Abstract
Identification of variable interaction is essential for an efficient implementation of a divide-and-conquer algorithm for large-scale black-box optimization. In this paper, we propose an improved variant of the differential grouping (DG) algorithm, which has a better efficiency and grouping accuracy. The proposed algorithm, DG2, finds a reliable threshold value by estimating the magnitude of roundoff errors. With respect to efficiency, DG2 reuses the sample points that are generated for detecting interactions and saves up to half of the computational resources on fully separable functions. We mathematically show that the new sampling technique achieves the lower bound with respect to the number of function evaluations. Unlike its predecessor, DG2 checks all possible pairs of variables for interactions and has the capacity to identify overlapping components of an objective function. On the accuracy aspect, DG2 outperforms the state-of-the-art decomposition methods on the latest large-scale continuous optimization benchmark suites. DG2 also performs reliably in the presence of imbalance among contribution of components in an objective function. Another major advantage of DG2 is the automatic calculation of its threshold parameter ( $\epsilon $ ), which makes it parameter-free. Finally, the experimental results show that when DG2 is used within a cooperative co-evolutionary framework, it can generate competitive results as compared to several state-of-the-art algorithms.
Highlights
L ARGE-SCALE global optimization has become an active field of research in the past decade due to the growing number of large-scale optimization problems in engineering and sciences [1], [2]
We use DG2 in a cooperative co-evolutionary framework to test its efficiency on the final optimization performance
By comparing (3) and (6) with (8), we can see that the calculation of in both DG2 and GDG is a function of the objective function value
Summary
L ARGE-SCALE global optimization has become an active field of research in the past decade due to the growing number of large-scale optimization problems in engineering and sciences [1], [2]. Differential grouping (DG) [32] is a competitive decomposition algorithm that can identify the nonseparable components of a continuous objective function and has shown superior performance as compared to other decomposition algorithms, such as variable interaction learning [33] on the CEC’2010 [50] large-scale benchmark suite [32]. This improved version, DG2, reduces the total number of objective function evaluations by half for fully separable functions which require the most function evaluations This allows the algorithm to check all pairs of variables for interaction at a much lower cost as compared to its predecessor.
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