Abstract
AbstractThe method of Simulated Annealing (SA) is investigated in the concrete problem of bandwidth reductio. We develop a very efficient way to compute the transitions, and this allows long annealing sessions (Monte Carlo runs) in reasonable time, enabling meaningful experimenting. It is demonstrated (empirically) that the neighbourhood relation in the space of states of the system greatly influences the convergence of the annealing. A pure SA algorithm is developed and used to obtain new lower bounds for the bandwidth in the 30 Everstine problems used as a benchmark for testing bandwidth reduction algorithms. An hybrid algorithm is also developed to be used in practice. It consists of an annealing session (without previous melting) run in cascade after the Cuthill‐McKee algorithm. The running times are of the same order as those of the deterministic algorithms now in use, and improvements of (typically) 20 per cent are obtained on the 30 Everstine problems.
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