The shape of space

The paper discusses "the shape of space", in terms of search algorithms and traversal operators. We point out that it is the combination of representation and traversal operators that defines an algorithm's view of a given search problem, and hence gives rise to a fitness landscape. We provide an intuitive background to some recent formal discussions on the limitations of search algorithms, and demonstrate how these issues arise in genetic algorithms (GAs) and encoded stochastic hill climbers. We suggest that randomly remapping space via base changes provides a simple means of applying multiple search strategies to a given search problem, and that this offers a pragmatic means for probing a cost function from many views. We introduce a number of new algorithms based on this technique and demonstrate their application on a range of standard cost functions.