Optimization Techniques in University Timetabling Problem:Constraints,Methodologies,Benchmarks,and Open Issues

University timetabling problems are a yearly challenging task and are faced repeatedly each semester.The problems are considered nonpolynomial time(NP)and combinatorial optimization problems(COP),which means that they can be solved through optimization algorithms to produce the aspired optimal timetable.Several techniques have been used to solve university timetabling problems,and most of them use optimization techniques.This paper provides a comprehensive review of the most recent studies dealing with concepts,methodologies,optimization,benchmarks,and open issues of university timetabling problems.The comprehensive review starts by presenting the essence of university timetabling as NP-COP,defining and clarifying the two formed classes of university timetabling:University Course Timetabling and University Examination Timetabling,illustrating the adopted algorithms for solving such a problem,elaborating the university timetabling constraints to be considered achieving the optimal timetable,and explaining how to analyze and measure the performance of the optimization algorithms by demonstrating the commonly used benchmark datasets for the evaluation.It is noted that meta-heuristic methodologies are widely used in the literature.Additionally,recently,multi-objective optimization has been increasingly used in solving such a problem that can identify robust university timetabling solutions.Finally,trends and future directions in university timetabling problems are provided.This paper provides good information for students,researchers,and specialists interested in this area of research.The challenges and possibilities for future research prospects are also explored.

Combined Timetabling Procedure and Complete Local Search for No-Wait Job Shop Scheduling with Total Tardiness

The strong non-deterministic polynomial-hard( NP-hard)character of job shop scheduling problem( JSSP) has been acknowledged widely and it becomes stronger when attaches the nowait constraint,which widely exists in many production processes,such as chemistry process, metallurgical process. However,compared with the massive research on traditional job shop problem,little attention has been paid on the no-wait constraint.Therefore,in this paper, we have dealt with this problem by decomposing it into two sub-problems, the timetabling and sequencing problems,in traditional frame work. A new efficient combined non-order timetabling method,coordinated with objective of total tardiness,is proposed for the timetabling problems. As for the sequencing one,we have presented a modified complete local search with memory combined by crossover operator and distance counting. The entire algorithm was tested on well-known benchmark problems and compared with several existing algorithms.Computational experiments showed that our proposed algorithm performed both effectively and efficiently.

An Enhanced Particle Swarm Optimization for ITC2021 Sports Timetabling

Timetabling problem is among the most difficult operational tasks and is an important step in raising industrial productivity,capability,and capacity.Such tasks are usually tackled using metaheuristics techniques that provide an intelligent way of suggesting solutions or decision-making.Swarm intelligence techniques including Particle Swarm Optimization(PSO)have proved to be effective examples.Different recent experiments showed that the PSO algorithm is reliable for timetabling in many applications such as educational and personnel timetabling,machine scheduling,etc.However,having an optimal solution is extremely challenging but having a sub-optimal solution using heuristics or metaheuristics is guaranteed.This research paper seeks the enhancement of the PSO algorithm for an efficient timetabling task.This algorithm aims at generating a feasible timetable within a reasonable time.This enhanced version is a hybrid dynamic adaptive PSO algorithm that is tested on a round-robin tournament known as ITC2021 which is dedicated to sports timetabling.The competition includes several soft and hard constraints to be satisfied in order to build a feasible or sub-optimal timetable.It consists of three categories of complexities,namely early,test,and middle instances.Results showed that the proposed dynamic adaptive PSO has obtained feasible timetables for almost all of the instances.The feasibility is measured by minimizing the violation of hard constraints to zero.The performance of the dynamic adaptive PSO is evaluated by the consumed computational time to produce a solution of feasible timetable,consistency,and robustness.The dynamic adaptive PSO showed a robust and consistent performance in producing a diversity of timetables in a reasonable computational time.

