A note on the convergence of a synchronously parallel Boltzmann machine for the Knapsack problem

This note elaborates on material that was presented earlier in the COSOR Memorandum 89-21, titled: Synchronously Parallel Boltzmann machines, a Mathematical Model. We discuss the main results obtained in a study of a mathematical model of synchronously parallel Boltzmann machines. We present supporting evidence for the conjecture that a synchronously parallel Boltzmann machine maximizes a consensus function that consists of a weighted sum of the regular consensus function and a pseudo consensus function. The weighting is determined by the fraction of units that can change their states simultaneously. The derived theoretical results are evaluated on the basis of a numerical study carried out for the knapsack problem. Keywords: Boltzmann machines, neural networks, synchronous parallelism, combinatorial optimization, simulated annealing.