Chaotic Potts Spin Model for Combinatorial Optimization Problems

In this paper we first show some of the bifurcation properties of Potts mean-field-theory annealing applied to traveling salesman problems. Due to these bifurcation properties, 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). CPS has several parameters, and bifurcations over each parameter are investigated. Next, experimental results are shown comparing CPS with several related approaches. CPS is good at obtaining optimal solutions for small-scale problems and semi-optimal solutions for relatively large-scale problems. We also describe a couple of CPS modifications: CPS with a heuristic method and CPS with a "chaotic annealing" method. These modified algorithms can produce even better CPS solutions. Copyright 1997 Elsevier Science Ltd.