Feasible Timetables Research Articles

Iterated local and very-large-scale neighborhood search for a novel uncapacitated exam scheduling model

We consider a novel uncapacitated exam scheduling model where the soft constraint stipulates that the exams should be spread over the periods so as to avoid adjacent conflicts as much as possible. The proposed method starts by constructing an initial feasible timetable. A two-phase method is then iterated. The first phase is a local search (LS) heuristic where two neighborhoods, ExamShift and KempeSwap, are searched using the token-ring strategy. The second phase takes as input the local optimum obtained during the first phase and performs a very-large-scale neighborhood (VLSN) search. We prove that searching the exponential neighborhood is NP-hard. Hence a polynomial-time heuristic based on reordering the periods is proposed for exploring a polynomial sized part of the neighborhood. The incumbent of the VLSN search is then perturbed and the method iterated. The practicability and effectiveness of our approach is studied by testing it on the university of Toronto benchmark instances and comparing it to an established method adapted to the new model.

도시철도 일반·급행 혼합 스케줄 작성을 위한 시뮬레이션 방법론

There has been much discussion of introducing express train service in urban railway transportation since the express train service was successfully launched in Seoul line 9. However the discussion is mainly focused on the infrastructure problem like how to install siding tracks or the corresponding costs. This study addresses the operational aspects in operating the express trains; for example, how to calculate of running times of express trains or headway between the trains, and then how to make up the timetable. These aspects have been found out by means of another special project. We suggest a simulation based approach to develop the mixed timetable. The approach consists of the several steps of calculating some fundamental times, adding the trains, and adjusting the arrival and departure times. The approach has some advantages that the running time and headway are automatically calculated within the simulation software so that the feasibility of timetable can be easily checked. We could yield a mixed feasible timetable of regular and express trains in the Seoul line 9 just by means of the suggested procedure.

Train timetabling by skip-stop planning in highly congested lines

We study the problem of scheduling passenger trains in a highly congested railway double-track line with the aim of increasing the number of scheduled trains. A feasible timetable of the trains currently scheduled in the network is given. Additional trains should be scheduled to meet the increasing passenger demand. To achieve this goal, we are allowed to increase the dwelling time of some trains at some stations, to let them stop at some additional stations and even to skip a few stops. Thereby, we need to take explicitly into account the deceleration and acceleration times that are needed by the train when it stops at a station. This problem integrates the choice of the train schedule with the choice of the train stops, the latter being usually made in the Line Planning process. To solve this problem, we propose a heuristic algorithm, extended from a previous method to include the new features of the studied application, and show its performance on real-world instances of the Chinese high-speed JingHu corridor (between Beijing and Shanghai) involving up to 387 trains.

A cycle time optimization model for generating stable periodic railway timetables

As train passengers expect a high degree of reliability from a railway network with minimal delays, during the timetabling process planners need to balance the goals of maximizing the offered capacity and delay resistance. This is often done in a two-step process where first a feasible timetable is found for a given line structure, and consecutively the stability of this timetable is evaluated and local modifications are performed to the timetable. This paper describes an optimization method to find a feasible periodic timetable that also ensures maximum stability for heterogeneous railway networks. The model is capable to handle flexible train orders, running and dwell times, and overtaking locations. We use the minimum cycle time of the periodic timetable as an indicator for stability, and define an optimization problem with this minimum cycle time as the objective function to be minimized. We also present dimension reduction methods and an iterative optimization approach to improve the mathematical optimization process. We show the applicability of the approach with case studies on the central part of the Dutch railway network.

Timetable Optimization for High-Speed Trains at Chinese Railways

We study the Train Timetabling Problem (TTP) of the high-speed trains at the Chinese railways. TTP calls for determining, in the planning phase, an optimal schedule for a given set of trains, while satisfying track capacity occupation constraints. In this work, we are given on input a set of feasible timetables for the trains already planned along a double-track high-speed line, and the main goal consists of scheduling as many additional trains as possible. Beside the main goal, a second objective is to obtain a regular schedule, i.e. a schedule showing regularity in the train frequency. We model TTP on a time-space graph and propose a heuristic algorithm for it. Preliminary computational results on real-world instances of the high-speed line from Beijing to Shanghai in China are reported.

