On the stability of the travelling salesman problem algorithm of Hopfield and Tank
Biological Cybernetics
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Optimization problems containing multiple, identical solutions, in particular the travelling salesman problem (TSP), are solved using networks of neural oscillators. Processing units are described by two state variables representing fast and slow membrane events, much like the Fitzhugh-Nagumo model neurons, and are passive oscillators in that at least two processing units with mutually inhibitory couplings are required to generate sustained oscillations. The emergent behavior of the network is to produce stable travelling waves (limit cycles) of firing rate impulses in the position coordinate of the network with the phase relationship between active (suprathreshold) processing units determining the TSP solution. This approach has the advantage of avoiding most local energy minima with the best or near-best solution being found every time for small networks (