Some Results on Evolving Cellular Automata Applied to the Production Scheduling Problem

Production scheduling is the process of allocating the resources and then sequencing of task to produce goods. Allocation and sequencing decision are closely related and it is very difficult to model mathematical interaction between them. The allocation problem is solved first and its results are supplied as inputs to the sequencing problem. High quality scheduling improves the delivery performance and lowers the inventory cost. They have much importance in this time based competition. This can be achieved when the scheduling is done in acceptable computation time, but it is difficult because of the NP-hard nature and large size of the scheduling problem. Based on the machine environment, sequence of operations for the jobs, etc. , the production scheduling problem is divided into the different types: one stage, one process or single machine; one stage, multiple processor or parallel machine; flow shop, job shop, open shop; static and dynamic etc. Job shop is a complex shop where there are finite number of machines, jobs and operation to be done on jobs. There is no direction of flow for jobs. The scheduling is done based on the selection of machine k to process an operation i on job j. Each job can be processed on a machine any number of times. Flexible job-shop scheduling problem (FJSP) extends the JSP by allowing each operations to be processed on more than machine. With this extension, we are now confronted with two subtask: assignment of each operation to an appropriate machine and sequencing operations on each machine. In the literature, different approaches (tabu search, simulated annealing, variable neighborhood, particle swarm optimization, clonal selection principle etc.) have been proposed to solve this problem (Fattahi,et al., 2007; Kacem, et al., 2002; Liu, et al., 2006; Ong, et. al., 2005; Preissl, 2006; Shi-Jin, et al., 2008; Tay, et al., 2008; Yazdani, et al., 2009). The genetic algorithms (GA), genetic programming, evolution strategies, and evolutionary programming for scheduling problem are described in (Affenzeller, et. al., 2004; Back, et al., 1997; Beham, et al., 2008; Koza, 1992; Mitchell, et. al., 2005; Zomaya, et. al., 2005; Stocher, et. al., 2007; Winkler, et. al., 2009), and cellular automata are presented in (De Castro, 2006; Tomassini, 2000; Seredyński, 2002). Using GA algorithm to behavior in cellular automata (CA), evolutionary design of rule changing CA, and other problems are described in (Back,