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

Abstract

Constraint Programming is a methodology for problem solving which allows user to describe data and constraints of problem without explicitly solving in declarative phase. Constraint Satisfaction Problems (CSP) can simply be defined as a set of variables and a set of constraints among values of variables. Typical method of solving CSP models is building solution by backtracking approach in which a partial assignment to variables is incrementally extended, while maintaining feasibility of current solution. The constraints are kept satisfied throughout 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 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 area has been researched for a long time. A survey in British universities (Zervoudakis 2001) showed that only 21% of universities use a computer in generation of exam timetables. Only 37% of universities use computer as assistance in 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 beginning of school year, almost 150 work days. Constraint satisfaction is usually not first choice for modelling scheduling problems, due to their high complexity. Only final schedule (hopefully) satisfies all imposed constraints. During schedule generation, most of constraints will be dissatisfied at some point. We created a system where 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, 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