A simulation-based optimization approach for passenger train timetabling with periodic track maintenance and stops for praying

This paper presents two optimization methods for solving the passenger train timetabling problem to minimize the total delay time in the single track railway networks. The goal of the train timetable problem is to determine departure and arrival times to or from each station in order to prevent collisions between trains and effective utilization of resources. The two proposed methods are based on integration of a simulation and an optimization method to simulate train traffic flow and generate near optimal train timetable under realistic con- straints including stops for track maintenance and praying. The first proposed method integrates a cellular automata （CA） simulation model with genetic algorithm optimiza- tion method. In the second proposed approach, a CA simulation model combines with dynamically dimensioned search optimization method. The proposed models are applied to hypothetical case study to demonstrate the merit of them. The Islamic Republic of Iran Railways （IRIR） data and regulations have been used to optimize train timetable. The results show the first method is more effi- cient than the second method to obtain near optimal train timetabling.

Timetabling optimization of classrooms and self-study rooms in university teaching buildings based on the building controls virtual test bed platform considering energy efficiency

The energy consumption of a teaching building can be effectively reduced by timetable optimization.However,in most studies that explore methods to reduce building energy consumption by course timetable optimization,self-study activities are not considered.In this study,an MATLAB-EnergyPlus joint simulation model was constructed based on the Building Controls Virtual Test Bed platform to reduce building energy consumption by optimizing the course schedule and opening strategy of self-study rooms in a holistic way.The following results were obtained by taking a university in Xi’an as an example:(1)The energy saving percentages obtained by timetabling optimization during the heating season examination week,heating season non-examination week,cooling season examination week,and cooling season non-examination week are 35%,29.4%,13.4%,and 13.4%,respectively.(2)Regarding the temporal arrangement,most courses are scheduled in the morning during the cooling season and afternoon during the heating season.Regarding the spatial arrangement,most courses are arranged in the central section of the middle floors of the building.(3)During the heating season,the additional building energy consumption incurred by the opening of self-study rooms decreases when duty heating temperature increases.

Mathematical model and simulated annealing algorithm for Chinese high school timetabling problems under the new curriculum innovation

As the first attempt,this paper proposes a model for the Chinese high school timetabling problems(CHSTPs)under the new curriculum innovation which was launched in 2011 by the Chine6e government.Aooording 10 the new our riculum innovation,students in high school can choose subjects that they are interested in instead of being forced to select one of the two study directions,namely,Science and Liberal Arts.Meanwhile,they also need to attend compulsory subjects as traditions.CHSTPs are student-oriented and involve more student constraints that make them more complex than the typi-cal"Class-Teacher model",in which the element"Teacher"is the primary constraint.In this paper,we first describe in detail the mathematical model of CHSTPs and then design a new two-part representation for the candidate solution.Based on the new representation,we adopt a two-phase simulated annealing(SA)algorithm to solve CHSTPs.A total number of 45 synthetic instances with different amounts of classes,teachers,and levels of student constraints are generated and used to ilustrate the characteristics of the CHSTP model and the effectiveness of the designed representation and algorithm.Finally,we apply the proposed model,the designed two-part representation and the two-phase SA on10 real high schools.

Robust graph coloring based on the matrix semi-tensor product with application to examination timetabling

This paper investigates the robust graph coloring problem with application to a kind of examination timetabling by using the matrix semi-tensor product, and presents a number of new results and algorithms. First, using the matrix semi-tensor product, the robust graph coloring is expressed into a kind of optimization problem taking in an algebraic form of matrices, based on which an algorithm is designed to find all the most robust coloring schemes for any simple graph. Second, an equivalent problem of robust graph coloring is studied, and a necessary and sufficient condition is proposed, from which a new algorithm to find all the most robust coloring schemes is established. Third, a kind of examination timetabling is discussed by using the obtained results, and a method to design a practicable timetabling scheme is presented. Finally, the effectiveness of the results/algorithms presented in this paper is shown by two illustrative examples.

COURSE TIMETABLING AT A TUNISIAN UNIVERSITY:A CASE STUDY

This paper deals with the Course Timetabling Problem at an institution in a Tunisian University. We introduce a heuristic procedure to construct a feasible timetable for all lectures and tutorials taken by different groups of each sub-section of any section. We describe the timetabling problem using a list of all specific hard and soft constraints. We formulate the problem as a set of linear constraints using two sets of binary variables corresponding to lectures and tutorials, respectively. This heuristic is illustrated with real data for a sub-section of the Faculty of Economics and Management Sciences of Sfax in Tunisia, and the resulting timetables are compared with those generated manually. The results of another full section have confirmed the good quality of the proposed heuristic when compared with the hand made solution.

