Solving the High School Scheduling Problem Modelled with Constraints Satisfaction using Hybrid Heuristic Algorithms

Constraint Programming is a methodology for problem solving which allows the user to describe data and constraints of the problem without explicitly solving in the declarative phase. Constraint Satisfaction Problems (CSP) can simply be defined as a set of variables and a set of constraints among the values of the variables. Typical method of solving CSP models is building the solution by backtracking approach in which a partial assignment to the variables is incrementally extended, while maintaining feasibility of the current solution. The constraints are kept satisfied throughout the solving process. Many optimization problems of practical as well as theoretical significance consist of finding "the best" configuration of values for a set of variables. Such problems where the solution is modelled using discrete variables belong to combinatorial optimization (CO). The problems of combinatorial optimization consist of a set of variables, their domains, constraints among variables and a goal function that requires to be optimized. School scheduling is a typical example of a CO problem. High school schedule generation includes both temporal and spatial scheduling. It is a computation demanding and usually a complex task. It is a NP hard optimization problem that requires a heuristic solving approach (Zhaohui & Lim, 2000). It is interesting to note that educational institutions rarely use automated tools for schedule generation, although the area has been researched for a long time. A survey in British universities (Zervoudakis 2001) showed that only 21% of the universities use a computer in the generation of exam timetables. Only 37% of the universities use the computer as assistance in the process, while 42% do not use a computer at all. Generation of schedules in some schools in Japan takes up to 100 man hours a year. In bigger schools, schedule generation begins in April and does not end until June, two months after the beginning of the school year, almost 150 work days. Constraint satisfaction is usually not the first choice for modelling scheduling problems, due to their high complexity. Only the final schedule (hopefully) satisfies all imposed constraints. During schedule generation, most of the constraints will be dissatisfied at some point. We created a system where the extent of constraint satisfaction is measured and compared, so CSP can be successfully used in scheduling (Chorbev et al. 2007). When a measurement of constraint satisfaction is included, the system becomes a Constraint Optimization Problem (COP). O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg