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Keywords = examination timetabling problem

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20 pages, 2885 KB  
Article
A Column Generation-Based Optimization Approach for the Train Loading Planning Problem with Simulation-Based Evaluation of Rail Forwarding at the Port of Valencia
by Zisis Maleas, Dimos Touloumidis, Pavlos Giannakou, Sofoklis Dais and Georgia Ayfantopoulou
Future Transp. 2025, 5(4), 196; https://doi.org/10.3390/futuretransp5040196 - 12 Dec 2025
Viewed by 517
Abstract
As ports evolve to meet sustainability targets, seamless coordination between road and rail operations becomes fundamental to success. This study addresses the Train Loading Planning Problem (TLPP) which focuses on assigning outbound containers to train wagons under slot, weight, and pattern constraints aiming [...] Read more.
As ports evolve to meet sustainability targets, seamless coordination between road and rail operations becomes fundamental to success. This study addresses the Train Loading Planning Problem (TLPP) which focuses on assigning outbound containers to train wagons under slot, weight, and pattern constraints aiming to examine its broader systemic implications. A compact mixed-integer programming formulation is developed and enhanced through a column-generation approach that efficiently prices feasible wagon plans. The optimization module is embedded within a discrete-event simulation of terminal processes including yard handling, gate operations, and train timetables. The study tests a TLPP-based rail planning algorithm within a DES of terminal and hinterland operations to quantify the impact under realistic variability. Using operational data from the Port of Valencia, realistic planning scenarios are evaluated across varying demand mixes and train frequencies. Results indicate that integrating rail capacity with optimized wagon loading reduces set-up time by 20%, delivery lead time by 54%, container dwell time by 80%, and greenhouse gas emissions by 54% compared with a trucking forwarding baseline, while maintaining throughput and alleviating congestion at terminal gates and yards. From a computational perspective, the column-generation approach achieves improved runtimes to the compact MIP and scales linearly to the number of variables. The proposed framework delivers ready to use load plans and practical insights for the deployment of additional rail capacity, supporting sustainable logistics in port environments. Full article
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21 pages, 2267 KB  
Review
A Review of Battery Electric Public Transport Timetabling and Scheduling: A 10 Year Retrospective and New Developments
by Yaoyao Wang, Shun Zhang, Liang Liu, Ping Gong, Weike Lu, Fuwei Wu, Jinggang Gu, Yuxuan Li and Zhichao Cao
Electronics 2025, 14(9), 1694; https://doi.org/10.3390/electronics14091694 - 22 Apr 2025
Cited by 2 | Viewed by 1990
Abstract
Battery electric vehicles (BEVs) have emerged as a cornerstone of sustainable transportation systems, driving a fundamental transformation in public transport (PT) operations over the past decade. The unique characteristics of BEVs, including range limitations and battery degradation dynamics, necessitate a multi-dimensional optimization framework [...] Read more.
Battery electric vehicles (BEVs) have emerged as a cornerstone of sustainable transportation systems, driving a fundamental transformation in public transport (PT) operations over the past decade. The unique characteristics of BEVs, including range limitations and battery degradation dynamics, necessitate a multi-dimensional optimization framework that simultaneously considers energy supply management, operational efficiency, and battery lifecycle optimization in transit scheduling and timetabling. This paper presents a systematic review of BEV timetabling and scheduling research, structured around three main contributions. First, it comprehensively examines the evolution of electric vehicle timetabling problems, providing a detailed comparative analysis of methodological approaches in this domain. Second, it identifies and critically evaluates key developments in electric vehicle scheduling, including extended research directions (such as the integration with crew scheduling) and their practical implications. Third, it investigates the integration of BEV scheduling and timetabling, synthesizing the strengths and limitations of current methodologies while outlining promising avenues for future research. By offering a comprehensive analysis of the advancements in battery electric public transport scheduling over the past decade, this review serves as both a technical reference and a strategic guide for researchers and practitioners in the field of sustainable transportation systems. Full article
(This article belongs to the Special Issue Sustainable Transportation Systems)
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25 pages, 7173 KB  
Article
Optimizing Fleet Structure for Autonomous Electric Buses: A Route-Based Analysis in Aachen, Germany
by Hubert Maximilian Sistig, Philipp Sinhuber, Matthias Rogge and Dirk Uwe Sauer
Sustainability 2024, 16(10), 4093; https://doi.org/10.3390/su16104093 - 14 May 2024
Cited by 6 | Viewed by 3348
Abstract
Intelligent transportation systems enhance the potential for sustainable, user-friendly, and efficient transport. By eliminating driver costs, autonomous buses facilitate the redesign of networks, timetables, and fleet structure in a cost-effective manner. The electrification of bus fleets offers the opportunity to further improve the [...] Read more.
