A general-purpose [school] timetable planner

Pao Yue-kong Library Electronic Theses Database

A general-purpose [school] timetable planner


Author: Lau, Chi-kan
Title: A general-purpose [school] timetable planner
Degree: M.Sc.
Year: 1996
Subject: Schedules, School -- Data processing
Hong Kong Polytechnic University -- Dissertations
Department: Multi-disciplinary Studies
Pages: iv, 158 leaves : ill. ; 30 cm
Language: English
InnoPac Record: http://library.polyu.edu.hk/record=b1235555
URI: http://theses.lib.polyu.edu.hk/handle/200/3628
Abstract: STP, or school timetabling problem, is NP-complete. There is no existing polynomial-time algorithm for this problem. What we could do is to look for a heuristic algorithm that might produce an acceptable, probably not the best, solution. The aim of this project is to develop a fully automatic general-purpose school timetabling package which can make timetables for secondary and primary schools in Hong Kong. In order to achieve this aim, in our first step, we analyze the nature of the STP to great detail. We produce three definitions to describe the problem in sequence, with each latter one refining the former one; we also relate the problem with three well established combinatorial problems in the literature - vertex-coloring, bin-packing and location-optimizing - to gain insight. Then we point out that school timetabling is often done in an over-constrained condition and the software should know how and when to make concession. Based on the third definition (Definition 5.1), we first map the STP to the constraint satisfaction problem (CSP) and then extend it to partial constraint satisfaction problems, PCSPs. We verify three classes of PCSPs relevant to our research and argue that the STP can be broken down into PCSPs and solved in the order of maximal utility problem(MUP), minimal violation problem (MVP) and constraint satisfaction optimization problem (CSOP). The algorithm we use to tackle the school timetabling problem is called TMA (standing for Tuen Mun algorithm). We use this name because the algorithm was first developed in a secondary school in Tuen Mun. TMA is inspired by Freuder's Constraint Synthesis Algorithm. It is basically a solution synthesis algorithm constructively synthesizing the local constraints, variable by variable, to produce a set of n-consistent compound label for the n variables in the problem. Horizontal restructuring procedures, instead of the vertical propagation procedures adopted by Freuder, are used to raise partial solutions from lower to higher levels of consistency. Heuristics like adjacent swapping, iterative repair, constraint ordering, soft-constraint relaxation and variable ordering are also adopted. The timetabling package we have developed is called TMSTP (standing for Tuen Mun School Timetable Programming). It is built upon a two-tiered database system and it turns out that a relational database is very helpful in representing constraint data and very efficient in implementing forward checking and backward checking. Experiments with eleven sets of data from four primary and three secondary schools show that the package can achieve 100% successful rate in all eleven cases. (We follow the practice in the literature that when the timetabler can assign all lectures to all slots without clashing, it is a 100% successful rate. Some minor adjustment is required in some instances.) The quality of timetables is comparable or better than those prepared by human timetablers.

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