School Schedule Creation and Optimization System

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1 5 th International Vilnius Conference EURO Mini Conference Knowledge-Based Technologies and OR Methodologies for Strategic Decisions of Sustainable Development (KORSD-2009) September 30 October 3, 2009, Vilnius, LITHUANIA ISBN M. Grasserbauer, L. Sakalauskas, E. K. Zavadskas (Eds.): KORSD-2009 Selected papers. Vilnius, 2009, pp Institute of Mathematics and Informatics, 2009 Vilnius Gediminas Technical University, 2009 School Schedule Creation and Optimization System Denis Strukov Kaunas University of Technology, Studentų g. 50, LT Kaunas, Lithuania. Abstract: Schedule creation is a common task in every school. All of Lithuanian schools (secondary and gymnasiums) offer high flexibility in the compilation of individual student s academic plan, while considering his/her abilities and interests. This task has a high level of complexity and is highly time consuming. To reduce the amount of time spent on creation and to increase the quality of such schedule, an automated school schedule creation system is needed. Reducing the time spent on creating a schedule means saving energy. Currently there are some commercial solutions on the market, but most of them do not offer the high flexibility required to fit the needs of profiled schools or are too expensive. To solve all these problems at once, an open source project has been considered. The goal of this project is to analyze the needs of a typical school and to create a fully automated school schedule creation and optimization system with a user friendly interface. To increase the quality of school schedule, local and global optimization method integration is planned. Currently a working prototype of this system is created. It implements a local optimization method to increase the quality of the created schedule. Results of this working solution are close to schedules created manually. Implementation of global optimization methods might increase the quality of automatically created schedule. To reduce the time of schedule creation and optimization, a multiprocessor system or computer cluster can be used. The system uses Java technologies to make the application publicly available online and reduce its hosting costs to the minimum. Keywords: school schedule creation, Monte Carlo method, optimization, computer cluster, global optimization, open source, energy saving 1 Introduction At least once or even several times a year every school has to deal with school schedule creation. This task is very difficult and highly time consuming. The time spent to create a schedule is proportional to the energy used by computers. In order to minimize the time and effort spent on schedule creation, automated scheduling software is needed. In this paper existing schedule creation and optimization solutions are reviewed and new open source software is introduced. The goal of this new project is to create an application that enables users to generate and optimize their schedules directly online. The new software has to decrease the complexity of schedule generation and increase or at least reach the level of quality that is offered by commercial products. To improve the quality of school schedules, several optimization methods are adopted. During the optimization, both subjective and objective criteria are taken in account. A special penalty point system is used to evaluate the created schedule. The goal of optimization algorithms is to minimize the value of a penalty function. 445

2 D. Strukov As schedule creation and optimization require high processing power, this software has to be able to run on a multiprocessor system as well as in a computer cluster environment. Java technology does not have a stable system to provide distributed computing capabilities. That means that custom methods have to be implemented to enable distributed computing in this software. 2 Existing solutions Currently there are several products on the market that are used to create and optimize school schedules. Most of them are desktop applications designed to run in MS Windows environment. The most popular of them are: Mimosa asc TimeTables Mimosa scheduling software allows users to create school schedules manually or generate them automatically. A mixture of these methods is also possible. When creating timetables manually, Mimosa prevents the creation of conflicts and gives hints of optimal actions for schedule creation. Mimosa s functionality is flexible enough to create individual schedules for each student. The schedule is evaluated using a penalty function which is represented by gap count. For schedule optimization Mimosa uses two different optimization algorithms. It is difficult to say which exact algorithms are used, as it is not specified in any documentation and no source code is available. From the optimization graphs it is possible to guess that the application uses local optimization algorithms as an amount of penalty points most of the time only decreases, but in some cases an increase of values is noticed (see figure 1). That might be a graphing problem. In other case it indicates that a global optimization method is being used. Figure 1. The increase of gap count during optimization The biggest disadvantage of Mimosa scheduling software is its complexity of use. It might require additional training to be able to manually create or automatically generate a time table. Although due to the possibility of the initial data to be imported using simple spreadsheets, this task can be performed by a person with average computer skills. The results of the application are presented in an easily readable format. A sample schedule fragment is shown in figure 2. The asc TimeTables application has a far more user friendly interface. Its look and feel is similar to MS Office The schedule creation mechanism of this application allows users to create the schedule manually as well as generate it automatically. The application has an easy to use data input interface, but to input one entity into the system the user is required to go through numerous windows. The switch between inputs (mouse, keyboard) is required quite often, which is time consuming. The amount of settings and features makes the application complicated, but a powerful tutorial system which is integrated into the application compensates its complexity flaw. 446

