Mapping of workflow tasks to computational resources in the cloud environment has engendered research interest in workflow scheduling. As workflow scheduling belongs to NP-complete problem, so building an optimum workflow scheduler with reasonable performance and computation speed is very challenging in the heterogeneous distributed environment of clouds. Many existing studies deal with cloud workflow scheduling as a single or bi-objective optimization problem without considering some important requirements of the users or the providers. Therefore, it is highly desirable to formulate scheduling of the workflow applications as a Multi-objective Optimization Problem (MOP) taking into account the requirements from the user and the service provider. For example, the cloud workflow scheduler might wish to consider user’s Quality of Service (QoS) objectives, such as makespan and cost, as well as provider’s objectives, such as energy efficiency over the Virtual Machines (VMs). In addition, early convergence in existing algorithms is a problem that increases the number of repetitions for reaching a global optimum. To overcome these drawbacks, in this paper, an enhanced multi-objective co-evolutionary algorithm, called ch-PICEA-g, is proposed as an effective heuristic algorithm, where the logistic and tent maps as two chaotic systems are applied in generating chaotic values to overcome the permute convergence in the initial population and the genetic operators. Also, an improved fitness function is applied to increase the performance of original PICEA-g. The functionality of the proposed algorithm is validated by extensive experiments. The obtained results indicate that this proposed algorithm outperforms its counterparts in terms of different performance metrics.

将工作流任务映射到云环境中的计算资源引起了对工作流调度的研究兴趣。由于工作流调度属于NP完全问题，因此在异构的云分布式环境中，构建具有合理性能和计算速度的最优工作流调度程序非常具有挑战性。现有的许多研究都将云工作流调度视为一个单目标或双目标优化问题，而没有考虑用户或提供商的一些重要要求。因此，非常需要考虑到用户和服务提供商的要求，将工作流应用程序的调度表述为多目标优化问题（MOP）。例如，云工作流调度程序可能希望考虑用户的服务质量（QoS）目标（例如制造期限和成本）以及提供商的目标（例如虚拟机（VM）的能效）。另外，现有算法中的早期收敛是一个问题，其增加了达到全局最优的重复次数。为了克服这些缺点，本文提出了一种改进的多目标协同进化算法，称为ch-PICEA-g，作为一种有效的启发式算法，其中将逻辑和帐篷映射作为两个混沌系统，用于生成混沌值克服初始种群和遗传算子的置换趋同。此外，还应用了改进的适应度函数来提高原始PICEA-g的性能。通过大量实验验证了所提出算法的功能。获得的结果表明，在不同的性能指标方面，该算法优于同类算法。