Cost Function Error in Asynchronous Parallel Simulated Annealing Algorithms

Abstract

Reducing synchronization constraints in parallel simulated annealing algorithms can improve performance. However, this introduces error in the global cost function. Previous work in parallel simulated annealing suggests that if the amount of error in the cost function is controlled, good quality results can still be obtained. In this paper, we present a model of error in asynchronous parallel simulated annealing algorithms to partition graphs and use it to predict the behavior of three different synchronization strategies. These three approaches were implemented on a 20-processor Encore, a shared memory, MIMD multiprocessor, and tested on a variety of graphs. As predicted, the strategy which allows controlled error yields solutions comparable to those of the serial algorithm with greatly improved running time. Speedups from 5 to 11 (depending on the density of the graphs) using 16 processors were obtained. In contrast, the more synchronized version exhibited unacceptably high running times, whereas the version characterized by uncontrolled error yielded significantly poorer results. This confirms behavior seen in parallel simulated annealing algorithms to perform placement in VLSI circuit layout systems. This work is supported in part by NSF grant # NSF-ASC-8808327 and DOE grant # DOE-W-31-109Eng-38.