Ricardo García-Ródenas | José Ángel Martín Baos

Optimization with constraint learning for pricing services under competition

Sun, 12 Jul 2026 00:00:00 +0000

Abstract

Revenue Management (RM) optimizes pricing and capacity allocation under demand uncertainty. We propose a data-driven RM framework that integrates neural networks or gradient boosting tree models with constraint learning to support joint pricing and capacity decisions. The approach adapts to arbitrary demand patterns learned directly from data, without requiring a predefined demand model, and captures competitive interactions between railway undertakings using only observable information. The methodology is illustrated through a case study of the Madrid-Barcelona high-speed rail corridor.

Code

The code for the experiments presented in this talk is available at under the Apache License 2.0. Please refer to the repository for instructions on how to reproduce the results and access the datasets used in the experiments. Note that the repository contains the current research implementation and the code is still under development, so it may change substantially before publication.

The time slot allocation problem in liberalised passenger railway markets: a multi-objective approach

Thu, 31 Jul 2025 00:00:00 +0000

Un enfoque práctico para la enseñanza de Álgebra y Matemática Discreta mediante clase invertida en Ingeniería Informática

Wed, 09 Jul 2025 00:00:00 +0000

Abstract

La enseñanza de conceptos abstractos en asignaturas técnico-científicas plantea un desafío recurrente en la educación universitaria, particularmente en los primeros cursos, donde el alumnado se enfrenta a contenidos complejos y herramientas nuevas. En concreto, en la asignatura de Álgebra y Matemática Discreta, impartida generalmente en el primer curso del Grado en Ingeniería Informática, estas dificultades se ven agravadas por la falta de estudio constante y la escasa participación en clase. Además, con frecuencia los contenidos se perciben como excesivamente abstractos y alejados de aplicaciones reales. Este trabajo describe como se han rediseñado las sesiones prácticas de esta asignatura mediante la implementación de una metodología de clase invertida. Se han desarrollado cuadernos interactivos en lenguaje MATLAB, además de vídeos explicativos, disponibles tanto en español como en inglés, que fomentan el estudio autónomo antes de las sesiones presenciales. Durante la clase, el alumnado resuelve de manera colaborativa un caso de estudio basado en un problema real, mientras el profesor adopta un rol de facilitador, orientando la discusión y atendiendo dudas específicas. La experiencia piloto, realizada durante el curso 2023/24, ha evidenciado mejoras significativas en la motivación, la comprensión y el rendimiento del estudiantado, generando un ambiente de aprendizaje más participativo y dinámico.

A model for pricing freight rail transport access costs: economic and environmental perspectives

Tue, 08 Apr 2025 00:00:00 +0000

Scalable kernel logistic regression with Nyström approximation: Theoretical analysis and application to discrete choice modelling

Fri, 07 Feb 2025 00:00:00 +0000

An Optimization Model for Determining Access Costs in Rail Freight Transportation

Sun, 30 Jun 2024 00:00:00 +0000

Abstract

The liberalization of European railway markets necessitates a vertical separation governance framework, with Infrastructure Managers (IMs) providing resources and Freight Operating Companies (FOCs) utilizing them. Effective pricing of track access between these entities is vital for profitability and system efficiency. Additionally, achieving a modal shift of freight from road to rail is crucial for road safety and EU objectives alignment. This paper introduces a novel pricing methodology for train paths, optimizing infrastructure utilization by IMs while considering competitive dynamics and environmental impacts. It addresses challenges such as elastic demand, integrating network capacity into pricing strategies, and managing non-additive costs and path interdependencies. The proposed model incorporates dynamic demand patterns, temporally variable capacities, and total revenue considerations across the planning horizon. A discretization-based approach, focusing on irregular time intervals and unit freight tonnage, is developed for solving the continuous model. This involves linking freight tonnage units to a prototype train, with a discrete event simulation model employed. The objective function is also discretized, yielding a finite set of optimization variables to be optimized subject to simulation model. An application of this approach is demonstrated through a case study of the Mediterranean Corridor.