Integrating a Repairing-based Genetic Algorithm-Neighborhood Search Structure in Solving the Course Timetabling Problem

The course timetabling problem is not a trivial task as it is an NP-hard and NP-complete problem and many solutions have been proposed due to its high complexity search landscape. In essence, the nature of the course timetabling problem is to assign a lecturer-course entity to existing teaching venue and timeslot in an academic institution. In this article, the authors propose a Genetic Algorithm-Neighborhood Search (GANS) to construct a feasible timetable for courses offered by a department in the faculty of a local university in Malaysia. The framework of the solution is as follow: The feasible timetable is first constructed by Genetic Algorithm, which includes are pair operator which attempts to repair infeasible timetables. Upon feasibility, the second phase exploits the initial feasible solution using three neighborhood structures to search for an improved solution and global optimum. The experimental results demonstrate the efficiency and effectiveness of the various neighborhood structures in exploiting the feasible solutions to yield the global optimum.

An integrated micro–macro approach to robust railway timetabling

With the increasing demand for railway transportation infrastructure managers need improved automatic timetabling tools that provide feasible timetables with enhanced performance in short computation times. This paper proposes a hierarchical framework for timetable design which combines a microscopic and a macroscopic model of the network. The framework performs an iterative adjustment of train running and minimum headway times until a feasible and stable timetable has been generated at the microscopic level. The macroscopic model optimizes a trade-off between minimal travel times and maximal robustness using an Integer Linear Programming formulation which includes a measure for delay recovery computed by an integrated delay propagation model in a Monte Carlo setting. The application to an area of the Dutch railway network shows the ability of the approach to automatically compute a feasible, stable and robust timetable. Practitioners can use this approach both for effective timetabling and post-evaluation of existing timetables.

A Rectification Strategy In Genetic Algorithms for Academic Timetabling Problem

The university course timetabling problem is both an NP-hard and NP-complete scheduling problem. The nature of the problem concerns with the assignment of lecturers-courses to available teaching space in an academic institution and may take on the form of high school timetabling, examination timetabling or university course timetabling. In this paper, the authors attempt to construct a feasible timetable for a faculty department in a local university in Malaysia which at the present moment; the scheduling task is performed manually by an academic registrar. The feasible timetable is constructed by means of Genetic Algorithm, embedded with a rectification strategy which transforms infeasible timetables into feasible timetables.

IJARCCE - Computer and Communication Engineering

4 Abstract: Timetable creation is a very arduous and time consuming task. To create timetable it takes lots of patience and man hours. Time table is created for various purposes like to organize lectures in school and colleges, to create timing charts for train and bus schedule and many more. To create timetable it requires lots of time and man power .In our paper we have tried to reduce these difficulties of generating timetable by Genetics Algorithm. By using Genetic algorithm we are able to reduce the time require to generate time table and generate a timetable which is more accurate, precise and free of human errors. The first phase contains all the common compulsory classes of the institute, which are scheduled by a central team. The second phase contains the individual departmental classes. Presently this timetable is prepared manually, by manipulating those of earlier years, with the only aim of producing a feasible timetable.

Developing a Decision Support System for University Course Timetabling: A Real World Problem

There are several characteristics that make timetabling problems particularly difficult to solve. Even the small instances of university course timetabling problem have huge search spaces, they are often highly constrained, they require sophisticated solution representation schemes, and they usually require very time-consuming fitness evaluation routines. Thus standard evolutionary algorithms lack of efficiency to deal with them. In this paper we have proposed a Genetic Algorithm (GA) with biased selection strategy for decoding chromosomes. Using this type of decoding strategy improves the feasibility ratio of the population. Since the resulted GA incorporates GA with problem specific knowledge for decoding and solution construction, we can call it a Memetic Algorithm (MA). Our developed MA incorporates the problem specific knowledge for decoding chromosomes in evaluation step such that most of the generated chromosomes are decoded into feasible timetables. This knowledge is used for selecting all five elements (i.e. course, professor, day, time-block, room) of each single event when decoding and evaluating a chromosome. Generating vast amount of feasible chromosomes makes the progress of search process possible in a time efficient manner. Developed solver package is coded in MATLAB and its data entry interface is coded in a spreadsheet to facilitate the application of the Decision Support System for a user without programming skills. Experimental results show the capability of the developed algorithm for generating feasible solutions.

