George M. White

Using tabu search with longer-term memory and relaxation to create examination timetables

Abstract Several methods have been developed over the past four decades for producing examination timetables in educational institutions. This has turned out to be a difficult problem for which even elementary instances have a NP-hard complexity. This paper describes a tabu search based algorithm called OTTABU that creates examination timetables that have an heuristically minimized penalty function or “discomfort level”. This algorithm incorporates two tabu lists, a tabu relaxation policy and several other novel features. The algorithm has been executed with 12 publicly available sets of data and the results obtained are compared with similar results from five other published algorithms that use the same penalty function. It has been found that OTTABU compares favourably with these other algorithms when presented with the same data.

A logic approach to the resolution of constraints in timetabling

Abstract The construction of timetables involving three or more variables taking values from domains having thousands of values with several dozen constraints having different priorities is a problem common to many organizations. Various heuristics solutions have been proposed using results based on graph theory, mathematical programming and manual methods. We propose an approach based on logic progamming using the first order predicate calculus. An algorithm has been developed, implemented in WPROLOG, and thoroughly tested on an Amdahl 5880 under VM HPL.

Towards The Construction Of Optimal Examination Schedules

AbstractAssume c courses to be examined in p e:samination periods. Let the c courses be the nodes (v1, v2,..., Vc) of a graph and let a student registered in both courses vi and vj be represented by an edge joining the node pair (vi, vj). Then the scheduling of the c courses into p periods is analogous to partitioning the nodes of the graph into no more than p disjoint sets (s1, s2, ...,sp) such that, in any given set, there is no edge joining any of its elements. An additional aim is to find the minimum closed path through an appropriate weighted undirected graph which traverses all nodes exactly once. The solution to this problem will provide an optimum timetable for students writing examinations. This paper describes one such solution which has been used for several years at the University of Ottawa.

Generating Complete University Timetables by Combining Tabu Search with Constraint Logic

Several small data sets representing a few university departments were used with both a constraint logic program and a tabu search program to cast a timetable. The constraint logic program used alone produced timetables rather quickly. The tabu search program used alone ultimately produced better solutions but at a much slower rate. The sequential use of a constraint logic program whose output was used to start the tahu search produced the best timetables of all in a time that was much longer than that of the logic program alone but shorter than that of the tabu search used alone.

Scheduling Doctors for Clinical Training Unit Rounds Using Tabu Optimization

Hospitals must be staffed 24 hours a day, seven days a week by teams of doctors having certain combinations of skills. The construction of schedules for these doctors and the medical students who work with them is known to be a difficult NP-complete problem known as personnel scheduling, employee timetabling, labour scheduling er rostering. We have constructed a program that uses a constraint logic formalism to enforce certain scheduling rules followed by a tabu search heuristic optimizing algorithm to produce a call schedule that is used at the Ottawa Hospital. This call schedule can be later changed by the chief resident to accommodate last-minute personnel changes by means of a spreadsheet-based program.

Examination Timetables and Tabu Search with Longer-Term Memory

The examination scheduling problem has been examined and a four-phase system using a tabu search algorithm, OTTABU, has been implemented. This system uses both recency-based short-term memory and move (or frequency)-based longer-term memory to improve the quality of the solutions found. The system was tested using real data obtained from the University of Ottawa registrars office and real examination schedules were produced. It was found that the use of longer-term memory produced better schedules that those produced without such memory - typically a 34% improvement was obtained due to this factor alone. The length of the long term memory list was also found to be important. A length that is too small can greatly reduce its effectiveness. A list that is too long only reduces the effectiveness by a small amount. A quantitative analysis method is applied to estimate the appropriate length of the longer-term tabu list and a controlled tabu relaxation technique is used to improve the effectiveness.

Investigations of a Constraint Logic Programming Approach to University Timetabling

The casting of university timetables is a problem which combines classical numerical scheduling techniques with important human considerations. It will be argued here that since the application involves the preferences of humans, the problem is qualitatively different than similar problems involving inanimate objects. The humane and profane facets are combined in this study by using the constraint logic programming approach. The constraints are hierarchical: the primary constraints are rigidly enforced and the secondary constraints are relaxed according to their priority if a solution cannot be found. We present a solution based on a Prolog description of the constraints and goals. Two working implementations are described, one using an IBM mainframe and one using a personal computer. Tests with synthetic data and real data from a university have shown that good timetables can be cast using this method in a reasonable amount of time.

Interactive timetabling in universities

Abstract There are several classes of algorithms which use heuristic methods for constructing school timetables. The first class of algorithms uses graph theoric methods to approximate an exact solution to a variant of the well-known graph colouring problem. The second class uses linear optimization methods to minimize a suitably defined objective function. These algorithms generally create solutions which satisfy a family of constraints but usually cause other problems specific to the institution involved. An algorithm which uses piece-wise incremental construction is described submitting such timetables to be east in interactive mode and allows small perturbations to the specifications without requiring that the program be re-run.

An evaluation of certain heuristic optimization algorithms in scheduling medical doctors and medical students

Four heuristic algorithms based on or inspired by the well-known Tabu Search method have been used to cast heuristically optimized schedules for a clinical training unit of a hospital. It has been found experimentally that the algorithm of choice for this problem depends on the exact goal being sought where the execution time is one of the components of the goal. If only one run is allowed, then classical Tabu Search with a tenure of 5 gave the schedule with the lowest average (and fixed) penalty. If time is not of concern and many runs are allowed then the Great Deluge algorithm may generate the schedule with the lowest penalty.

Complete university timetabling using logic

The scheduling of lectures, laboratories, seminars and the like at universities and schools is an activity carried out often. Because of its importance, it has been studied intensively both theoretically and practically for a long time[l,2]. The complete timetabling problem for universities concerns professors, students, courses, classrooms and timeslots and casts schedules such that the professors and students meet during one or more timeslots during the week in certain classrooms for their courses. Since there are a limited number of human and material resources available and because of conservation laws, the schedules have to be constrained so that certain conditions are met, e.g. a student cannot be in more than one classroom at a time and the classrooms must be large enough to contain the students scheduled into them. Some of the constraints are absolute and must be observed at all costs. Other constraints are desirable and should be observed if possible but may be relaxed if required to cast the schedule. This category includes such considerations as: lectures should not be held on Friday afternoons. A rich variety of techniques has been brought to bear on the timetabling problem but there are no generally accepted solutions in existence yet. Far more success has been obtained for various subsets, notably the examination scheduling problem[2-4]. This problem deals with courses, students and timeslots only where it is required to assign each course to a timeslot such that no student has to be present at two or more examinations simultaneously. There may, in addition, be further requirements such as requiring the number of consecutive courses to be minimized. Another such problem is the classroom assignment problem[5] where a set of professor-course meetings, already assigned to a set of timeslots is given and it is required to place these into a set of available classrooms. The difficulty of solving the complete problem is confounded because even simple versions of the problem are known to be NP-hard[6] and solutions to practical problems can involve thousands of values of five or more variables. A formal definition of the complete timetabling problem has been given elsewhere [7]. These constraints may be expressed formally as follows: Let there be m time periods, k = 1 . . . m; n2 teachers, j = 1 . . . n,; n, classes, i = 1 . . . n,; and n, rooms, I = 1 . . . n,. There is a requirements matrix R = (rij) and two vectors. E is an n,-vector whose ith element is the enrollment in class i and C is an n,-vector whose ith element gives the capacity of room i. Determine whether there is a function