arXiv subjects

Richard Martin Lusby

Publications and source records attributed to Richard Martin Lusby.

5 recordsLinked to original sources

arXiv2026

An ALNS Heuristic for Large-Scale Line Planning with Mode Choice and Line Generation

Demand responsiveness is an important consideration in public transport line planning, as network design and service quality influence passenger demand. However, accounting for this interaction further complicates an already challenging combinatorial optimization problem. To address this challenge, we propose a scalable Adaptive Large Neighborhood Search (ALNS) algorithm for large-scale line planning with endogenous demand. The algorithm jointly optimizes lines and frequencies while accounting for passenger mode choice, passenger assignment, and vehicle capacities. Candidate lines are generated dynamically throughout the search, and solutions are evaluated using an embedded evaluation procedure for passenger assignment and demand estimation, together with a dedicated local search procedure for frequency optimization. The proposed methodology is evaluated on the public transport network of Odense, Denmark, comprising approximately 1,800 origin-destination pairs. Computational results demonstrate the applicability of the approach to realistic, large-scale instances. The optimized networks concentrate resources on fewer, higher-frequency services, reducing average headways from approximately 41 minutes to 6.8-13 minutes while substantially increasing public transport ridership. Furthermore, the results show that network design is highly sensitive to assumptions regarding passenger behavior, highlighting the importance of carefully calibrated demand models when incorporating demand responsiveness into line planning.

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arXiv2026

A column generation-based fixed-point heuristic for the service-aware multi-commodity flow problem

We study the Service-Aware Multi-Commodity Flow (SAMCF) problem, in which demand is elastic and governed by a logit choice model while routing is subject to hard capacity constraints. In a centralized, system-optimal setting, the network operator jointly determines how much demand to serve and how to route it. We formulate the SAMCF as a nonlinear program and propose an iterative fixed-point heuristic that alternates between solving an inelastic MCF via column generation and updating demand from the resulting service levels. Two linear approximations based on piecewise-linear demand functions and McCormick envelopes serve as benchmarks, while a piecewise-linear outer-approximation of the demand function is used to provide valid lower bounds. Computational experiments on public transport instances show that the heuristic finds near-optimal solutions in under two seconds - orders of magnitude faster than the benchmark methods - while matching their solution quality on all instances they can solve within a ten-minute time limit.

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arXiv2026

An Exact Algorithm for Public Transport Line Planning Considering Passenger and Operational Costs and Lost Demand

Line planning in public transport is the strategic problem of selecting lines and their operating frequencies. This problem is important as it defines the passenger service, based on available connections and expected travel times, and drives operational cost in terms of the number of vehicles required. This paper presents a line planning model that minimizes the weighted sum of passenger travel time, including in-vehicle time and frequency-dependent waiting and transfer times, and operating costs for the public transport agency. Unlike traditional approaches that assume demand to be fixed, our approach requires a minimum service level for demand to be captured, ensuring that services are provided only when they are attractive to users and cost-efficient to operate. The introduced capacity constraints ensure sufficient capacity on the lines and help guide the trade-off between expected demand on selected lines and their frequencies. The resulting mixed-integer program presents a challenging combinatorial problem as the number of passenger paths grows rapidly in relation to the number of lines and frequencies considered. To address this, we propose an iterative exact algorithm that utilizes a reduced problem representation and dynamically expands it with additional frequencies and paths. Evaluated on four networks with varying complexity and cost trade-offs, our method achieves significant speed-ups and tighter bounds compared to solving the complete model directly by CPLEX, particularly when operator and passenger costs are more evenly balanced in the objective. Furthermore, we demonstrate how accounting for lost demand leads to more efficient resource use from an overall perspective.

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arXiv2025

Sufficient A Priori Conditions for the Linear Relaxation of the Energy Storage Scheduling Problem

When modeling energy storage systems, an essential question is how to account for the physical infeasibility of simultaneous charge and discharge. The use of complementarity constraints or of binary variables is common, but these formulations do not scale well. Alternatively, assumptions such as perfect efficiencies or positive prices are often used to justify the choice of a linear model. In this paper, we establish new a priori conditions that guarantee the existence of an optimal solution without simultaneous charge and discharge when solving the linear relaxation of the storage scheduling problem. They are based on the characteristics of the storage system, in particular, the duration of charge. They can be valid for negative prices and with inefficiencies, thereby enlarging the set of conditions for which the complementarity constraints can be relaxed. We prove mathematically the validity of these conditions and illustrate them with practical examples. We also introduce a refined mixed-integer linear equivalent, in which the number of binary variables can be drastically reduced.

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arXiv2024

Solving the train-platforming problem via a two-level Lagrangian Relaxation approach

High-speed railway stations are crucial junctions in high-speed railway networks. Compared to operations on the tracks between stations, trains have more routing possibilities within stations. As a result, track allocation at a station is relatively complicated. In this study, we aim to solve the train platforming problem for a busy high-speed railway station by considering comprehensive track resources and interlocking configurations. A two-level space-time network is constructed to capture infrastructure information at various levels of detail from both macroscopic and microscopic perspectives. Additionally, we propose a nonlinear programming model that minimizes a weighted sum of total travel time and total deviation time for trains at the station. We apply a Two-level Lagrangian Relaxation (2-L LR) to a linearized version of the model and demonstrate how this induces a decomposable train-specific path choice problem at the macroscopic level that is guided by Lagrange multipliers associated with microscopic resource capacity violation. As case studies, the proposed model and solution approach are applied to a small virtual railway station and a high-speed railway hub station located on the busiest high-speed railway line in China. Through a comparison of other approaches that include Logic-based Benders Decomposition (LBBD), we highlight the superiority of the proposed method; on realistic instances, the 2-L LR method finds solution that are, on average, approximately 2% from optimality. Finally, we test algorithm performance at the operational level and obtain near-optimal solutions, with optimality gaps of approximately 1%, in a very short time.

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