Review of Generation of Time Table Using Genetic Algorithm Implemented in Java

An educational timetabling is a multi-dimensional and highly constrained problem. Making educational timetables manually often involves number of rounds of changes before they can be satisfied. In Fact such a process can be time consumings, and often the quality of the timetables is compromised due to pressure to release the TT on time. Automatic generation of timetables then seems to be an attractive to manual approach. But this approach is with problems. In reality, most timetabling problems are NP-complete and most professors and researchers are interested in developing efficient algorithms for solving the time table problem. In this, a college timetable problem formulation is introduced lowed by recent approaches for solving the problem. After that, a genetic algorithm (GA) is presented to efficiently and effectively solve the problem. The proposed GA has a malleable (flexible) representation that handles all the college timetables at once. It includes repair strategies to always guarantee the creation of a feasible timetable which satisfies constraints that must not be destroyed. The algorithm is implemented and applied to create timetables for the Arab Academy for Science and Technology (AAST) in Egypt and it shows promising results. Keywords— Genetic Algorithm (GA), Time Table Problem (TTP), Non Polynomial Problem (NP-Problem), Chromosome, Fitness, Mutation, Crossover.

Using particle swarm optimization to solve effectively the school timetabling problem

A new hybrid adaptive algorithm based on particle swarm optimization (PSO) is designed, developed and applied to the high school timetabling problem. The proposed PSO algorithm is used to create feasible and efficient timetables for high schools in Greece. Experiments with real-world data coming from different high schools have been conducted to show the efficiency of the proposed PSO algorithm. As well as that, the algorithm has been compared with four other effective techniques found in the literature to demonstrate its efficiency and superior performance. In order to have a fair comparison with these algorithms, we decided to use the exact same input instances used by these algorithms. The proposed PSO algorithm outperforms, in most cases, other existing attempts to solve the same problem as shown by experimental results.

The periodic service intention as a conceptual framework for generating timetables with partial periodicity

Many railway companies in Europe operate periodic timetables. Yet most timetables are not entirely periodic but have a mixture of different periodicities and many exceptions to cope with changing demand. Current approaches for automatic timetable generation are not able to deal with such partially periodic structures but consider only fully periodic inputs. We therefore introduce the periodic Service Intention (pSI) as a framework where customer-relevant information about train services can be described, including their periodicity information. We then address the problem of finding a feasible timetable that fulfills the requirements specified in a pSI without the need for manual post-processing. We solve this problem by projecting intended train runs over equivalence classes and thereby reducing the pSI to an augmented instance of periodic timetabling. Thus it is possible to use existing models for periodic scheduling, such as Periodic Event Scheduling Problem, to generate periodic timetables with partial periodicity, which are finally rolled out to obtain the desired daily schedule according to the commercial requirements of the pSI. Results for a test case from the timetable for central Switzerland in 2008 show that this approach needs only slightly longer computation time than for a fully periodic instance, but the additional time is compensated by the fact that post-processing becomes unnecessary and by the better quality of the solution. The approach is particularly well suited for offers with a strong periodicity but some irregularities, which could not be treated properly by existing methods.

A clique-based algorithm for constructing feasible timetables

Constructing a feasible solution, where the focus is on ‘hard’ constraints only, is an important part of solving timetabling problems. For the University Course Timetabling Problem, we propose a heuristic algorithm to schedule events to timeslots based on cliques, each representing a set of events that could be scheduled in the same timeslot, which the algorithm constructs. Our algorithm has been tested on a set of well-known instances, and the experimental results show that our algorithm is efficient and can compete with other effective algorithms.