Enhancing the convergence speed of line search methods: Applications in Neural Network training

Sun, 30 Jun 2024 00:00:00 +0000

Abstract

The training of machine learning models, such as neural networks, relies on optimisation techniques that necessitate large volumes of data. The algorithms that have demonstrated satisfactory performance on this task frequently use linear searches on subsets of the data. This ensures that, despite the potential low quality of the search direction, the overall computational cost remains low, making this strategy globally efficient. In these methods, strategies employing a constant learning rate have proven to be particularly effective. This paper introduces a novel scheme designed to significantly expedite the convergence process of line search-based methods. Our approach incorporates additional high-quality linear searches derived from the convergence process of the methods, and by making use of an Armijo rule, it dynamically adjusts the step size through successive reductions or expansions based on the evaluated quality of the descent direction. This strategic adjustment enables more substantial progress in the search direction, potentially reducing the number of iterations needed to reach an optimal solution. We have applied our proposed solution to accelerate the performance of widely-used algorithms such as Gradient Descent (GD), Momentum GD, and Adaptive Moment Estimation (Adam). To illustrate the practical implications and effectiveness of our approach, we present a comprehensive case study focusing on the training of Deep Neural Networks and Kernel Logistic Regression.

An optimal control model for determining freight rail transport access costs

Sun, 19 May 2024 00:00:00 +0000

Abstract

The liberalization of European railway markets, as outlined in European Directive EU 91/440/EEC, mandates a vertical separation governance structure within the railway industry. This vertical separation involves the establishment of two distinct entities: the Infrastructure Manager (IM), responsible for providing railway resources, and the Freight Operating Company (FOC), which operates freight services utilizing the infrastructure provided by the IM. Determining track access pricing between these entities is of utmost interest for European countries extensive monitorings are carried out has emerged as a significant and urgent challenge, one that has profound implications not only for the profitability of IMs and FOCs but also for the efficiency and quality of the entire railway system.

Furthermore, this issue is pivotal in achieving the target objectives set by the European Union (EU), which aims to achieve a modal shift away from road freight transport towards more sustainable modes of transportation. Specifically, the EU has set a goal of achieving a modal shift of 30% by 2030 and at least 50% by 2050 for shipments exceeding 300 km. In this context, rail freight transport is widely recognized as a potentially cost-effective and environmentally sustainable alternative due to its ability to realize economies of scale, reduce pollutant emissions, and mitigate other externalities.

In this paper, we propose an optimal control method for pricing train paths so that the IM maximizes the utilization of public funding while promoting competition in the rail freight market and taking into account both environmental impact and road safety.

The methodology presents several challenges. First, the model needs to account for elastic demand to capture the effect of costs and travel times on modal split. For this reason, road freight transportation is simplified, and a modal split is performed using a logit model.

Second, it involves replacing a basic toll per kilometer scheme with one that incorporates the capacity of the railway network into the pricing process. This means that congested routes should be subject to higher charges than less-demand routes. Hence, a dynamic cargo flow model with capacities on arcs has been chosen. The temporal aspect of the model allows for consideration of dynamic demand patterns and temporally variable capacities (day/night).

The third element of the model deals with a non-additive cost structure and interdependence of train paths when sharing railway segments. This has been achieved by pricing the total revenue received for the use of train paths over the entire planning period.

