UMOTS: an uncertainty-aware multi-objective genetic algorithm-based static task scheduling for heterogeneous embedded systems

Abstract

Increasing manufacturing process variations due to aggressive technology scaling in addition to heterogeneity in design components are expected to cause serious challenges for future embedded system design steps including task scheduling. Process variation effects along with increased complexity in embedded applications result in design uncertainties, which in turn, reduce the accuracy and efficiency of traditional design approaches with deterministic values for the design component parameters. In this paper, a multi-objective task scheduling framework is proposed for embedded systems considering uncertainties in both hardware and software component parameters. The tasks which are modeled as a task graph are scheduled on a specific hardware platform consisting of processors and communication parts. Uncertainty is considered in both software (task parameters) and hardware (processor and communication parameters) of the embedded system. UMOTS takes advantages of a Monte-Carlo-based approach within a multi-objective genetic algorithm to handle the uncertainties in model parameters. The proposed approach finds the Pareto frontier, which is robust against uncertainties, in the objective space formed by performance, energy consumption, and reliability. The efficiency of UMOTS is investigated in the experimental results using real-application task graphs. In terms of Scheduling Length Ratio (SLR) and speedup, UMOTS provides 27.8% and 28.6% performance improvements in comparison to HSHD, one state-of-the-art task scheduling algorithm. Additionally, UMOTS, which is based on a multi-objective genetic optimization algorithms, finds robust Pareto frontier with 1%, 5% and 10% uncertainty in design indicators with respect to design limitations.

Appendix

To prove that the genetic operators maintain the order of tasks and would not result in invalid orders, they have to fulfill the following conditions [42]:

• Correctness following the prioritized dependency of tasks.

• Competence and uniqueness non-repeated occurrence of all tasks in a given chromosome

Theorem 1

A task orders is an execution order if the tasks keep their dependencies orders. In this case if we remove T_i from the task orders, the remaining tasks still keep the topological order of tasks without violating precedence constrains (Correctness condition).

Proof 1

When ${T}_{i}$ is removed from a topological order, the remaining tasks are actually a topological order of the new graph created by removing ${T}_{i}$ from the original graph. Therefore, all priority constraints of the new graph are preserved in the remaining task orders.

Theorem 2

Task T_i can be inserted into any position among tasks with higher and lower priority then T_i which can provide a new task orders without violating priority constraints; i.e., competence and uniqueness conditions.

Proof 2

All tasks with the same higher and lower priority as T_i are independent of T_i. It means if we change the position of these tasks with each other there is no threat for priority constraints. Hence, the relative order between them in any task orders can be acceptable.

In the following, it is proved that the mutation operator maintains the order of tasks and will not result in invalid orders by fulfilling the necessary conditions [42].

Theorem 3

For mutation, task orders can be replaced in any order without violating priority constraints (Correctness condition).

Proof 3

This is because of the fact that we only replace the tasks in the same segment and the tasks in a segment have the capacity of parallel execution.