Intelligent transportation systems enhance the potential for sustainable, user-friendly, and efficient transport. By eliminating driver costs, autonomous buses facilitate the redesign of networks, timetables, and fleet structure in a cost-effective manner. The electrification of bus fleets offers the opportunity to further improve the environmental sustainability of transportation networks, but requires adjustments to vehicle schedules due to the limited range and charging requirements. This paper examines the intricate relationship between electrification and autonomous buses. To this end, timetables for autonomous electric buses of different sizes were developed for a real bus route in Aachen, Germany. The resulting electric vehicle scheduling problem was then solved using an adaptive large neighborhood search to determine the number of vehicles needed and the total cost of ownership. By eliminating driver costs, vehicles with lower passenger capacity become much more attractive, albeit at a slightly higher cost. In comparison, the incremental costs of electrification are low if the right approach is taken. Fluctuations in typical passenger numbers can be used to modify timetables and vehicle schedules to accommodate the charging needs of autonomous electric buses. In particular, electric bus concepts with fewer charging stations and lower charging power benefit from adapting the timetable to passenger numbers. The results demonstrate that the specific requirements of electric buses should be considered when adapting networks and timetables in order to design a sustainable transport network. Full article
(This article belongs to the Special Issue Autonomous Systems and Intelligent Transportation Systems)
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27 pages, 12022 KB  
Article
Optimizing the Three-Dimensional Multi-Objective of Feeder Bus Routes Considering the Timetable
by Xinhua Gao, Song Liu, Shan Jiang, Dennis Yu, Yong Peng, Xianting Ma and Wenting Lin
Mathematics 2024, 12(7), 930; https://doi.org/10.3390/math12070930 - 22 Mar 2024
Cited by 8 | Viewed by 2727
Abstract
To optimize the evacuation process of rail transit passenger flows, the influence of the feeder bus network on bus demand is pivotal. This study first examines the transportation mode preferences of rail transit station passengers and addresses the feeder bus network’s optimization challenge [...] Read more.
To optimize the evacuation process of rail transit passenger flows, the influence of the feeder bus network on bus demand is pivotal. This study first examines the transportation mode preferences of rail transit station passengers and addresses the feeder bus network’s optimization challenge within a three-dimensional framework, incorporating an elastic mechanism. Consequently, a strategic planning model is developed. Subsequently, a multi-objective optimization model is constructed to simultaneously increase passenger numbers and decrease both travel time costs and bus operational expenses. Due to the NP-hard nature of this optimization problem, we introduce an enhanced non-dominated sorting genetic algorithm, INSGA-II. This algorithm integrates innovative encoding and decoding rules, adaptive parameter adjustment strategies, and a combination of crowding distance and distribution entropy mechanisms alongside an external elite archive strategy to enhance population convergence and local search capabilities. The efficacy of the proposed model and algorithm is corroborated through simulations employing standard test functions and instances. The results demonstrate that the INSGA-II algorithm closely approximates the true Pareto front, attaining Pareto optimal solutions that are uniformly distributed. Additionally, an increase in the fleet size correlates with greater passenger volumes and higher operational costs, yet it substantially lowers the average travel cost per customer. An optimal fleet size of 11 vehicles is identified. Moreover, expanding feeder bus routes enhances passenger counts by 18.03%, raises operational costs by 32.33%, and cuts passenger travel time expenses by 21.23%. These findings necessitate revisions to the bus timetable. Therefore, for a bus network with elastic demand, it is essential to holistically optimize the actual passenger flow demand, fleet size, bus schedules, and departure frequencies. Full article
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19 pages, 1100 KB  
Article
School Timetabling Optimisation Using Artificial Bee Colony Algorithm Based on a Virtual Searching Space Method
by Kaixiang Zhu, Lily D. Li and Michael Li
Mathematics 2022, 10(1), 73; https://doi.org/10.3390/math10010073 - 26 Dec 2021
Cited by 11 | Viewed by 5691
Abstract
Although educational timetabling problems have been studied for decades, one instance of this, the school timetabling problem (STP), has not developed as quickly as examination timetabling and course timetabling problems due to its diversity and complexity. In addition, most STP research has only [...] Read more.
