By Weise T.
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Extra resources for Global optimization algorithms. Theory and application
7 on page 413) which maps the elements of search space G to elements in the problem space X. 27) 26 1 Introduction 0 0 0 0 0 0 0 1 0 0 1 0 ... searchOp gÎG x=gpm(g) 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 - Allele = ,,11`` - Locus = 1 genome G genotype gÎG Gene xÎX 3 2 1 0 1 2 3 phenotype xÎX 3 2 1 0 1 3 2 phenome X Fig. 15: The relation of genome, genes, and the problem space. The only hard criterion we impose on genotype-phenotype mappings in this book is left-totality, i. , that they map each element of the search space to at least one solution candidate.
When minimizing a real function, we could use such an approach (Evolution Strategies, for instance, see Chapter 5 on page 191) and set G = X = R. However, we will hardly ﬁnd default search procedures that work on conﬁgurations of cars. Assume that such a conﬁguration consists of k features, which can either be included or excluded from an oﬀer to the customer. 1 on page 113) do. By using their optimization capabilities, we do not need to mess with the search and selection techniques but can rely on well-researched standard operations.
In all experiments, we had divided X in a regular lattice. searchOp2 : X → X, used in the second experiment, the new solution candidates are direct neighbors of the old ones in this lattice. 18. Both operators are complete, since each point in the search space can be reached from each other point by applying them. 41) In both experiments, the ﬁrst probabilities of the elements of the search space of being discovered are very low, near to zero in the ﬁrst few iterations. To put it precise, since our problem space is a 36 × 36 lattice, this probability is 1/362 in the ﬁrst iteration.