Abstract

This paper introduces a new optimization technique called hyperplane annealing. It is similar to the mean field annealing approach to combinatorial optimization. Both annealing techniques rely on a parallel relaxation dynamic. A connection is shown to a formal model of selforganized pattern formation, the activator-inhibitormodel. The unifying principle of all these relaxation models is a mechanism for the modulation of the nonlinearity of the relaxation dynamic: Activator-inhibitor-systems show spatial modulation by diffusion, whereas the optimization approach uses functional modulation by gradients as well as temporal modulation by annealing of nonlinearity controlling system parameters. The new hyperplane annealing technique combines these modulation mechanisms within an algorithmic formulation with smaller computational complexity than mean field annealing. At a critical nonlinearity a phase transition leads to selforganized pattern formation in the relaxation matrix with the resulting structure corresponding to a solution of the optimization problem. As a concrete example the hyperplane annealing technique is used to solve instances of the NP-complete graph coloring problem