice and operational efficiency. We study the Dynamic Offering and Pricing of Mixed Delivery Options problem, in which a logistics service provider dynamically selects and prices attended home-delivery time slots and out-of-home pickup options for sequentially arriving customers. Each decision affects immediate revenue, customer acceptance, and the route-dependent fulfillment cost realized at the end of the booking horizon. We formulate DOPMDO as a finite-horizon Markov decision process and propose State-Value Anchored Pricing via Approximate Dynamic Programming. The method learns a continuation-value approximation on an aggregate state representation of the mixed-delivery system and uses accepted-versus-rejected value differences to estimate option-level opportunity costs. These opportunity costs are embedded in an anchored trust-region pricing problem around a calibrated fine-static benchmark. Computational experiments on the real-world Seattle instance show that SVAP--ADP increases mean episode profit by 7.0\% relative to current practice (95\% CI: 6.7--7.2\%), primarily by reducing terminal fulfillment cost while maintaining a stable home--locker--opt-out mix. Assortment-control experiments show that dynamic pricing is most effective when the menu exposes operationally valuable locker alternatives, with richer candidate pools delivering substantially larger gains than restricted nearest-locker menus. These results indicate that anticipatory pricing and assortment control are complementary: pricing steers customers toward lower-cost options, but the menu determines whether high-value consolidation opportunities are available in the first place.

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arXiv2026

Probabilistic Physics-Aware Machine Learning Predictions of Electric Truck Energy Consumption with Field Data

In this work, we incorporate first principle physics into the construction of data-driven methods by considering a model that accounts for the different sources of energy losses during vehicle operations. Our results show that Bayesian linear regression based on this physics-aware model can improve the reliability of the expected energy consumption, as compared with standard linear regression. Further, it is shown that more complex machine learning models such as neural networks and gradient boosted regression trees, based on the same physical model, can further improve the accuracy in energy forecasting and significantly outperform standard versions of the same machine learning models. In addition to point predictions of the energy consumption, we develop a framework for estimating the corresponding uncertainty in the form of predicted standard deviation. Our results show that all of the models learn to estimate the uncertainty reasonably well.

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arXiv2026

Joint Planning and Scheduling of Modular Vehicles for Passenger-Freight Integration

This paper proposes a modular vehicle system for passenger-freight integration along a bidirectional transit corridor. The system uses homogeneous units that can be coupled into vehicles and assigned to either passenger or freight service. Freight is carried by dedicated units, with loading and unloading coordinated with docking and undocking and separated from passenger boarding and alighting. To better respond to uncertain passenger demand and integrate freight transport, vehicles can be reconfigured at intermediate stations, where they can also depart and terminate. We jointly optimize departure-specific service routes, timetables, vehicle compositions, unit schedules, and passenger-freight demand assignments, with unit reuse constrained by explicit docking and undocking times. These decisions are modeled on a space-time-state network and formulated as a stochastic mixed-integer program that minimizes unit deployment costs, passenger waiting costs, and penalties for unmet freight demand. Passenger demand uncertainty is addressed using linearized chance constraints. To solve the problem, we develop an exact Benders decomposition algorithm with valid inequalities and a warm-start strategy, together with a tailored decomposition-based heuristic for larger instances. Computational experiments on instances generated from representative transit corridors in Gothenburg demonstrate the effectiveness of the Benders algorithm for small- and medium-sized instances and the scalability of the heuristic for larger problems. Sensitivity analyses highlight the value of accounting for passenger demand uncertainty and the effects of temporal overlap between passenger and freight demand. Comparisons with benchmark transit systems further demonstrate the operational advantages of the proposed modular integrated system.

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arXiv2026

Combined Stochastic and Robust Optimization for Electric Autonomous Mobility-on-Demand with Nested Benders Decomposition

The electrification and automation of mobility are reshaping how cities operate on-demand transport systems. Managing Electric Autonomous Mobility-on-Demand (EAMoD) fleets effectively requires coordinating dispatch, rebalancing, and charging decisions under multiple uncertainties, including travel demand, travel time, energy consumption, and charger availability. We address this challenge with a combined stochastic and robust model predictive control (MPC) framework. The framework integrates spatio-temporal Bayesian neural network forecasts with a multi-stage stochastic optimization model, formulated as a large-scale mixed-integer linear program. To ensure real-time applicability, we develop a tailored Nested Benders Decomposition that exploits the scenario tree structure and enables efficient parallelized solution. Stochastic optimization is employed to anticipate demand and infrastructure variability, while robust constraints on energy consumption and travel times safeguard feasibility under worst-case realizations. We evaluate the framework using high-fidelity simulations of San Francisco and Chicago. Compared with deterministic, reactive, and robust baselines, the combined stochastic and robust approach reduces median passenger waiting times by up to 36% and 95th-percentile delays by nearly 20%, while also lowering rebalancing distance by 27% and electricity costs by more than 35%. We also conduct a sensitivity analysis of battery size and vehicle efficiency, finding that energy-efficient vehicles maintain stable performance even with small batteries, whereas less efficient vehicles require larger batteries and greater infrastructure support. Our results emphasize the importance of jointly optimizing predictive control, vehicle capabilities, and infrastructure planning to enable scalable, cost-efficient EAMoD operations.

