Claudia Ruth Gatica

Conventional and Multirecombinative Evolutionary Algorithms for the Parallel Task Scheduling Problem

The present work deals with the problem of allocating a number of non identical tasks in a parallel system. The model assumes that the system consists of a number of identical processors and that only one task may be executed on a processor at a time. All schedules and tasks are nonpreemptive. Grahams [1] well-known list scheduling algorithm (LSA) is contrasted with different evolutionary algorithms (EAs), which differ on the representations and the recombinative approach used. Regarding representation, direct and indirect representation of schedules are used. Concerning recombination, the conventional single crossover per couple (SCPC) and a multiple crossover per couple (MCPC) are used [2]. Outstanding behaviour of evolutionary algorithms when contrasted against LSA was detected. Results are shown and discussed.

Evolutionary approaches with multirecombination for the parallel machine scheduling problem

Parallel machine scheduling, also known as parallel task scheduling, involves the assignment of multiple tasks onto the system architectures processing components (a bank of machines in parallel). Parallel machine scheduling is important from both the theoretical and practical points of view. From the theoretical viewpoint, it is a generalization of the single machine scheduling problem. From the practical point of view it permits to take full advantage of the processing power provided by resources in parallel. Two basic models involving m machines and n jobs are the foundations of more complex models. In the first problem the jobs are allocated according to resource availability following some allocation rule. In the second one, besides that, jobs are subject to precedence constraints. The completion time of the last job to leave the system, known as the makespan (C/sub max/), is one of the most important objective functions to be minimized, because it usually implies high utilization of resources. These problems, minimizing the makespan, are known in the literature (Pinedo, 1995) as the unrestricted parallel machine scheduling (Pm|C/sub max/) and the parallel machine scheduling with job precedence constraints (Pm|prec|C/sub max/). Evolutionary algorithms (EAs) have also been used to solve scheduling problems. This paper proposes a multirecombination scheme to solve both parallel machine scheduling problems.

Performance of Evolutionary Approaches for Parallel Task Scheduling under Different Representations

Task scheduling is known to be NP-complete in its general form as well as in many restricted cases. Thus to find a near optimal solution in, at most, polynomial time different heuristics were proposed. The basic Grahams task graph model [1] was extended to other list-based priority schedulers [2] where increased levels of communication overhead were included [3]. Evolutionary Algorithms (EAs) have been used in the past to implement the allocation of the components (tasks) of a parallel program to processors [4], [5]. In this paper five evolutionary algorithms are compared. All of them use the conventional Single Crossover Per Couple (SCPC) approach but they differ in what is represented by the chromosome: processor dispatching priorities, tasks priority lists, or both priority policies described in a bipartite chromosome. Chromosome structure, genetic operators, experiments and results are discussed.