PyKernelLogit: Penalised maximum likelihood estimation of Kernel Logistic Regression in Python

Fri, 01 Mar 2024 00:00:00 +0000

A prediction and behavioural analysis of machine learning methods for modelling travel mode choice

Wed, 01 Nov 2023 00:00:00 +0000

ROBIN: Rail mOBIlity simulatioN

Wed, 06 Sep 2023 00:00:00 +0000

Abstract

The use of simulators is frequent in the study of complex systems. They replicate a real system and allow obtaining data from the simulated process as well as providing a mathematical model that helps answer What If? questions. This opens up the possibility of evaluating laboratory environment techniques and processes that will later be implemented in the real system. Competitive passenger rail services are complex systems. The efficient design of market mechanisms that encourage competition to offer more and better services requires analytical tools on which to test these new policies. This makes it essential to develop a simulator, as real and complete as possible, to carry out this analysis. This paper presents the development of a microscopic simulator, called ROBIN (Rail mOBIlity simulatioN), to simulate rail mobility in a competitive regime. The developed simulator is parameterizable and general enough to simulate passenger flows in competing railway systems. The tests carried out with ROBIN using the Spanish railway market as a case of study are proof of its usefulness, allowing disaggregated modelling of passenger behaviour and their travel choices in a competitive railway market.

The time slots allocation problem in liberalised passenger railway markets: a multi-objective approach

Wed, 06 Sep 2023 00:00:00 +0000

Abstract

The liberalisation of the European passenger railway markets through the European Directive EU 91/440/EEC states a new scenario where different Railway Undertakings (RUs) compete with each other in an auction or bidding process for time slots to optimise its profit. The infrastructure resources are provided by the Infrastructure Manager (IM) who analyses and assesses the bids received, allocating the resources to each RU. Time slots allocation is a fact that drastically influences the market equilibrium and a problem whose resolution makes it possible to ensure competitiveness within the market. In this paper, time slots allocation problem is modeled in the context of a liberalised passenger railway market. Then, the problem is addressed using two approaches: the first one allocates time slots to each company according to a set of priorities, while the second one introduces a criterion of fairness in the treatment of companies to ensure competition. A multi-objective algorithm has been developed and evaluated for its effectiveness in solving the time slots allocation problem in a liberalized high-speed corridor of the Spanish railway network.

A comparative study of machine learning, deep neural networks and random utility maximization models for travel mode choice modelling

Fri, 11 Mar 2022 00:00:00 +0000

IoT based monitoring of air quality and traffic using regression analysis

Sat, 01 Jan 2022 00:00:00 +0000

A Python package for performing penalized maximum likelihood estimation of conditional logit models using Kernel Logistic Regression

Wed, 08 Dec 2021 00:00:00 +0000

A comparative study of machine learning, deep neural networks and random utility maximization models for travel mode choice modelling

Wed, 08 Sep 2021 00:00:00 +0000

Abstract

Traditionally, Random Utility Maximization (RUM) models have been widely applied to travel mode choice modelling. Currently, Machine Learning (ML) models are being applied as an alternative to RUM models, since they provide better results in terms of prediction capability and they can manage large volumes of data. In this paper, a comprehensive comparison between classic RUM models and ML models, including single and ensemble classifiers as well as Deep Neural Networks (DNNs), is provided in order to assess systematically the performance of different models over two different datasets which have different sizes and nature of data. Numerical experiments show Random Forest (RF) is the best classifier in terms of accuracy index and the computational cost to train the model.

A Python package for performing penalized maximum likelihood estimation of conditional logit models using Kernel Logistic Regression

Tue, 06 Jul 2021 00:00:00 +0000

DOI:

Abstract

In the last few years, Machine Learning (ML) methods have acquired great popularity due to their success in numerous applications such as autonomous cars, image and voice recognition systems, automatic translation systems, etc. This success has led to an increase in the use of ML methods and the extension of their applications to areas such as transport planning.

One of the main tasks within transport planning is the analysis of transport demand. To do so, it is necessary to analyse the way in which users make their decisions about the trips they make and, therefore, be able to predict the number of passengers on the transport network in relation to respect to interventions made on the transport system. Consequently, transport policies and plans can be evaluated according to the behaviour of the passengers. Discrete choice models based on random utility maximization have been developed over the last four decades and currently they have acquired a high degree of sophistication, becoming the canonical tool for transport demand analysis. Nowadays, the use of ML methods could provide an alternative to discrete choice models, as they offer a high level of accuracy in their predictions. In addition, the analyst is relieved from the need of specifying the functional expressions for the utility functions beforehand.