A memetic algorithm based on hyper-heuristics for examination timetabling problems

Purpose–The examination timetabling problem is an NP-hard problem.A large number of approaches for this problem are developed to find more appropriate search strategies.Hyper-heuristic is a kind of representative methods.In hyper-heuristic,the high-level search is executed to construct heuristic lists by traditional methods(such as Tabu search,variable neighborhoods and so on).The purpose of this paper is to apply the evolutionary strategy instead of traditional methods for high-level search to improve the capability of global search.Design/methodology/approach–This paper combines hyper-heuristic with evolutionary strategy to solve examination timetabling problems.First,four graph coloring heuristics are employed to construct heuristic lists.Within the evolutionary algorithm framework,the iterative initialization is utilized to improve the number of feasible solutions in the population;meanwhile,the crossover and mutation operators are applied to find potential heuristic lists in the heuristic space(high-level search).At last,two local search methods are combined to optimize the feasible solutions in the solution space(low-level search).Findings–Experimental results demonstrate that the proposed approach obtains competitive results and outperforms the compared approaches on some benchmark instances.Originality/value–The contribution of this paper is the development of a framework which combines evolutionary algorithm and hyper-heuristic for examination timetabling problems.

Transformer-Based Macroscopic Regulation for High-Speed Railway Timetable Rescheduling

Unexpected delays in train operations can cause a cascade of negative consequences in a high-speed railway system.In such cases,train timetables need to be rescheduled.However,timely and efficient train timetable rescheduling is still a challenging problem due to its modeling difficulties and low optimization efficiency.This paper presents a Transformer-based macroscopic regulation approach which consists of two stages including Transformer-based modeling and policy-based decisionmaking.Firstly,the relationship between various train schedules and operations is described by creating a macroscopic model with the Transformer,providing the better understanding of overall operation in the high-speed railway system.Then,a policy-based approach is used to solve a continuous decision problem after macro-modeling for fast convergence.Extensive experiments on various delay scenarios are conducted.The results demonstrate the effectiveness of the proposed method in comparison to other popular methods.

Real-time high-speed train rescheduling based on a Human-Computer Interaction framework

During railway operations,trains normally run as scheduled,but the occurrence of unexpected events will disrupt traffic flow and cause train deviation from the original timetable.In order to assist dispatchers in rescheduling trains,this paper introduces an innovative Human-Computer Interaction framework.This framework enables train dispatchers to propose different timetable adjustment instructions to the original or adjusted timetable.These instructions will be processed,stored,analyzed,and digested by computer program,which finally lead to the modification and calculation of the embedded mathematical model,then a new adjusted timetable will be produced and provided to dispatchers for checking and modifying.This framework can iterate for unlimited times based on dispatchers'intentions,until the final results satisfy them.A demonstration system named RTARS(Real-time Timetable Automatic Rescheduling System)is developed based on this framework and it has been applied in Beijing Railway Administration,which shows its effectiveness in reality.

Last train timetable optimization for metro network to maximize the passenger accessibility over the end-of-service period

Purpose-This study aims to improve the passenger accessibility of passenger demands in the end-ofoperation period.Design/methodology/approach-A mixed integer nonlinear programming model for last train timetable optimization of the metro was proposed considering the constraints such as the maximum headway,the minimum headway and the latest end-of-operation time.The objective of the model is to maximize the number of reachable passengers in the end-of-operation period.A solution method based on a preset train service is proposed,which significantly reduces the variables of deciding train services in the original model and reformulates it into a mixed integer linear programming model.Findings-The results of the case study of Wuhan Metro show that the solution method can obtain highquality solutions in a shorter time;and the shorter the time interval of passenger flow data,the more obvious the advantage of solution speed;after optimization,the number of passengers reaching the destination among the passengers who need to take the last train during the end-of-operation period can be increased by 10%.Originality/value-Existing research results only consider the passengers who take the last train.Compared with previous research,considering the overall passenger demand during the end-of-operation period can make more passengers arrive at their destination.Appropriately delaying the end-of-operation time can increase the proportion of passengers who can reach the destination in the metro network,but due to the decrease in passenger demand,postponing the end-of-operation time has a bottleneck in increasing the proportion of passengers who can reach the destination.

