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...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.展开更多
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, usin...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.展开更多
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 man...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.展开更多
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...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.展开更多
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 det...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.展开更多
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 ou...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.展开更多
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,se...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.展开更多
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 g...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.展开更多
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 met...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.展开更多
Intercity high-speed rail (HSR) is a type of mass transit built in densely populatedmetropolitan areas and has become an essential part of sustainable transportation systemsin some countries. One of the most challengi...Intercity high-speed rail (HSR) is a type of mass transit built in densely populatedmetropolitan areas and has become an essential part of sustainable transportation systemsin some countries. One of the most challenging problems is how to jointly optimize thetrain line plan and timetable with simultaneous consideration of the system efficiency,cost, and level of service. In this paper, we focus on optimizing the train line plan and timetableof intercity HSR given actual time-dependent demand while appropriately consideringthe operational constraints including overtaking. First, we formulate the optimizationproblem as a mixed integer nonlinear programming (MINLP). Its objective is to minimizethe total system cost comprised of the trains’ fixed and variable operation costs, passengers’travel time cost, and penalties for passengers’ departure time deviation and passengers’failing to board a train. We then design a double-layer simulated annealing (SA)algorithm, in which the inner layer algorithm optimizes the stop plan, the departure andarrival times at each station, while the outer layer algorithm optimizes the number oftrains, their origin–destination stations, and their departure times at origin stations.Next a case study is conducted on Shanghai-Nanjing intercity HSR using actual timedependentdemand. The numerical results show that the proposed model can help significantlyreduce the total number of trains used by increasing the average seat occupancy,while creating little impact on the average passenger travel time and departure time.The study provides valuable guidance for optimizing HSR train line plan and timetablebased on real-world time-dependent demand.展开更多
The rapid growth of passenger flow in urban rail transit has led to great service pressures for metro companies in organizing train services to provide higher transportation capacities in order to satisfy passengers&#...The rapid growth of passenger flow in urban rail transit has led to great service pressures for metro companies in organizing train services to provide higher transportation capacities in order to satisfy passengers' travel demand, especially on those metro lines with insufficient rolling stock. In order to cope with high passenger flow service pressure, a mixed integer nonlinear programming(MINLP) model is proposed to optimize the line plan, timetable and rolling stock circulation simultaneously, to reduce the number of rolling stocks and increase the number of full-length services. A two-step algorithm strategy is proposed. In the first stage, the train timetable is optimized under the assumption that all the train services are the full-length services. In the second stage, the rolling stock plan is optimized based on the timetable optimized in the first stage. To ensure a feasible rolling stock circulation, certain full-length services are shortened to the short-length services due to the limited number of rolling stocks. Numerical experiments are performed based on the real-life data of Shanghai Metro Line 8. Results show that the proposed method can efficiently optimize the timetable and rolling stock circulation of the whole operation day. The optimized results are beneficial for both the service and the operational costs.展开更多
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 c...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.展开更多
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 i...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.展开更多
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...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.展开更多
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 th...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.展开更多
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 resu...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.展开更多
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 resc...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.展开更多
基金This research work was supported by the University Malaysia Sabah,Malaysia.
文摘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.
基金This work was supported by the National Natural Science Foundation of China （Nos. G61374065, G61034007, G61374002） the Fund for the Taishan Scholar Project of Shandong Province, the Natural Science Foundation of Shandong Province （No. ZR2010FM013） the Scientific Research and Development Project of Shandong Provincial Education Department （No. J11LA01 ）
文摘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.
基金National Natural Science Foundations of China(Nos.61174040,61104178)Shanghai Commission of Science and Technology,China(No.12JC1403400)the Fundamental Research Funds for the Central Universities,China
文摘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.
基金supported by Deanship of Scientific Research at Imam Abdulrahman Bin Faisal University,under the Project Number 2019-383-ASCS.
文摘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.
文摘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.
