International Journal of Engineering and Advanced Technology (IJEAT) ISSN: 2249 – 8958, Volume-3, Issue-2, December 2013 22 Abstract — An efficient assignment and scheduling of tasks of a multiprocessor system is one of the key elements in the effective utilization of multiprocessor systems. This problem is extremely hard to solve, consequently several methods have been developed to optimally tackle it which is called NP-hard problem. This paper presents two new approaches, Modified List Scheduling Heuristic (MLSH) and enhanced genetic algorithm by constructing promising chromosomes. Furthermore, this paper proposes three different representations for the chromosomes of the genetic algorithm: Min-min task list, processor list and combination of both. Extensive simulation experiments have been conducted on different random and real-world application graphs such as Gauss-Jordan, LU decomposition, Gaussian elimination and Laplace equation solver problems. Comparisons have been performed with the most related algorithms, LSHs, Bipartite GA (BGA) and Priority based Multi-Chromosome (PMC). The achieved results show that the proposed approaches significantly surpass the other approaches in terms of task makespan and processor efficiency. Index Terms— Multiprocessors, Task scheduling, Genetic algorithm, Makespan, Parallel and distributed system, List Scheduling Heuristic I. INTRODUCTION The proliferation in the use of multiprocessor systems these days in a great variety of applications is the result of many breakthroughs over the last two decades. These developments of multiprocessor systems are being used for several applications, including fluid flow, weather modeling, database systems, real-time, and image processing. The data for these applications can be distributed evenly on the processors of multiprocessor systems and maximum benefits from these systems can be obtained by employing an efficient task assignment and scheduling strategy [1]. The multiprocessor task scheduling problem considered in this paper is based on the deterministic model, which is the execution time of tasks and the data communication time between tasks that are assigned; and the directed acyclic task graph (DAG) that represents the precedence relations of the tasks of a parallel processing system [2]. The goal of the scheduler is to assign tasks to available processors such that precedence requirements among tasks are satisfied and the overall length of time required to execute the entire program, the schedule length or makespan, is minimized. Medhat Awadalla, Department of Electrical and Computer Engineering, Sultan Qaboos University, PO Box 33, Zip Code 123, Oman. Afaq Ahmad, Department of Electrical and Computer Engineering, Sultan Qaboos University, PO Box 33, Zip Code 123, Oman Samir Al-Busaidi, Department of Electrical and Computer Engineering, Sultan Qaboos University, PO Box 33, Zip Code 123, Oman Many heuristic approaches for task scheduling have been proposed [3]. The reason for such proposals is because the precedence constraints between tasks can be non-uniform, therefore rendering the need for a uniformity solution. We assume that the parallel processor system is uniform and non-preemptive. Recently, Genetic Algorithms (GAs) have been widely reckoned as a useful vehicle for obtaining high quality solutions or even optimal solutions for a broad range of combinatorial optimization problems including task scheduling problem [4]. Another merit of a genetic search is that their inherent parallelisms that can be exploited so as to further reduce its running time. Thus, several methods have presented to solve this problem based on GAs [5-8]. To tackle the multiprocessor task scheduling problem (MTSP), this paper presents two approaches: a modified list scheduling heuristic and hybrid approach composed of GA and MLSH. GA used three new different types of chromosomes: Min-min task list, processor list, and a combination of both. This paper is organized as follows: The multiprocessor task scheduling problem on the general models of a DAG is presented in section 2. Section 3 outlines the most related work to the theme of this paper. Section 4 proposes MLSH. Hybrid approach composed of genetic algorithm and MLSH comprising three different new types of chromosomes is presented in section 5. Genetic operators are presented in section 6. Simulated experiments and discussions are presented in section 7. Section 8 concludes the paper. II. MULTIPROCESSOR TASK SCHEDULING PROBLEM Multiprocessor scheduling problems can be classified into many different classes based on the following characteristics: 1. The number of tasks and their precedence. 2. Execution time of the tasks and the communication cost which is the cost to transmit messages from a task on one processor to a succeeding task on a different processor (Communication cost between two tasks on the same processor is assumed to be zero). 3. Number of processors and processors uniformity (A homogeneous multiprocessor system is composed of a set P = {P1… Pm} of ‘m’ identical processors. 4. Topology of the representative task graph. Directed Acyclic Graph (DAG) can represent applications executed within each multiprocessor system. A DAG G = (V, E) consists of a set of vertices V representing the tasks to be executed and a set of directed edges E representing communication dependencies among tasks. The edge set E contains directed edges eij for each task Ti V that task Tj V depends on. The computation weight of a task is represented by the number of CPU clock Min–min GA Based Task Scheduling In Multiprocessor Systems Medhat Awadall, Afaq Ahmad, Samir Al-Busaidi