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A Constraint Logic Programming Solution to the Teacher Relocation Problem Nagehan Ilhan Assoc.Prof.Dr Zeki Bayram Eastern Mediterranean University Famagusta Turkish Republic of Northern Cyprus

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Constraint Logic Programming Constraint Logic Programming, abbreviated as CLP is the general term for a programming paradigm specialized to solve a large class of combinatorial problems flexibly and efficiently. It is well suited for scheduling problems since it allows the formulation of the constraints of the problem in a high-level, declarative way

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Problem Specification The teacher relocation problem concerns school teachers wishing to relocate to other schools and who state their preferences in terms of which schools they want to move to. Each teacher who wishes to relocate can state two choices in order of preference. An implicit, but undesirable third choice on the part of the teacher is to stay in his/her current school

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Problem Specification-Cont Teachers who do not wish to relocate do not make any choices, and are not forcibly relocated. Teachers state their choices in order of preference. A specific teacher’s happiness is given by order(teacher, assignment(teacher)), where order(t,s) is the position (first, second etc.) of school s in the preference declaration of teacher t.

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Problem Specification-Cont The goal of the system is to maximize the overall happiness of the teachers, which corresponds to minimizing the value of the objective function.

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Constraints For each school, the following constraint must be satisfied: Another obvious constraint is that a teacher cannot be assigned to more than one school.

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Time Complexity For N teachers, the best case time complexity is N, where each teacher is assigned to his/her first choice without violating any constraints. For the worst case analysis, all possible combinations of assignments must be considered, which gives us 3 N.

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Data Structures To store the information of teachers, we use the structure teacher(Teachername, ALSchool) for each teacher. -Teachername is the name of the teacher. -ALSchool is the current school of the teacher.

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Data Structures-Cont A teacher’s choices are represented as choice(Teachername, SchoolName, ChoiceNo, AppYear). -Teachername is the name of the teacher. -SchoolName specifies the name of the school which the teacher wants relocate to. -ChoiceNo represents the order of preference of this school. - AppYear is the application year of the teacher for relocation.

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Data Structures Information about schools is given by school(Schoolname, Countyname, Quota, MaxCapacity) -SchoolName is the name of the school -Countyname specifies the county which the school belongs to -Quota is the number of vacancies at the school -MaxCapacity specifies the maximum number of teachers which the school can employ

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Technique Used teacher-school pairs are assigned -1 or 0 to indicate whether teacher is assigned to school. -1 means that teacher is assigned to school, 0 means teacher is not assigned to school. The list which will be assigned in labeling procedure has structure as follows: [(Teachername,Schoolname,R,Cost),….] Two techniques are used to prune the search space : Incremental search of the state space Baseline value used to prune the search space

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Inremental Search Initially only the first choice of each teacher is considered. If no solution is possible, then the first two are considered etc.

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Baseline Value An initial solution is obtained. If a partial solution is guaranteed to lead to a solution which exceeds the base value, that branch of the search space is pruned.

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Results It is possible to solve the problem “without incremental domain”. To see if there is any significant difference, both approaches trained using simulated data, varying the number of teachers and the quotas of schools. The number of schools fixed at ten.

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Quota Changes 1 to 5 With the incremental domain technique, the problem is solved much more quickly.

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Quota Changes 1 to 10 As the quotas increase, the problem becomes easier. Teachers can then be assigned to schools without requiring that other teachers leave the school.

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Worst Case The program is forced to tries almost all possibilities to find the solution and search space increases to its maximum level. The incremental domain approach still outperforms the other.

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Conclusion We defined the teacher relocation problem, modeled it using constraints, implemented a solution as an ECLiPSe program, and tested our solution under various scenarios. We devised several strategies for reducing the search space, and generating results faster. The first is using a baseline value for pruning solution paths that cannot possibly improve the baseline value. Second is the usage of “incremental domains,” where preferences of teachers are considered incrementally. Our simulation runs confirm that the incremental domain approach outperforms the non- incremental one.

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Future Work We plan to improve the “cost function” by taking into account the needs of the schools and how long a teacher has been waiting for relocation. A Web based user interface is also being planned.

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1 Optimisation Although Constraint Logic Programming is somehow focussed in constraint satisfaction (closer to a “logical” view), constraint optimisation.

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