Dynamic hard-real-time scheduling using genetic algorithm for multiprocessor task with resource and timing constraints

Abstract

Most publications in shop scheduling area focus on the static scheduling problems and seldom take into account the dynamic disturbances such as machine breakdown or new job arrivals. Motivated by the computational complexity of the scheduling problems, genetic algorithms (GAs) have been applied to improve both the efficiency and the effectiveness for NP-hard optimization problems. However, a pure GA-based approach tends to generate illegal schedules due to the crossover and the mutation operators. It is often the case that the gene expression or the genetic operators need to be specially tailored to fit the problem domain or some other schemes may be combined to solve the scheduling problems. This study presents a GA-based approach combined with a feasible energy function for multiprocessor scheduling problems with resource and timing constraints in dynamic real-time scheduling. Moreover, an easy-understood genotype is designed to generate legal schedules. The results of the experiments demonstrate that the proposed approach performs rapid convergence to address its applicability and generate good-quality schedules.

Introduction

The multiprocessor task scheduling problem (MTS) is a generalization of the classical scheduling problem that allows tasks (jobs) to be processed on more than one processor at a time (Drozdowski, 1996). Although MTS problems were motivated mainly by computer systems (Krawczyk & Kubale, 1985). However, Chen and Lee (1999) demonstrated that applications of multiprocessor tasks can also be found in work-force assignment for manufacturing processes. Furthermore, another application of the MTS problem can also be applied in real-time machine-vision systems (Ercan & Fung, 1999). Extensive surveys on the MTS problems were proposed by Drozdowski (1997) and Lee, Lei, and Pinedo (1997). In particular, Brucker, Knust, Roper, and Zinder (2000) and Du and Leung (1989) presented the computational complexity of different MTS problems, and the MTS problems in different shop environments were also demonstrated by Brucker and Kramer, 1995, Brucker and Kramer, 1996.

Because of the complexity of shop scheduling problems, different solution approaches have been developed. Usually, the optimum approach provides optimum solution. When it applies to large problems, the optimum approach can take hours or days to obtain a solution. Wang (2005) concluded that the branch and bound solution method is an exact method, which provides optimal solution. One major limitation is that the branch and bound method is computationally expensive and impractical for even modestly sized problems. Thus, heuristics are the most common approach to shop scheduling problems because of the low computational requirements. However, heuristics have difficulty in measuring solution quality (optimal or near optimal). Therefore, adaptive search approaches have been implemented to generate good-quality schedules in a reasonable time. Chen and Huang, 2001a, Huang and Chen, 1999 proposed an energy function for the Hopfield neural network (HNN) to schedule multiprocessor job with resource and timing constraints. Subsequently, they integrated fuzzy c-means clustering strategies into a Hopfield neural network to solve scheduling problems (Chen & Huang, 2001b). More recently, Chen, Lo, and Huang (2007) also proposed the competitive Hopfield neural network with slack neurons to solve real time job scheduling problem with processing time and deadline constraints. Furthermore, Lo, Chen, Huang, and Wu (2007) proposed an enchanced ant colony optimization (ACO) approach for the multiprocessor scheduling problems with precedence and resource constraints.

Recently, there are several types of artificial intelligence (AI) search techniques in solving optimization problems: neural networks, genetic algorithm, tabu search and simulated annealing. Most AI search approaches try to find a better solution or escape from a local optimal to obtain the globally better solution. AI search techniques, such as genetic algorithms (GAs), have shown the feasibility to solve the job-shop scheduling problems. Correa, Ferreira, and Rebreyend (1999) proposed a knowledge-augmented genetic approach to schedule multiprocessor tasks. Hajri, Liouane, Hammadi, and Borne (2000) presented a controlled GA based on fuzzy logic and belief functions to solve job-shop scheduling problems. Dorndorf and Pesch (1995) also presented a GA approach for job-shop environment. Some applications of multiprocessor task using the GA approach can also be found for manufacturing activities (Oğuz and Ercan, 2005, Şerifoğlu and Ulusoy, 2004). Chang, Chen, and Lin (2005) applied a two-phase subpopulation GA approach to solve parallel machine-scheduling problems. Moreover, Yang (2001) developed a GA-based discrete dynamic programming approach for scheduling in flexible manufacturing system (FMS) environments. However, a pure GA-based approach tends to produce illegal schedules due to the crossover and the mutation operators, therefore, the gene expression or the genetic operators need to be specially designed or some other schemes may be combined to solve the scheduling problems.

For the shop scheduling problems such as flow-shop, job-shop, open-shop and mixed-shop, most of the existing research focuses on the static conditions and seldom take into consideration dynamic disturbances such as machine breakdown and new job arrivals (Liu, Ong, & Ng, 2005). In the following, some research works related to dynamic shop scheduling are reviewed. Holloway and Nelson (1974) initially implemented a multi-pass procedure in a dynamic job-shop environment by generating schedules periodically. Subsequently, Muhleman, Lockett, and Farn (1982) analyzed the periodic scheduling policy in a dynamic and stochastic job-shop system. In addition, Church and Uzsoy (1992) considered periodic and event-driven rescheduling approaches in a single machine system with dynamic job arrivals. Subramaniam, Lee, Ramesh, Hong, and Wong (2000) also demonstrated that the performance of dispatching in a dynamic job-shop could be improved significantly through the simple machine selection rule.

To the best of our knowledge, no published work deals with the MTS problem with resource and timing constraints in dynamic real-time scheduling. This study focuses on dynamic real-time scheduling in the event of new job arrivals for the MTS problem. To explore the effectiveness, a GA-based approach with a feasible energy function and an easy-understood genotype is proposed to generate legal and good-quality schedules. An energy function designed to illustrate the timing and resource constraints is proposed as in Huang and Chen (1999).

The rest of the study is organized as follows. Section 2 describes the problem definition. The energy function of the scheduling problem is defined in Section 3. Next, the genetic algorithms are reviewed and the energy function is translated into the fitness function in Section 4. The mathematical proof of the convergence of the energy function is then illustrated in Section 5. The simulation examples and experimental results are presented in Section 6. Finally, concluding remarks of this study are made in Section 7.