Dynamical System Approaches to Combinatorial Optimization

This article describes and compares several dynamical system approaches to combinatorial optimization problems. These include penalty methods, the approach of Hopfield and Tank, self-organizing maps, i.e., Kohonen networks, coupled selection equations, and hybrid methods. Many of them are investigated analytically and the costs of the solutions are compared numerically with those of solutions obtained by simulated annealing and the costs of a global optimal solution. In order to get reproducible simulation results, a pseudo-random number generator with integer arithmetic is used to produce the data sets.