In this paper, we show some of the procedural properties of Potts mean field theory annealing applied to travelling salesman problems. This approach, in general, produces non-optimal and non-unique solutions. As an alternative approach, we propose a nonequilibrium version of the Potts spin neural network, called chaotic Potts spin (CPS). Experimental results are shown comparing CPS with several related approaches. CPS is good at obtaining the optimal solutions for small-scale problems and semi-optimal solutions for relatively large-scale problems. We also describe a modified algorithm in which a heuristic method is employed. This modified algorithm can produce even better CPS solutions.
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