eess.SY↗
arXiv2026

Beyond Simple Graphs: Neural Multi-Objective Routing on Multigraphs

Learning-based methods for routing have gained significant attention in recent years, both in single-objective and multi-objective contexts. Yet, existing methods are unsuitable for routing on multigraphs, which feature multiple edges with distinct attributes between node pairs, despite their strong relevance in real-world scenarios. In this paper, we propose two graph neural network-based methods to address multi-objective routing on multigraphs. Our first approach operates directly on the multigraph by autoregressively selecting edges until a tour is completed. The second model, which is more scalable, first simplifies the multigraph via a learned pruning strategy and then performs autoregressive routing on the resulting simple graph. We evaluate both models empirically, across a wide range of problems and graph distributions, and demonstrate their competitive performance compared to strong heuristics and neural baselines.

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arXiv2026

GREAT-EER: Graph Edge Attention Network for Emergency Evacuation Responses

Emergency situations that require the evacuation of urban areas can arise from man-made causes (e.g., terrorist attacks or industrial accidents) or natural disasters, the latter becoming more frequent due to climate change. As a result, effective and fast methods to develop evacuation plans are of great importance. In this work, we identify and propose the Bus Evacuation Orienteering Problem (BEOP), an NP-hard combinatorial optimization problem with the goal of evacuating as many people from an affected area by bus in a short, predefined amount of time. The purpose of bus-based evacuation is to reduce congestion and disorder that arises in purely car-focused evacuation scenarios. To solve the BEOP, we propose a deep reinforcement learning-based method utilizing graph learning, which, once trained, achieves fast inference speed and is able to create evacuation routes in fractions of seconds. We can bound the gap of our evacuation plans using an MILP formulation. To validate our method, we create evacuation scenarios for San Francisco using real-world road networks and travel times. We show that we achieve near-optimal solution quality and are further able to investigate how many evacuation vehicles are necessary to achieve certain bus-based evacuation quotas given a predefined evacuation time while keeping run time adequate.

cs.AI↗
arXiv2026

Learning to Dial-a-Ride: A Deep Graph Reinforcement Learning Approach to the Electric Dial-a-Ride Problem

Urban mobility systems are transitioning toward electric, on-demand services, creating operational challenges for fleet management under energy and service-quality constraints. The Electric Dial-a-Ride Problem (E-DARP) extends the classical dial-a-ride problem by incorporating limited battery capacity and nonlinear charging dynamics, increasing computational complexity and limiting the scalability of exact methods for real-time use. This paper proposes a deep reinforcement learning approach based on an edge-centric graph neural network encoder and an attention-driven route construction policy. By operating directly on edge attributes such as travel time and energy consumption, the method captures non-Euclidean, asymmetric, and energy-dependent routing costs in real road networks. The learned policy jointly optimizes routing, charging, and service quality without relying on Euclidean assumptions or handcrafted heuristics. The approach is evaluated on two case studies using ride-sharing data from San Francisco. On benchmark instances, the method achieves solutions within 0.4% of best-known results while reducing computation times by orders of magnitude. A second case study considers large-scale instances with up to 250 request pairs, realistic energy models, and nonlinear charging. On these instances, the learned policy outperforms Adaptive Large Neighborhood Search (ALNS) by 9.5% in solution quality while achieving 100% service completion, with inference times under 10 seconds compared to hours for the metaheuristic. Finally, sensitivity analyses quantify the impact of battery capacity, fleet size, ride-sharing capacity, and reward weights, while robustness experiments show that deterministically trained policies generalize effectively under stochastic conditions.