A train timetable rescheduling approach based on multi-train tracking optimization of high-speed railways

Purpose–This paper aims to propose a train timetable rescheduling(TTR)approach from the perspective of multi-train tracking optimization based on the mutual spatiotemporal information in the high-speed railway signaling system.Design/methodology/approach–Firstly,a single-train trajectory optimization(STTO)model is constructed based on train dynamics and operating conditions.The train kinematics parameters,including acceleration,speed and time at each position,are calculated to predict the arrival times in the train timetable.A STTO algorithm is developed to optimize a single-train time-efficient driving strategy.Then,a TTR approach based on multi-train tracking optimization(TTR-MTTO)is proposed with mutual information.The constraints of temporary speed restriction(TSR)and end of authority are decoupled to calculate the tracking trajectory of the backward tracking train.The multi-train trajectories at each position are optimized to generate a timeefficient train timetable.Findings–The numerical experiment is performed on the Beijing-Tianjin high-speed railway line and CR400AF.The STTO algorithm predicts the train’s planned arrival time to calculate the total train delay(TTD).As for the TSR scenario,the proposed TTR-MTTO can reduce TTD by 60.60%compared with the traditional TTR approach with dispatchers’experience.Moreover,TTR-MTTO can optimize a time-efficient train timetable to help dispatchers reschedule trains more reasonably.Originality/value–With the cooperative relationship and mutual information between train rescheduling and control,the proposed TTR-MTTO approach can automatically generate a time-efficient train timetable to reduce the total train delay and the work intensity of dispatchers.

Closing the loop between data mining and fast decision support for intelligent train scheduling and traffic control

The existing Big Data of transport flows and railway operations can be mined through advanced statistical analysis and machine learning methods in order to describe and predict well the train speed, punctuality, track capacity and energy consumption. The accurate modelling of the real spatial and temporal distribution of line and network transport, traffic and performance stimulates a faster construction and implementation of robust and resilient timetables, as well as the development of efficient decision support tools for real-time rescheduling of train schedules. In combination with advanced train control and safety systems even (semi-.) automatic piloting of trains on main and regional railway lines will become feasible in near future.

Annealing Harmony Search Algorithm to Solve the Nurse Rostering Problem

A real-life problem is the rostering of nurses at hospitals.It is a famous nondeterministic,polynomial time(NP)-hard combinatorial optimization problem.Handling the real-world nurse rostering problem(NRP)constraints in distributing workload equally between available nurses is still a difficult task to achieve.The international shortage of nurses,in addition to the spread of COVID-19,has made it more difficult to provide convenient rosters for nurses.Based on the literature,heuristic-based methods are the most commonly used methods to solve the NRP due to its computational complexity,especially for large rosters.Heuristic-based algorithms in general have problems striking the balance between diversification and intensification.Therefore,this paper aims to introduce a novel metaheuristic hybridization that combines the enhanced harmony search algorithm(EHSA)with the simulated annealing(SA)algorithm called the annealing harmony search algorithm(AHSA).The AHSA is used to solve NRP from a Malaysian hospital.The AHSA performance is compared to the EHSA,climbing harmony search algorithm(CHSA),deluge harmony search algorithm(DHSA),and harmony annealing search algorithm(HAS).The results show that the AHSA performs better than the other compared algorithms for all the tested instances where the best ever results reported for the UKMMC dataset.