A Python software package called PyKernelLogit was developed to apply a ML method called Kernel Logistic Regression (KLR) to the problem of predicting the transport demand. This package allows the user to specify a set of models using KLR and the estimation of those using a Penalized Maximum Likelihood Estimation procedure. Moreover, this tool also provides a set of indicators for goodness of fit and the application of model validation techniques. Finally, it allows to obtain the willingness to pay or value of time indicators commonly used in transport planning.

Revisiting kernel logistic regression under the random utility models perspective. An interpretable machine-learning approach

Tue, 16 Mar 2021 00:00:00 +0000

A python package for performing penalized maximum likelihood estimation of conditional logit models using kernel logistic regression

Wed, 24 Jun 2020 00:00:00 +0000

Abstract

A comparison of general-purpose optimization algorithms for finding optimal approximate experimental designs

Wed, 01 Apr 2020 00:00:00 +0000

Discrete choice modeling using Kernel Logistic Regression

Wed, 01 Jan 2020 00:00:00 +0000

Discrete choice modeling using Kernel Logistic Regression

Wed, 18 Sep 2019 00:00:00 +0000

Abstract

The Kernel Logistic Regression is a popular technique in machine learning. In this work this tech- nique is applied to the field of discrete choice modeling. This approach is equivalent to specifying non-parametric utilities in random utility models. A Monte Carlo simulation experiment has been carried out to compare this approach with Multinomial Logit models, comparing the goodness of fit and the capability of obtaining the specified utilities.

A methodology for monitoring traffic flow and air pollution in urban areas

Mon, 29 Jul 2019 00:00:00 +0000

Abstract

Road transportation has become the main source of air pollution in urban areas, which has a major impact on local air quality and human health. For this reason, it is increasingly necessary to accurately estimate the contribution of road transport to air pollution in the cities, so that pollution-reduction measures can be properly designed and implemented appropriately. These pollution reduction measures are becoming increasingly important due to the continued growth in vehicle use and the deterioration of driving conditions (traffic congestion). Authorities find it difficult to meet their environmental objectives and, therefore, reliable mathematical emission models are needed to accurately predict the impact of road transport on air pollution.

Nowadays, intelligent cities are essential to prevent high-level pollution situations and to act when such situations occur. Cities must anticipate pollution peaks and take mitigating measures, such as restricting traffic to a certain number of vehicles or according to their license plates, closing traffic on certain streets, reducing speed limits, etc. In addition, traffic flows must be monitored as they affect pollution levels in that city.

Typical pollution monitoring and control systems often consist of large and expensive devices that are only limited to a few points in the city, hence, they provide information for vast areas and sometimes these systems are not scalable. However, cities are distributed environments where events occur in real time and on a massive scale. Therefore, cities should rely on a low-cost Internet of Things (IoT) infrastructure connected to a cloud platform that supports this type of systems, as well as sensor-based big data applications. These pollution control systems can be combined with a traffic monitoring infrastructure to provide a complete system that can be used as a Decision Support System (DSS) to help authorities make decisions about the environmental impacts caused by pollution before they occur.

In this work, a methodology has been developed for determining the traffic flow and the air pollution in several streets of a city using low-cost devices. An artificial intelligence heuristic algorithm has been employed to process video images from a camera and estimate the traffic flow in the street. This algorithm uses statistical techniques to process the motion vectors generated by the GPU when the video is encoded. Moreover, the computational time required by the algorithm is in the order of 2.5 milliseconds, which allows to count the number of vehicles in real time. This algorithm has been tested proving 90% of accuracy. Finally, this information is uploaded to a cloud service where machine learning techniques can be applied to predict the pollution levels in the city or recommend palliative actions.