Dynamic Multiobjective Optimization Problems (DMOPs) challenge Multiobjective Evolutionary Algorithms (MOEAs) because those problems change rapidly over time. The class of DMOPs whose objective functions change over time steps, in ways that exhibit some hidden patterns has gained much attention. Their predictability indicates that the problem exhibits some correlations between solutions obtained in sequential time periods. Most of current approaches use linear models or similar strategies to describe the correlations between historical solutions obtained, and predict the new solutions in the following time period as an initial population from which the MOEA can begin searching in order to improve its efficiency. However, nonlinear correlations between historical solutions and current solutions are more common in practice, and a linear model may not be suitable for the nonlinear case. In this paper, we present a Support Vector Regression-based predictor to generate the initial population for the MOEA in the new environment. The basic idea of this predictor is to map the historical solutions into a high-dimensional feature space via a nonlinear mapping, and to do linear regression in this space. Support Vector Regression is used to implement this process. We incorporate this predictor into the Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D) to construct a novel algorithm for solving the aforementioned class of DMOPs. Comprehensive experiments have shown the effectiveness and competitiveness of our proposed predictor, comparing with the state-of-the-art methods.

Few-shot Semantic Segmentation (FSS) was proposed to segment unseen classes in a query image, referring to only a few annotated examples named support images. One of the characteristics of FSS is spatial inconsistency between query and support targets, e.g., texture or appearance. This greatly challenges the generalization ability of methods for FSS, which requires to effectively exploit the dependency of the query image and the support examples. Most existing methods abstracted support features into prototype vectors and implemented the interaction with query features using cosine similarity or feature concatenation. However, this simple interaction may not capture spatial details in query features. To address this limitation, some methods utilized pixel-level support information by computing pixel-level correlations between paired query and support features implemented with the attention mechanism of Transformer. Nevertheless, these approaches suffer from heavy computation due to dot-product attention between all pixels of support and query features. In this paper, we propose a novel framework, termed ProtoFormer, built upon the Transformer architecture, to fully capture spatial details in query features. ProtoFormer treats the abstracted prototype of the target class in support features as the Query and the query features as Key and Value embeddings, which are input to the Transformer decoder. This approach enables better capture of spatial details and focuses on the semantic features of the target class in the query image. The output of the Transformer-based module can be interpreted as semantic-aware dynamic kernels that filter the segmentation mask from the enriched query features. Extensive experiments conducted on PASCAL- $$5^{i}$$5 i and COCO- $$20^{i}$$20 i datasets demonstrate that ProtoFormer significantly outperforms the state-of-the-art methods in FSS.