Parallel Multiple Tabu Search for Multiobjective Urban Transit Scheduling Problem

Urban Transit Scheduling Problem (UTSP) is concerned with determining reliable transit schedules for buses and drivers by considering the preferences of both passengers and operators based on the demand and the set of transit routes. This paper considered a UTSP which consisted of frequency setting, timetabling, and simultaneous bus and driver scheduling. A mixed integer multiobjective model was constructed to optimize the frequency of the routes by minimizing the number of buses, passenger’s waiting times and overcrowding. The model was further extended by incorporating timeslots in determining the frequencies during peak and off-peak hours throughout the time period. The timetabling problem studied two different scenarios which reflected the preferences of passengers and operators to assign the bus departure times at the first and last stop of a route. A set covering model was then adopted to minimize the number of buses and drivers simultaneously. A parallel tabu search algorithm was proposed to solve the problem by modifying the initialization process and incorporating intensification and diversification approaches to guide the search effectively from the different feasible domain in finding optimal solutions with lesser computational effort. Computational experiments were conducted on the well-known Mandl’s and Mumford’s benchmark networks to assess the effectiveness of the proposed algorithm. Competitive results are reported based on the performance metrics, as compared to other algorithms from the literature.

颗粒增强低成本钛基复合材料

采用TiC颗粒和熔铸法制备TiCp/TIMETAL 62S复合材料 ,研究了钛基复合材料的显微组织和室温力学性能。结果表明 :TiCp/TIMETAL 62S复合材料的组织由针状α相、少量 β相和TiC颗粒组成 ;TiC颗粒改变了基体合金原有组织 ,促进了复合材料组织的细化 ;钛基复合材料具有良好的室温强度和塑性 ,复合效果良好。

A simulation model for estimating train and passenger delays in large-scale rail transit networks

A simulation model was proposed to investigate the relationship between train delays and passenger delays and to predict the dynamic passenger distribution in a large-scale rail transit network. It was assumed that the time varying original-destination demand and passenger path choice probability were given. Passengers were assumed not to change their destinations and travel paths after delay occurs. CapaciW constraints of train and queue rules of alighting and boarding were taken into account. By using the time-driven simulation, the states of passengers, trains and other facilities in the network were updated every time step. The proposed methodology was also tested in a real network, for demonstration. The results reveal that short train delay does not necessarily result in passenger delays, while, on the contrary, some passengers may get benefits from the short delay. However, large initial train delay may result in not only knock-on train and passenger delays along the same line, but also the passenger delays across the entire rail transit network.

一种亚稳β钛合金中疲劳短裂纹穿晶扩展晶体学特征的EBSD研究

简单介绍一种疲劳短裂纹扩展跨越晶界的晶体学模型和利用EBSD技术判定活动滑移系的简便方法.作为实际应用的示例,利用EBSD技术应用晶体学模型研究了一种亚稳β钛合金--TIMETAL LCB中疲劳短裂纹穿晶扩展的晶体学特征.实现了穿晶裂纹活动滑移系的判定.结果表明:除在试样表面晶粒两侧的裂纹走向偏折因素外,裂纹面(活动滑移面)间角是更重要的控制短裂纹穿晶扩展的晶体学因素.

High-Speed Railway Train Timetable Conflict Prediction Based on Fuzzy Temporal Knowledge Reasoning

Trains are prone to delays and deviations from train operation plans during their operation because of internal or external disturbances. Delays may develop into operational conflicts between adjacent trains as a result of delay propagation, which may disturb the arrangement of the train operation plan and threaten the operational safety of trains. Therefore, reliable conflict prediction results can be valuable references for dispatchers in making more efficient train operation adjustments when conflicts occur. In contrast to the traditional approach to conflict prediction that involves introducing random disturbances, this study addresses the issue of the fuzzification of time intervals in a train timetable based on historical statistics and the modeling of a high-speed railway train timetable based on the concept of a timed Petri net. To measure conflict prediction results more comprehensively, we divided conflicts into potential conflicts and certain conflicts and defined the judgment conditions for both. Two evaluation indexes, one for the deviation of a single train and one for the possibility of conflicts between adjacent train operations, were developed using a formalized computation method. Based on the temporal fuzzy reasoning method, with some adjustment, a new conflict prediction method is proposed, and the results of a simulation example for two scenarios are presented. The results prove that conflict prediction after fuzzy processing of the time intervals of a train timetable is more reliable and practical and can provide helpful information for use in train operation adjustment, train timetable improvement, and other purposes.