A step‐wise‐overlapped parallel annealing algorithm on a message‐passing multiprocessor system

Abstract

AbstractThis paper proposes a parallel annealing algorithm, called step‐wise‐overlapped parallel annealing, that can provide a massive speed‐up utilizing a multiprocessor system with a large number of processors. We improve the parallel annealing scheme of the systolic algorithm that was proposed by Aart et al. Instead of the temperature decrement at each subchain, it decides the decrement ratio at the start of each Markov chain using the standard deviation of the cost distribution in the previous Markov chain of the full length. Thus the improved annealing schedule keeps a good temperature profile even with a large number of processors. We also enhance the communication pattern.The new parallel annealing algorithm has a simple communication pattern and thus less communication overheads. The decomposition strategy of this parallel annealing algorithm is independent of application problems. Experimental results of the step‐wise‐overlapped parallel annealing algorthm for the travelling salesman problems show high efficiencies even when a large number of processors are used; it produces near optimal solutions with a speedup of 70.8 by using 128 processors. It can be implemented efficiently on a message‐passing multiprocessor system with a large number of processors, such as a hypercube computer.