The Quadratic Assignment Problem in Code Optimization for a Simple Universal Turing Machine

The author’s simple universal Turing machine requires the description of a specific Turing machine as data. In this article the coding of a specific Turing machine for unary multiplication is described. The description is a list of transitions with unary coded links between them. The order of the transitions in the list therefore makes a large difference in the size of the resulting code and the speed at which it runs. Finding the optimum ordering is a quadratic assignment problem. A simple neighborhood search procedure starting from random initial samples is described. It was sufficient to locate the optimum solution for a Turing machine with 23 transitions. The reason for the success was found to be due to the large basins of attraction for good solutions.