Divide and Conquer (DC) is conceptually well suited to high-dimensional
optimization by decomposing a problem into multiple small-scale sub-problems.
However, appealing performance can be seldom observed when the sub-problems are
interdependent. This paper suggests that the major difficulty of tackling
interdependent sub-problems lies in the precise evaluation of a partial
solution (to a sub-problem), which can be overwhelmingly costly and thus makes
sub-problems non-trivial to conquer. Thus, we propose an approximation
approach, named Divide and Approximate Conquer (DAC), which reduces the cost of
partial solution evaluation from exponential time to polynomial time.
Meanwhile, the convergence to the global optimum (of the original problem) is
still guaranteed. The effectiveness of DAC is demonstrated empirically on two
sets of non-separable high-dimensional problems.Comment: 7 pages, 2 figures, conferenc

Tang, Ke

Yang, Peng

Yao, Xin

English

arXiv

Divide-and-Conquer (DC) is conceptually well suited to deal with high-dimensional optimization problems by decomposing the original problem into multiple lowdimensional sub-problems, and tackling them separately. Nevertheless, the dimensionality mismatch between the original problem and sub-problems makes it non-trivial to precisely assess the quality of a candidate solution to a sub-problem, which has been a major hurdle for applying the idea of DC to non-separable highdimensional optimization problems. In this paper, we suggest that searching a good solution to a sub-problem can be viewed as a computationally expensive problem and can be addressed with the aid of meta-models. As a result, a novel approach, namely Self-Evaluation Evolution (SEE) is proposed. Empirical studies have shown the advantages of SEE over 4 representative compared algorithms increase with the problem size on the CEC2010 large scale global optimization benchmark. The weakness of SEE is also analysed in the empirical studies

High-dimensional Black-box Optimization via Divide and Approximate Conquer

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