A DEA-GA multi-objective scheduling algorithm for Chip-Multiprocessor

Abstract

In this paper, a Data Envelopment analysis based Genetic Algorithm (DEA-GA) is proposed for multi-objective scheduling on Chip-Multiprocessor. The proposal adopts modified GA as the searching heuristic to explore the solution space, and the fitness of each individual (schedule) is evaluated using the DEA approach. Three of the schedule metrics, namely makespan, energy and load balance are used to construct the multi-input multi-output Decision Making Units in the DEA, and the BCC super efficiency of each schedule is calculated. In the modified genetic algorithm, the metapopulation is divided into three subpopulations each optimizing a single metric. The top performance individuals in each subpopulation are then regrouped and applied DEA evaluation. Comparing to other multi-objective scheduling algorithm in simulations, our proposal always produces more efficient schedule solutions. Introduction The task scheduling problem on Chip Multiprocessors (CMPs) has been a research hotspot in recent years [1]. Current scheduling algorithm always performs optimization on multiple metrics, such as makespan [2], energy [3], workload balance [4] and etc. Some of these optimizations are even in conflict with each other, like makespan and energy optimization [5]. In order to make sure that the scheduling algorithm makes the ‘right’ tradeoff between the observed metrics; we introduce the Data Envelopment Analysis (DEA) to the algorithm design, and propose a DEA-based Genetic Algorithm (GA) for the real-time task scheduling problem on the CMP. DEA is a non-parametric analytic method for measuring the relative efficiency of Decision Making Units (DMUs) [6]. The target objects, which in our case are the schedule solutions, are modeled as multi-input multi-output DMU, and the efficiency of each DMU, which representing the performance of the DMU, are calculated using the weighted sum of all the outputs divided by the weight sum of it inputs. The essence of DEA is that it allows the DMU to choose a set of weight coefficients that favors itself, under the constraint that the efficiencies of all DMUs calculated by this set of coefficients are not exceed one. In this paper, we focus on the real-time task scheduling problem on CMP and propose a multi-metric scheduling algorithm using both super efficiency analyses in DEA and GA technique. The rest of this paper is organized as follow: Section 2 summarizes the related works of multi-objective scheduling algorithms on CMP and the DEA evaluation; our proposal is presented in Section 3; the simulations and results are given in Section 4; Section 5 concludes the paper. Related Work The multi-objective scheduling algorithms have been widely researched in recent years. In [7], a modified algorithm which combines bacteriological algorithm and genetic algorithm is proposed to maximize the system reliability and reduce makespan. A two-phase cellular genetic scheduling algorithm is proposed in [8] to reduce both energy consumption and makespan. An NSGA-II based schedule algorithm is proposed in [9] to simultaneously optimize makespan and workload balance. In 2nd International Conference on Science and Social Research (ICSSR 2013) © 2013. The authors Published by Atlantis Press 666 [10], the problem of joint optimization of performance, energy, and temperature is addressed, and multi-objective evolutionary algorithm (MOEA) based schedule heuristic is proposed. Proposed Algorithm DEA evaluation of schedule solutions. The multi-input multi output DMU model is constructed using schedule metrics. The observed metric in our proposal are makespan, energy consumed and workload balance. Makespan (M), or the schedule length, is the time length of the CMP finishing all the tasks. The energy metric (E), is the amount of energy consumed during the execution of the tasks. The last metric, workload balance (B), is defined to be the inverse coefficient of variant of the total workload on each processor. The larger metric value suggests better balanced schedule.