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arXiv2024

Robust $H_{\infty}$ Position Controller for Steering Systems

This paper presents a robust position controller for electric power assisted steering and steer-by-wire force-feedback systems. A position controller is required in steering systems for haptic feedback control, advanced driver assistance systems and automated driving. However, the driver's \textit{physical} arm impedance causes an inertial uncertainty during coupling. Consequently, a typical position controller, i.e., based on single variable, becomes less robust and suffers tracking performance loss. Therefore, a robust position controller is investigated. The proposed solution is based on the multi-variable concept such that the sensed driver torque signal is also included in the position controller. The subsequent solution is obtained by solving the LMI$-H_{\infty}$ optimization problem. As a result, the desired loop gain shape is achieved, i.e., large gain at low frequencies for performance and small gain at high frequencies for robustness. Finally, frequency response comparison of different position controllers on real hardware is presented. Experiments and simulation results clearly illustrate the improvements in reference tracking and robustness with the proposed $H_\infty$ controller.

eess.SY↗
arXiv2024

Less Is More -- On the Importance of Sparsification for Transformers and Graph Neural Networks for TSP

Most of the recent studies tackling routing problems like the Traveling Salesman Problem (TSP) with machine learning use a transformer or Graph Neural Network (GNN) based encoder architecture. However, many of them apply these encoders naively by allowing them to aggregate information over the whole TSP instances. We, on the other hand, propose a data preprocessing method that allows the encoders to focus on the most relevant parts of the TSP instances only. In particular, we propose graph sparsification for TSP graph representations passed to GNNs and attention masking for TSP instances passed to transformers where the masks correspond to the adjacency matrices of the sparse TSP graph representations. Furthermore, we propose ensembles of different sparsification levels allowing models to focus on the most promising parts while also allowing information flow between all nodes of a TSP instance. In the experimental studies, we show that for GNNs appropriate sparsification and ensembles of different sparsification levels lead to substantial performance increases of the overall architecture. We also design a new, state-of-the-art transformer encoder with ensembles of attention masking. These transformers increase model performance from a gap of $0.16\%$ to $0.10\%$ for TSP instances of size 100 and from $0.02\%$ to $0.00\%$ for TSP instances of size 50.

cs.LG↗
arXiv2023

Integrated Charging Scheduling and Operational Control for an Electric Bus Network

The last few years have seen the massive deployment of electric buses in many existing transit networks. However, the planning and operation of an electric bus system differ from that of a bus system with conventional vehicles, and some key problems have not yet been studied in the literature. In this work, we address the integrated operational control and charging scheduling problem for a network of electric buses with a limited opportunity charging capacity. We propose a hierarchical control framework to solve this problem, where the charging and operational decisions are taken jointly by solving a mixed-integer linear program in the high-level control layer. Since this optimization problem might become very large as more bus lines are considered, we propose to apply Lagrangian relaxation in such a way as to exploit the structure of the problem and enable a decomposition into independent subproblems. A local search heuristic is then deployed in order to generate good feasible solutions to the original problem. This entire Lagrangian heuristic procedure is shown to scale much better on transit networks with an increasing number of bus lines than trying to solve the original problem with an off-the-shelf solver. The proposed procedure is then tested in the high-fidelity microscopic traffic environment Vissim on a bus network constructed from an openly available dataset of the city of Chicago. The results show the benefits of combining the charging scheduling decisions together with the real-time operational control of the vehicles as the proposed control framework manages to achieve both a better level of service and lower charging costs over control baselines with predetermined charging schedules.

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arXiv2023

Critical Zones for Comfortable Collision Avoidance with a Leading Vehicle

This paper provides a general framework for efficiently obtaining the appropriate intervention time for collision avoidance systems to just avoid a rear-end crash. The proposed framework incorporates a driver comfort model and a vehicle model. We show that there is a relationship between driver steering manoeuvres based on acceleration and jerk, and steering angle and steering angle rate profiles. We investigate how four different vehicle models influence the time when steering needs to be initiated to avoid a rear-end collision. The models assessed were: a dynamic bicycle model (DM), a steady-state cornering model (SSCM), a kinematic model (KM) and a point mass model (PMM). We show that all models can be described by a parameter-varying linear system. We provide three algorithms for steering that use a linear system to compute the intervention time efficiently for all four vehicle models. Two of the algorithms use backward reachability simulation and one uses forward simulation. Results show that the SSCM, KM and PMM do not accurately estimate the intervention time for a certain set of vehicle conditions. Due to its fast computation time, DM with a backward reachability algorithm can be used for rapid offline safety benefit assessment, while DM with a forward simulation algorithm is better suited for online real-time usage.

