A space-reduction based three-phase approach for large-scale optimization

Abstract

With the rapid development of science and technology, large-scale global optimization (LSGO) has received more and more attention. However, large-scale problem is very challenging due to its high dimensionality, nonlinearity, and countless local optimal solutions. In this paper, a space-reduction based three-phase approach (SRTP) is proposed to solve this problem. In the first phase, a space-reduction based line search method is designed to roughly locate good solutions as well as to explore important information such as promising search regions and characteristics of each variable (dimension). In the second phase, a multi-grouping strategy is proposed for fully non-separable large-scale problems. This new decomposition method provides dozens of grouping results for non-separable large-scale problems that not only reduces the dimensionality but also maintains the correlation of variables to the most extent. Then in the third phase, a space-reduction based group search method is designed to optimize the sub-groups. By decomposing the large-scale problem as well as reducing the huge search space to focus on promising areas, this group search method can gain better efficiency. Experiments are conducted on 35 widely used benchmark functions and the proposed SRTP is compared with state-of-the-art LSGO algorithms. Experimental results show that SRTP is effective and efficient.