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This paper analyzes the relative advantages between crossover and mutation on a class of deterministic and stochastic additively separable problems with substructures of nonuniform salience. This study assumes that the recombination and mutation operators have the knowledge of the building blocks (BBs) and effectively exchange or search among competing BBs. Facetwise models of convergence time and population sizing have been used to determine the scalability of each algorithm. The analysis shows that for deterministic exponentiallyscaled additively separable, problems, the BBwise mutation is more efficient than crossover yielding a speedup of Θ(<em>l</em> log<em>l</em>), where <em>l</em> is the problem size. For the noisy exponentiallyscaled problems, the outcome depends on whether scaling on noise is dominant. When scaling dominates, mutation is more efficient than crossover yielding a speedup of Θ(<em>l</em> log<em>l</em>). On the other hand, when noise dominates, crossover is more efficient than mutation yielding a speedup of Θ(<em>l</em>).
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