基金This work was supported in part by the Outstanding Young Scholar Program of National Natural Science Foundation of China(NSFC)(Grant No.61522311)in part by the General Program of NSFC(Grant No.61773300)+1 种基金in part by the Key Program of Fundamental Research Project of Natural Science of Shaanxi Province,China(2017JZ017)in part by the Doctoral Students'Short-Term Study Abroad Scholarship Fund of Xidian University.
文摘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.
基金supported by the National Natural Science Foundation of China (52008328)National Key Research and Development Project (2018YFD1100202)+1 种基金the Science and Technology Department of Shaanxi Province (2020SF-393,2018ZDCXL-SF-03-04)the State Key Laboratory of Green Building in Western China (LSZZ202009).
文摘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.
文摘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.
文摘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.
基金supported by Changsha Municipal Natural Science Foundation(No.KQ2014146)National Natural Science Foundation of China(Grant No.52072264,71771150,72171175,71890970,72021002)National Key Research and Development Program of China(Grant No.2018YFB1600900).
文摘Intercity high-speed rail (HSR) is a type of mass transit built in densely populatedmetropolitan areas and has become an essential part of sustainable transportation systemsin some countries. One of the most challenging problems is how to jointly optimize thetrain line plan and timetable with simultaneous consideration of the system efficiency,cost, and level of service. In this paper, we focus on optimizing the train line plan and timetableof intercity HSR given actual time-dependent demand while appropriately consideringthe operational constraints including overtaking. First, we formulate the optimizationproblem as a mixed integer nonlinear programming (MINLP). Its objective is to minimizethe total system cost comprised of the trains’ fixed and variable operation costs, passengers’travel time cost, and penalties for passengers’ departure time deviation and passengers’failing to board a train. We then design a double-layer simulated annealing (SA)algorithm, in which the inner layer algorithm optimizes the stop plan, the departure andarrival times at each station, while the outer layer algorithm optimizes the number oftrains, their origin–destination stations, and their departure times at origin stations.Next a case study is conducted on Shanghai-Nanjing intercity HSR using actual timedependentdemand. The numerical results show that the proposed model can help significantlyreduce the total number of trains used by increasing the average seat occupancy,while creating little impact on the average passenger travel time and departure time.The study provides valuable guidance for optimizing HSR train line plan and timetablebased on real-world time-dependent demand.
基金Sponsored by the National Key R&D Program of China (Grant No.2021YFB1600100)。
文摘The rapid growth of passenger flow in urban rail transit has led to great service pressures for metro companies in organizing train services to provide higher transportation capacities in order to satisfy passengers' travel demand, especially on those metro lines with insufficient rolling stock. In order to cope with high passenger flow service pressure, a mixed integer nonlinear programming(MINLP) model is proposed to optimize the line plan, timetable and rolling stock circulation simultaneously, to reduce the number of rolling stocks and increase the number of full-length services. A two-step algorithm strategy is proposed. In the first stage, the train timetable is optimized under the assumption that all the train services are the full-length services. In the second stage, the rolling stock plan is optimized based on the timetable optimized in the first stage. To ensure a feasible rolling stock circulation, certain full-length services are shortened to the short-length services due to the limited number of rolling stocks. Numerical experiments are performed based on the real-life data of Shanghai Metro Line 8. Results show that the proposed method can efficiently optimize the timetable and rolling stock circulation of the whole operation day. The optimized results are beneficial for both the service and the operational costs.
文摘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.
文摘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.
文摘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.
基金Project(51008229)supported by the National Natural Science Foundation of ChinaProject supported by Key Laboratory of Road and Traffic Engineering of Tongji University,China
文摘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.
文摘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.
基金supported partially by the National Natural Science Foundation of China(61790573,61790575)the Center of National Railway Intelligent Transportation System Engineering and Technology(RITS2019KF03)+3 种基金China Academy of Railway Sciences Corporation LimitedChina Railway Project(N2019G020)China Railway Project(L2022X002)the Key Project of Science and Technology Research Plan of China Academy of Railway Sciences Group Co.Ltd.(2022YJ326)。
文摘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.