Parallelizing a CLIPS-based course timetabling expert system

Course timetabling is a complex task that cannot be achieved using only a few general principles. This work integrates expert systems and constraint programming to generate a novel artificial intelligence approach for a course timetabling system. This approach can be easily reformulated and customized to sup-port requirement changes. Furthermore, the difference between hard and soft constraints can be also addressed easily. However, achieving a feasible timetable is very time consuming because the inference engine is CLIPS-based. Notably, CLIPS is a rule-based language that relies on the repeated matching of facts with rules to generate conclusions. To overcome the problem, this work parallelizes the execution of the timetabling system in emerging cluster systems. However, scheduling courses in parallel without solving assignment conflicts is difficult. To conquer the inherent serialization of the inference of course timetabling, courses are scheduled one by one and the schedule for one course is parallelized. This work utilizes the inference process for scheduling one course that behaves similar to the nested if–then–else structure. The rules for the inference process of scheduling one course are partitioned into multiple rule clusters, where each rule cluster is inferred by a slave process. After receiving all feasible solutions generated by slave processes, the master decides which solution to adopt for a current course according to rule priorities. However, improper division of rules can result in a false conclusion or runtime errors. To ensure that a correct timetable is obtained, two possible problems caused by improper rule division are identified. Three partitioning guidelines are then used to cope with these problems. For implementation, this work applied a novel programming model that transmits facts in C and infers rules in CLIPS. Experimental results demonstrate that the proposed parallel timetabling system achieves superlinear speedup when running in a cluster system. The proposed method also helps parallelize CLIPS-based expert systems that have similar inference behavior to that in the course timetabling system.

A genetic algorithm approach to school timetabling

An adaptive algorithm based on computational intelligence techniques is designed, developed and applied to the timetabling problem of educational organizations. The proposed genetic algorithm is used in order to create feasible and efficient timetables for high schools in Greece. In order to demonstrate the efficiency of the proposed genetic algorithm, exhaustive experiments with real-world input data coming from many different high schools in the city of Patras have been conducted. As well as that, in order to demonstrate the superior performance of the proposed algorithm, we compare its experimental results with the results obtained by another effective algorithm applied to the same problem. Simulation results showed that the proposed algorithm outperforms other existing attempts. However, the most significant contribution of the paper is that the proposed algorithm allows for criteria adaptation, thus producing different timetables for different constraints priorities. So, the proposed approach, due to its inherent adaptive capabilities, can be used, each time satisfying different specific constraints, in order to lead to different timetables, thus meeting the different needs that each school may have.

Lecture timetabling at a Tunisian university

This paper deals with the lecture timetabling problem at an institution in a Tunisian university. The objective is to construct a feasible timetable for all the lectures taken by the students sections in the institution. For this, we give a formulation of the problem as a set of linear constraints. Then we develop a heuristic procedure that starts by assigning student sections having the biggest size to classrooms with the smallest capacity that can fit the students. This heuristic is illustrated with real data of one section at the Faculty of Economics and Management Sciences of Sfax (FEMSS) in Tunisia. In addition, it is fully implemented to solve the lecture timetabling problem for all the students sections in the same faculty.

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.

Stochastic Optimisation Timetabling Tool for university course scheduling

University timetabling is an NP-hard problem, which means that the amount of computation required to find solutions increases exponentially with problem size. Timetabling is subject to hard constraints that must be satisfied in order to produce feasible timetables and soft constraints, which are not absolutely essential. This paper describes the Stochastic Optimisation Timetabling Tool (SOTT) that has been developed for university course timetabling. Genetic Algorithms (GA), Simulated Annealing (SA) and random search are embedded in the SOTT. The algorithms include a repair process, which ensures that all infeasible timetables are rectified. This prevents clashes and ensures that the rooms are sufficiently large to accommodate the classes. The algorithms also evaluate timetables in terms of soft constraints: minimising student movement; avoiding fragmentation in the timetables for students and lecturers; and satisfying lecturers’ preferences for the timing of classes. The algorithms were tested using two sets of timetabling data from a collaborating university. Both GA and SA produced very good timetables, but the results obtained from SA were slightly better than those using GA. However, the GA was 54% faster than SA.

Generation of classes of robust periodic railway timetables

In this paper we discuss the problem of randomly sampling classes of fixed-interval railway timetables from a so-called timetable structure. Using a standard model for the timetable structure, we introduce a natural partitioning of the set of feasible timetables into classes. We then define a new probability distribution where the probability of each class depends on the robustness of the timetables in that class. Due to the difficulty of sampling directly from this distribution, we propose a heuristic sampling method and illustrate using practical data that our method indeed favors classes containing robust timetables over others.