The Structure of the State Space

Abstract

To formulate an optimization problem for the annealing algorithm we have to specify the state space (S,μ), the score function ε(s), and the selection function β. The states and the score function are strongly suggested by the problem. Often we may choose to optimize an estimate of the real object function, because computing that function would be too time consuming. Also we may restrict the search to a subset of all possible configurations, because we know that this subset contains, if not an optimum configuration, plenty of good solutions. Nevertheless, the options for manipulating the state set and the score function are quite limited. In contrast, there usually is a wide range of possibilities in selecting a move set when implementing the annealing algorithm for a given problem. Of course, the move set has to be transitively closed, reflexive and symmetric, but that still leaves substantial latitude, and therefore the question, what has to be taken into consideration in using that freedom.