The Shape of Space
نویسندگان
چکیده
Typically a search problem is posed as an optimisation task in which a cost, or fitness, function must be maximised or minimised, subject to various parameter constraints. This paper discusses “the shape of space”, in terms of search algorithms. We point out that it is the combination of representation and traversal operators that define an algorithm's view of a given search problem, and hence gives rise to a fitness landscape. In this sense a fitness landscape only exists in terms of a given search algorithm, and that notions of landscape difficulty are therefore algorithm dependent. We demonstrate these issues for genetic algorithms (GAs) and encoded hill-climbers. We show that both styles of algorithm have attractive features in terms of the way a landscape can be dynamically adjusted, providing a simple means for applying multiple search strategies to a given search problem. We illustrate the techniques for a range of standard cost functions and algorithms.
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Hypersurfaces of a Sasakian space form with recurrent shape operator
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