Interpolation guided optimization and composite grouping method for large-scale problems

Large-scale global optimization (LSGO) problems pose significant challenges due to high dimensionality, complex variable interactions and unknown search landscapes. To address these challenges, an interpolation guided optimization and composite grouping method (IGOCG) is proposed. Firstly, a quadratic interpolation based search method (QI search) is designed to explore the landscape in a dimension-wise way in order to not only scan the search space but also collect the performance information of each dimension (decision variable). This QI search method can gather and extract variable improvement information of each dimension by quickly detecting superior region through progressive compression of the search space. Secondly, to make reasonable decomposition of fully non-separable large-scale problems, a composite grouping method is proposed. To make the decomposition more adaptable and diverse, four distinct grouping (decomposing) strategies are designed which are quartile-based hierarchical grouping, clustering-based hybrid grouping, variability grouping, and extended grouping. By decomposing large-scale problems, the search space and optimization complexity is reduced, thus better results can be achieved more efficiently. Extensive experiments are conducted on two widely used benchmark suites and comparisons are made with state-of-the-art LSGO algorithms. The results demonstrate that the proposed algorithm achieves competitive performance, validating its effectiveness and efficiency in solving large-scale problems.