A hybrid particle swarm optimization for a university course scheduling problem with flexible preferences
Introduction
Scheduling problems are concerted with how to optimally assign the limited resources to tasks over time. Most scheduling problems are categorized as NP complete or combinatorial problems, such as communications, industrial control, operational research and production planning. This study focuses on a special class of scheduling problems, known as the university course scheduling problem (UCSP) and has been proved to be an NP-hard (Bardadym, 1996). The UCSP is simple to understand, yet complex enough to admit a wide range of solutions at varying levels of difficulty in implementation (Combs et al., 2005). The most important tasks of UCSP involve various constraints, such as instructors’ preferences, curriculum planning policies of school, student scheduling, classroom assignment and available teaching resources. Moreover, other constraints such as administrative rules and regulations of institutions, administration’s coordination, the cost consideration and individual expectation also constitute the additional constraints of the course scheduling. This fact implies that an optimal or near-optimal solution for a large scheduling problem can be quite time-consuming. Therefore, it is necessary to adopt efficient search algorithms to generate optimal or near-optimal solutions that satisfy those constraints.
A large variety of approaches have been applied to course scheduling problems, such as genetic algorithms (GA) and simulated annealing (SA) (Merlot et al., 2002, Valdes et al., 2002, Wang, 2002). Because of the intractable nature of the course scheduling problem, it is desirable to explore other avenues for developing good algorithms for UCSP. The emphasis of this study proposes a novel meta-heuristic method, named particle swarm optimization (PSO) to solve UCSP.
The particle swarm optimization (PSO) is first proposed by Kennedy and Eberhart (1995). In PSO, a swarm of particles spread in the space and the position of a particle presents a solution. Each particle would move to a new position decided with the global experience and the individual experience heading for the global optimum. Previous study (Lo, Chen, Shiau, & Wu, 2008) demonstrated that the approach is able to obtain more optima or near-optima solutions for the cases of resource-constrained scheduling problems. Luo, Wang, Tang, and Tu (2006) used PSO to solve the resource-constrained project scheduling problem; they showed that PSO is applicable to various combinatorial and scheduling problems. Furthermore, Salman, Ahmad, and Al-Madani (2002) presented PSO for task assignment problem; they also demonstrated that the proposed PSO-based algorithm solution quality is better than that of genetic algorithm (GA) in most of cases. Moreover, the PSO algorithm runs faster as compared with GA. Tseng and Liao (2008) demonstrated that the proposed PSO algorithm outperforms over GA and ant colony optimization (ACO) for the flow shop scheduling problem. More recently, other applications of PSO for scheduling problem can be found in Kuo et al., 2009, Sha and Hsu, 2006. This study introduces an approach based on PSO for UCSP. The proposed hybrid PSO (HPSO) algorithm contains several features. The first is to design an ‘absolute position value’ representation for the particle. The second is to allow instructors that they are willing to teach based on flexible preferences, such as their preferred days and time periods, the maximum number of teaching-free time periods and the lecturing format (consecutive time periods or separated into different time periods). The third, a repair process is involved, which ensures that all infeasible timetables are rectified. Furthermore, since the solution space of UCSP is discrete, and a local search scheme is incorporated to explore a better solution improvement. The experimental results demonstrate that the hybrid approach yields an optimal satisfaction of course scheduling for instructors and class scheduling arrangements.
The remainder of this study is organized as follows. In Sections 2 Literature review, 3 Problem description and assumptions for UCSP, a survey of literature and the university course scheduling problem are discussed, respectively. The structure of HPSO is presented in Section 4. In Section 5, experimental results and discussion are made. Finally, some conclusions follow in Section 6.
Section snippets
Literature review
The university course scheduling problem (UCSP) is one of the scheduling problems that has been extensively studied over the last 25 years (Valdes et al., 2002). Many studies solve UCSP using the meta-heuristics based methods, such as simulated annealing (Pongcharoen et al., 2008, Thompson and Dowsland, 1998), genetic algorithms (Drexl and Salewski, 1997, Pongcharoen et al., 2008, Wang, 2002, Wang, 2003), tabu search (TS) (Alvarez-Valdes, Crespo, & Tamarit, 2002) and ant colony optimization (
Problem description and assumptions for UCSP
Marriott and Stuckey (1998) showed that the problem of generating course schedules is a classic example of a constraint satisfaction problem. The UCSP has arisen in the context of a university in Taiwan. It consists of a set of courses to be scheduled in 40 timeslots across five days and eight periods. At the beginning of new semester, several courses are offered to students (classes) and each course can be divided into various sections according to the number of students enrolled. The UCSP
Hybrid particle swarm optimization (HPSO) and UCSP
The particle swarm optimization (PSO) was designed, developed and tested to solve UCSP. Before presenting the algorithm, the PSO meta-heuristic is introduced as follows.
Preliminary experiment
The HPSO approach described in Section 4 was implemented in visual C++ to conduct necessary experimentation (including a user friendly Graphical User Interface). The experiments are tested on a Pentium 4 – 3.40 GHz CPU with 512 MB RAM. The tested problems were performed using the data sets from the department of information management of Kun-Shan University in Taiwan, shown in Table 2. The performance of the PSO algorithm depends on the parameters chosen. The preliminary experiment used small
Conclusions
This study has investigated the HPSO approach in a course scheduling problem. The proposed HPSO algorithm contains several features. The first is to design an ‘absolute position value’ representation for the particle. The second is to allow instructors that they are willing to lecture based on flexible preferences, such as their preferred days and time periods, the maximum number of teaching-free time periods and the lecturing format (consecutive time periods or separated into different time
Acknowledgements
This work was supported by the National Science Council, Taiwan, Republic of China, under grant number NSC 99-2221-E-242-006.
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