3 SCHOOL SCHEDULE CREATION AND OPTIMIZATION SYSTEM Figure 2. Result of Mimosa scheduling application for student Andreas1 The output of the application is presented in a graphical way (see figure 3) and allows users to make modifications to the resulted schedule. If the application fails to schedule any lessons, the user gets the chance to do it manually. Figure 3. A part of asc TimeTables generated schedule The main disadvantage of this application is that it creates schedules for student groups (e.g. 5c, 7a, etc.) or in the best case group divisions (boys, girls). To suit the needs of today s schools, an application should have the flexibility to generate individual student schedules. Both of the applications mentioned above are commercial and provide only a fraction of the functionality in a free version of the software. Both applications require installation on the Microsoft Windows system and need to be run locally. 3 Open Source online scheduling The new scheduling software is open source. The application is made with a future development and expansion possibilities in mind. Its core design allows easy modifications of data input modules. The application design also allows any user interface to be attached to the core scheduling engine. For core development, the program is kept in a form of desktop application and uses console input. 447

4 D. Strukov Bearing in mind that most of Lithuanian school staff uses Microsoft Office Excel in their everyday work, current implementation of data input uses MS Excel compatible XML structures to store data. In this case data can be inputted and modified using MS Office. The structure of the XML file is being kept as simple as possible. Data is logically divided and placed in separate sheets. Figure 4 displays a fragment of an MS Excel sheet designated for Teacher data input. Figure 4. Teacher data in MS Office Excel Student input and their individual academic plan is also inputted in the same manner. Here students are divided in groups by levels (e.g. 5a, 7b, etc.). Every student group has its own sheet in an Excel workbook. Student s academic plan is inputted by using the provided template (see figure 5). This is a common practice in Lithuanian schools to store information about students in this format. Figure 5. The template for student input During schedule creation, the application tests data integrity and prompts the user about possible mistakes in the input. The resulting school s or individual student s schedule can be outputted to XML, so it can be used for further manipulations or analysis. 4 Optimization methods In order to increase the quality of generated schedules there should be a way to evaluate ones. The application uses a penalty point system. Penalty points are assigned for every constraint violation. Only physical constrains are enforced and do not have any penalty points assigned. Physical constraints include: 448

5 SCHOOL SCHEDULE CREATION AND OPTIMIZATION SYSTEM A teacher can give only one lesson at certain period of time A student can attend only one lesson at certain period of time There is a maximum of 24 lessons (hours) a day Every operation which violates any of these constraints is considered to be invalid and may not be executed. To find a better schedule, a Monte Carlo optimization method is used. It is a local optimization method, but it proved itself to be considerably efficient. The realization of this optimization is quite simple: 1. Generate a valid schedule and record it as best found. 2. Generate a new valid schedule and compare it to the current best. a) If the new schedule is better than the current best, replace the current best with the new instance 3. Repeat step 2 for n times To improve the search for a better schedule, more complex optimization methods have to be implemented. Simulated Annealing is a popular global optimization method and seems to be a good candidate for this task. This method for the sake of finding a global minimum of a penalty function on every optimization step, with some probability (1), sacrifices schedule quality hoping that the next step will result in a much better schedule than the current one. h x / ln(1+ N) r= e. (1) Simulated Annealing method s optimization results depend on its optimization parameters: initial temperature and cooling rate. In order to get the best results, these parameters can be optimized using a method based on a Bayesian heuristic approach. This method predicts future results based on experimental data. 5 Distributed optimization All these optimization methods require high computing power. Time and speed of schedule optimization is directly related to available computing resources. Super computers are very expensive, so a cheaper computer cluster would be an affordable solution. Java technology does not have a direct and stable solution for distributed computing. That means that a custom mechanism has to be implemented. For a local optimization method that is implemented in the current application, simply running the application with the same initial data input on multiple servers would result in a linear increase of optimization speed. A simple choice of the best schedule between the servers will have to be made at the end of the optimization on all servers. In case of a global optimization method an instance of a valid schedule has to be provided as an input to each optimization server. RMI (Remote Method Invocation) technology is a perfect solution for inter-server communication. It allows the execution of remote services over the network as they would be on the same virtual machine. Using Java and RMI technology make possible to create a small specialized framework for distributed schedule optimization. 6 Conclusion An open source scheduling software provides essential scheduling functionality while leaving user input to the minimum. In order to generate a schedule which is more than just valid, local and global optimization methods are adopted. To decrease the time spent on schedule creation and optimization, the application will support distributed optimization. It will distribute 449

6 D. Strukov optimization tasks between multiple computers, which will linearly increase the speed of optimization. The final application will be deployed online with a web user interface. The use of Java technology enables the application to run on any platform. This fact will reduces the application hosting costs to minimum and allow users to use the application free of charge. By centralising the application online and making it available to multiple schools, the power consumption can be reduced by reducing the amount of comupters used to create a schedule and amount of time spent on creating one. Reference Mockus, J Bayesian heuristic approach to discrete and global optimization. Mimosa Software Ltd Mimosa Booklet. Available from Internet: < asc Timetables Documentation. Available from Internet: Pupeikienė, L.; Mockus, J Optimizacijos metodų taikymas profiliuotų mokyklų tvarkaraščiams sudaryti, in 12-oji Lietuvos jaunųjų mokslininkų konferencija Mokslas Lietuvos ateitis. Informatika. 450