Best Practices for Simulated Annealing in Multiprocessor Task Distribution Problems

Abstract

Simulated Annealing (SA) is a widely used meta-algorithm for complex optimization problems. This chapter presents methods to distribute executable tasks onto a set of processors. This process is called task mapping. The most common goal is to decrease execution time via parallel computation. However, the presented mapping methods are not limited to optimizing application execution time because the cost function is arbitrary. The cost function is also called an objective function in many works. A smaller cost function value means a better solution. It may consider multiple metrics, such as execution time, communication time, memory, energy consumption and silicon area constraints. Especially in embedded systems, these other metrics are often as important as execution time. A multiprocessor system requires exploration to find an optimized architecture as well as the proper task distribution for the application. Resulting very large design space must be pruned systematically with fast algorithms, since the exploration of the whole design space is not feasible. Iterative algorithms evaluate a number of application mappings for each architecture, and the best architecture and mapping is selected in the process. The optimization process is shown in Figure 1(a). The application, the HW platform and an initial solution are fed to a mapping component. The mapping component generates a new solution that is passed to a simulation component. The simulation component determines relevant metrics of the solution. The metrics are passed to a cost function which will evaluate the badness (cost) of the solution. The cost value is passed back to the mapping component. The mapping component will finally terminate the optimization process and output a final solution. The system that is optimized is shown in Figure 1(b). The system consists of the application and the HW platform. The application consists of tasks which are mapped to processing elements (PEs). The PEs are interconnected with a communication network. The chapter has two focuses: • optimize the cost function and • minimize the time needed for simulated annealing. First, the task distribution problem is an NP problem which implies that a heuristic algorithm is needed. The focus is on reaching as good as possible mapping. Unfortunately the true optimum value is unknown for most applications, and therefore the relative O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m