A Hybrid Deep Grouping Algorithm for Large Scale Global Optimization

Many real-world problems contain a large number of decision variables which can be modeled as large scale global optimization (LSGO) problems. One effective way to solve an LSGO problem is to decompose it into smaller subproblems to solve. The existing works mainly focused on designing methods to decompose separable problems, while seldom focused on the decomposition of nonseparable large scale problems. Also, the existing decomposition methods only learn the interaction (correlation or interdependence) among variables to make the decomposition. In this article, we make the decomposition deeper: we not only consider the variable interaction but also take the essentialness of the variable into account to form a deep grouping method. To do this, we first design an essential/trivial variable detection scheme to support the deep decomposition for both separable problems and nonseparable problems. Based on it, we propose a new decomposition method called deep grouping method. Then, we design a new differential evolution (DE) algorithm with a new mutation strategy. By integrating all these, we propose a hybrid deep grouping (HDG) algorithm. Finally, the experiments are conducted on the widely used and most challenging LSGO benchmark suites, and the comparison results of the proposed algorithm with the state-of-the-art algorithms indicate the proposed algorithm is more effective.