cs.RO↗
arXiv2023

Controlled Descent Training

In this work, a novel and model-based artificial neural network (ANN) training method is developed supported by optimal control theory. The method augments training labels in order to robustly guarantee training loss convergence and improve training convergence rate. Dynamic label augmentation is proposed within the framework of gradient descent training where the convergence of training loss is controlled. First, we capture the training behavior with the help of empirical Neural Tangent Kernels (NTK) and borrow tools from systems and control theory to analyze both the local and global training dynamics (e.g. stability, reachability). Second, we propose to dynamically alter the gradient descent training mechanism via fictitious labels as control inputs and an optimal state feedback policy. In this way, we enforce locally $\mathcal{H}_2$ optimal and convergent training behavior. The novel algorithm, \textit{Controlled Descent Training} (CDT), guarantees local convergence. CDT unleashes new potentials in the analysis, interpretation, and design of ANN architectures. The applicability of the method is demonstrated on standard regression and classification problems.

math.OC↗
arXiv2023

A Predictive Chance Constraint Rebalancing Approach to Mobility-on-Demand Services

This paper considers the problem of supply-demand imbalances in Mobility-on-Demand (MoD) services, such as Uber or DiDi Rider. Such imbalances are due to uneven stochastic travel demand and can be prevented by proactively rebalance empty vehicles. To this end we propose a method that include estimated stochastic travel demand patterns into stochastic model predictive control (SMPC) for rebalancing of empty vehicles MoD ride-hailing service. More precisely, we first estimate passenger travel demand using Gaussian Process Regression (GPR), which provides demand uncertainty bounds for time pattern prediction. We then formulate a SMPC for the autonomous ride-hailing service and integrate demand predictions with uncertainty bounds into a receding horizon MoD optimization. In order to guarantee constraint satisfaction in the above optimization under estimated stochastic demand prediction, we employ a probabilistic constraining method with user defined confidence interval. Receding horizon MoD optimization with probabilistic constraints thereby calls for Chance Constrained Model Predictive Control (CCMPC). The benefits of the proposed method are twofold. First, travel demand uncertainty prediction from data can naturally be embedded into the MoD optimization framework. We show that for a given minimal fleet size the imbalance in each station can be kept below a certain threshold with a user defined probability. Second, CCMPC can further be relaxed into a Mixed-Integer-LP (MILP) and we show that the MILP can be solved as a corresponding Linear-Program which always admits a integral solution. Finally, we demonstrate through high-fidelity transportation simulations, that by tuning the confidence bound on the chance constraint close to optimal oracle performance can be achieved. The corresponding median customer wait time is reduced by 4% compared to using only the mean prediction of the GPR.

eess.SY↗
arXiv2022

Conflict-free Charging and Real-time Control for an Electric Bus Network

The rapid adoption of electric buses by transit agencies around the world is leading to new challenges in the planning and operation of bus networks. In particular, the limited driving range of electric vehicles imposes operational constraints such as the need to charge buses during service. Research on this topic has mostly focused on the strategic and tactical planning aspects until now, and very little work has been done on the real-time operational aspect. To remedy this, we propose integrating the charging scheduling problem with a real-time speed control strategy in this paper. The control problem is formulated as a mixed-integer linear program and solved to optimality with the branch-and-bound method. Simulations are carried out by repeatedly solving the control problem in a receding horizon fashion over a full day of operation. The results show that the proposed controller manages to anticipate and avoid potential conflicts where the charging demand exceeds the charger capacity. This feature makes the controller achieve lower operational costs, both in terms of service regularity and energy consumption, compared to a standard first-come, first-served charging scheme.

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arXiv2022

Constrained Policy Gradient Method for Safe and Fast Reinforcement Learning: a Neural Tangent Kernel Based Approach

This paper presents a constrained policy gradient algorithm. We introduce constraints for safe learning with the following steps. First, learning is slowed down (lazy learning) so that the episodic policy change can be computed with the help of the policy gradient theorem and the neural tangent kernel. Then, this enables us the evaluation of the policy at arbitrary states too. In the same spirit, learning can be guided, ensuring safety via augmenting episode batches with states where the desired action probabilities are prescribed. Finally, exogenous discounted sum of future rewards (returns) can be computed at these specific state-action pairs such that the policy network satisfies constraints. Computing the returns is based on solving a system of linear equations (equality constraints) or a constrained quadratic program (inequality constraints, regional constraints). Simulation results suggest that adding constraints (external information) to the learning can improve learning in terms of speed and transparency reasonably if constraints are appropriately selected. The efficiency of the constrained learning was demonstrated with a shallow and wide ReLU network in the Cartpole and Lunar Lander OpenAI gym environments. The main novelty of the paper is giving a practical use of the neural tangent kernel in reinforcement learning.

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