Although educational timetabling problems have been studied for decades, one instance of this, the school timetabling problem (STP), has not developed as quickly as examination timetabling and course timetabling problems due to its diversity and complexity. In addition, most STP research has only focused on the educators’ availabilities when studying the educator aspect, and the educators’ preferences and expertise have not been taken into consideration. To fill in this gap, this paper proposes a conceptual model for the school timetabling problem considering educators’ availabilities, preferences and expertise as a whole. Based on a common real-world school timetabling scenario, the artificial bee colony (ABC) algorithm is adapted to this study, as research shows its applicability in solving examination and course timetabling problems. A virtual search space for dealing with the large search space is introduced to the proposed model. The proposed approach is simulated with a large, randomly generated dataset. The experimental results demonstrate that the proposed approach is able to solve the STP and handle a large dataset in an ordinary computing hardware environment, which significantly reduces computational costs. Compared to the traditional constraint programming method, the proposed approach is more effective and can provide more satisfactory solutions by considering educators’ availabilities, preferences, and expertise levels. Full article
(This article belongs to the Special Issue Recent Advances in Multiple Criteria Decision Making Approaches)
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19 pages, 2278 KB  
Article
The Problem of Train Scheduling in the Context of the Load on the Power Supply Infrastructure. A Case Study
by Szymon Haładyn
Energies 2021, 14(16), 4781; https://doi.org/10.3390/en14164781 - 6 Aug 2021
Cited by 9 | Viewed by 3111
Abstract
This article deals with the new challenges facing modernising railways in Poland. We look at the problem of the efficiency of the power supply system (3 kV DC) used in the context of the increasing use of electric vehicles, which have a higher [...] Read more.
This article deals with the new challenges facing modernising railways in Poland. We look at the problem of the efficiency of the power supply system (3 kV DC) used in the context of the increasing use of electric vehicles, which have a higher demand for electricity than the old type. We present and characterise the power supply system in use, pointing out its weaknesses. We consider a case study. The load of the power supply network generated by the rolling stock used in Poland was examined using a microsimulation. A real train timetable was taken into account on a fragment of one of the most important railway line sections in one of the urban agglomerations. Then the results were compared with the results of a microsimulation in which old units were replaced by new trains. These tests were carried out in several variants. We found critical points in the scheduling of railway system use. Our results indicate that it is becoming increasingly necessary to take into account the permissible load capacity of the supply network in certain traffic situations in the process of timetable construction. Full article
(This article belongs to the Special Issue Power Quality in Electrified Transportation Systems)
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28 pages, 585 KB  
Article
Addressing Examination Timetabling Problem Using a Partial Exams Approach in Constructive and Improvement
by Ashis Kumar Mandal, M. N. M. Kahar and Graham Kendall
Computation 2020, 8(2), 46; https://doi.org/10.3390/computation8020046 - 17 May 2020
Cited by 23 | Viewed by 8217
Abstract
The paper investigates a partial exam assignment approach for solving the examination timetabling problem. Current approaches involve scheduling all of the exams into time slots and rooms (i.e., produce an initial solution) and then continuing by improving the initial solution in a predetermined [...] Read more.
The paper investigates a partial exam assignment approach for solving the examination timetabling problem. Current approaches involve scheduling all of the exams into time slots and rooms (i.e., produce an initial solution) and then continuing by improving the initial solution in a predetermined number of iterations. We propose a modification of this process that schedules partially selected exams into time slots and rooms followed by improving the solution vector of partial exams. The process then continues with the next batch of exams until all exams are scheduled. The partial exam assignment approach utilises partial graph heuristic orderings with a modified great deluge algorithm (PGH-mGD). The PGH-mGD approach is tested on two benchmark datasets, a capacitated examination dataset from the 2nd international timetable competition (ITC2007) and an un-capacitated Toronto examination dataset. Experimental results show that PGH-mGD is able to produce quality solutions that are competitive with those of the previous approaches reported in the scientific literature. Full article
(This article belongs to the Section Computational Engineering)
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33 pages, 503 KB  
Article
Solving the Examination Timetabling Problem in GPUs
by Vasileios Kolonias, George Goulas, Christos Gogos, Panayiotis Alefragis and Efthymios Housos
Algorithms 2014, 7(3), 295-327; https://doi.org/10.3390/a7030295 - 3 Jul 2014
Cited by 6 | Viewed by 8894
Abstract
The examination timetabling problem belongs to the class of combinatorial optimization problems and is of great importance for every University. In this paper, a hybrid evolutionary algorithm running on a GPU is employed to solve the examination timetabling problem. The hybrid evolutionary algorithm [...] Read more.
The examination timetabling problem belongs to the class of combinatorial optimization problems and is of great importance for every University. In this paper, a hybrid evolutionary algorithm running on a GPU is employed to solve the examination timetabling problem. The hybrid evolutionary algorithm proposed has a genetic algorithm component and a greedy steepest descent component. The GPU computational capabilities allow the use of very large population sizes, leading to a more thorough exploration of the problem solution space. The GPU implementation, depending on the size of the problem, is up to twenty six times faster than the identical single-threaded CPU implementation of the algorithm. The algorithm is evaluated with the well known Toronto datasets and compares well with the best results found in the bibliography. Moreover, the selection of the encoding of the chromosomes and the tournament selection size as the population grows are examined and optimized. The compressed sparse row format is used for the conflict matrix and was proven essential to the process, since most of the datasets have a small conflict density, which translates into an extremely sparse matrix. Full article
(This article belongs to the Special Issue Bio-inspired Algorithms for Combinatorial Problems)
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