arXiv subjects

Bernardo Martin-Iradi

Publications and source records attributed to Bernardo Martin-Iradi.

5 recordsLinked to original sources

arXiv2025

Solving Integrated Periodic Railway Timetabling with Satisfiability Modulo Theories: A Scalable Approach to Routing and Vehicle Circulation

This paper introduces a novel approach for jointly solving the periodic Train Timetabling Problem (TTP), train routing, and Vehicle Circulation Problem (VCP) through a unified optimization model. While these planning stages are traditionally addressed sequentially, their interdependencies often lead to suboptimal vehicle usage. We propose the VCR-PESP, an integrated formulation that minimizes fleet size while ensuring feasible and infrastructure-compliant periodic timetables. We present the first Satisfiability Modulo Theories (SMT)-based method for the VCR-PESP to solve the resulting large-scale instances. Unlike the Boolean Satisfiability Problem (SAT), which requires time discretisation, SMT supports continuous time via difference constraints, eliminating the trade-off between temporal precision and encoding size. Our approach avoids rounding artifacts and scales effectively, outperforming both SAT and Mixed Integer Program (MIP) models across non-trivial instances. Using real-world data from the Swiss narrow-gauge operator RhB, we conduct extensive experiments to assess the impact of time discretisation, vehicle circulation strategies, route flexibility, and planning integration. We show that discrete models inflate vehicle requirements and that fully integrated solutions substantially reduce fleet needs compared to sequential approaches. Our framework consistently delivers high-resolution solutions with tractable runtimes, even in large and complex networks. By combining modeling accuracy with scalable solver technology, this work establishes SMT as a powerful tool for integrated railway planning. It demonstrates how relaxing discretisation and solving across planning layers enables more efficient and implementable timetables.

math.OC↗

arXiv2025

A Double Decomposition Algorithm for Network Planning and Operations in Deviated Fixed-route Microtransit

Microtransit offers opportunities to enhance urban mobility by combining the reliability of public transit and the flexibility of ride-sharing. This paper optimizes the design and operations of a deviated fixed-route microtransit system that relies on reference lines but can deviate on demand in response to passenger requests. We formulate a Microtransit Network Design (MiND) model via two-stage stochastic integer optimization, with a first-stage network design and service scheduling structure and a second-stage vehicle routing structure. We derive a tight second-stage relaxation using a subpath-based representation of microtransit operations in a load-expanded network. We develop a double-decomposition algorithm combining Benders decomposition and subpath-based column generation. We prove that the algorithm maintains a valid optimality gap and converges to an optimal solution in a finite number of iterations. Results obtained with real-world data from Manhattan show that the methodology scales to large and otherwise-intractable instances, with up to 10-100 candidate lines and hundreds of stops. Comparisons with transit and ride-sharing suggest that microtransit can provide win-win outcomes toward efficient mobility (high demand coverage, low costs, high level of service), equitable mobility (broad geographic reach) and sustainable mobility (limited environmental footprint). We provide an open-source implementation to enable replication.

math.OC↗

arXiv2023

An adaptive large neighborhood search heuristic for the multi-port continuous berth allocation problem

In this paper, we study a problem that integrates the vessel scheduling problem with the berth allocation into a collaborative problem denoted as the multi-port continuous berth allocation problem (MCBAP). This problem optimizes the berth allocation of a set of ships simultaneously in multiple ports while also considering the sailing speed of ships between ports. Due to the highly combinatorial character of the problem, exact methods struggle to scale to large-size instances, which points to exploring heuristic methods. We present a mixed-integer problem formulation for the MCBAP and introduce an adaptive large neighborhood search (ALNS) algorithm enhanced with a local search procedure to solve it. The computational results highlight the method's suitability for larger instances by providing high-quality solutions in short computational times. Practical insights indicate that the carriers' and terminal operators' operational costs are impacted in different ways by fuel prices, external ships at port, and the modeling of a continuous quay.

math.OC↗

arXiv2021

The multi-port berth allocation problem with speed optimization: Exact methods and a cooperative game analysis

We consider a variant of the berth allocation problem-i.e., the multi-port berth allocation problem-aimed at assigning berthing times and positions to vessels in container terminals. This variant involves optimizing vessel travel speeds between multiple ports, thereby exploiting the potentials of a collaboration between carriers (shipping lines) and terminal operators. Using a graph representation of the problem, we reformulate an existing mixed-integer problem into a generalized set partitioning problem, in which each variable refers to a sequence of feasible berths in the ports that the vessel visits. By integrating column generation and cut separation in a branch-and-cut-and-price procedure, our proposed method is able to outperform commercial solvers in a set of benchmark instances and adapt better to larger instances. In addition, we apply cooperative game theory methods to efficiently distribute the savings resulting from a potential collaboration and show that both carriers and terminal operators would benefit from collaborating.

math.OC↗

arXiv2021

A column-generation-based matheuristic for periodic train timetabling with integrated passenger routing

In this study, the periodic train timetabling problem is formulated using a time-space graph formulation. Three solution methods are proposed and compared where solutions are built by what we define as a dive-and-cut-and-price procedure. An LP relaxed version of the problem with a subset of constraints is solved using column generation where each column corresponds to the train paths of a line. Violated constraints are added by separation and a heuristic process is applied to help to find integer solutions. The passenger travel time is computed based on a solution timetable and Benders' optimality cuts are generated allowing the method to integrate the routing of the passengers. We propose two large neighborhood search methods where the solution is iteratively destroyed and repaired into a new one and one random iterative method. The problem is tested on the morning rush hour period of the Regional and InterCity train network of Zealand, Denmark. The solution approaches show robust performance in a variety of scenarios, being able to find good quality solutions in terms of travel time and path length relatively fast. The inclusion of the proposed Benders' cuts provides stronger relaxations to the problem. In addition, the graph formulation covers different real-life constraints and has the potential to easily be extended to accommodate more constraints.

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