Cooperative coevolutionary differential evolution with adjacent intensity matrix with linkage identification for large-scale optimization problems in noisy environments

This paper proposes a novel decomposition method named Adjacent Intensity Matrix with Linkage Identification (ALI) which collaborates with the Cooperative Coevolution (CC) framework to solve large-scale optimization problems (LSOPs) in noisy environments. Conventional Differential Grouping (DG)-based methods in the CC framework can detect the interactions by the absolute interaction intensity. In noisy environments, the uncertainty of fitness will be amplified and the absolute interaction intensity is easily larger than the threshold, which results in all decision variables being grouped into one component. Although it is difficult to detect interactions through absolute interaction intensity in noisy environments, the relative difference between separable and non-separable decision variables may exist, which can help us determine the separability to form the sub-components. We propose the Adjacent Intensity Matrix (AIM) by an additive identification criterion and determine the significant intensity (SI) to classify the interactions by learning the regularity of intensity. Since the conventional performance indicator of decomposition accuracy (DA) cannot fully reflect the inner structure of a non-separable sub-component, we introduce a more rigorous metric to evaluate the decomposition named the similarity of dependency structure matrix ( \(S_{DSM}\) $S_{\mathit{DSM}}$ ). In the optimization phase after the decomposition, we employ an advanced optimizer named Modified Differential Evolution with Distance-based Selection (MDE-DS) to adapt to noisy environments. Experimental results on the CEC2013 Suite with noise show that our proposal has a broad prospect to solve LSOPs in noisy environments.