On Cellular Automata Training

This article introduces multiprocessor scheduling algorithms based upon cellular automata. To design cellular automata corresponding to a given program graph a generic definition of program graph neighborhood is used, transparent to the various kinds, sizes and shapes of program graphs. The cellular automata-based scheduler works in two modes. In learning mode a genetic algorithm (GA) is applied to discover rules of cellular automata (CAs) suitable for solving instances of a scheduling problem. In operation mode discovered rules of cellular automata are able to find automatically an optimal or suboptimal solution of the scheduling problem for any initial allocation of a program graph in two-processor system graph. Discovered rules are typically suitable for sequential cellular Automata working as a scheduler. Experimental results concerning scheduling algorithms discovered in the context of cellular automata based scheduling system are presented. INTRODUCTION Multiprocessor scheduling belongs to a special category of computational problems. On one side it is closely related to the issue of practical performance of current and future computers. On the other side, the problem even limited to the simplest case considered in the paper when we have to do with the two processor system but any parallel program is an example of computationally difficult unsolved research problem, known to be as an NP-complete problem [2]. Therefore heuristics based in particular on genetic algorithms (GA) , neural networks and simulated annealing are effectively used today (see, e.g. [7]) to solve scheduling problems. One of the problems which still remains is a high computational cost of a scheduler. Among sources of scheduling overhead is neglecting the potential knowledge about the scheduling problem which could be gained during solving instances of the scheduling problem. The motivation of our work is to develop a framework for designing scheduling algorithms where knowledge about scheduling process can be extracted and potentially used for solving new instances of scheduling problem. For this purpose we propose to use a recently emerged and very promising hybrid technique combining evolutionary computation and computation with cellular automata (CA). The remainder of the paper is organized as follows. The next section presents the scheduling problem. Section 3 gives an overview of CA. Section 4 presents the concept of multiprocessor scheduling with use of CA. Section 5 contains experimental results concerning sequential CA applied to scheduling and introduces a coevolutionary GA based engine for