Explore the vast range of titles available.

Decomposition is an effective and popular strategy used by evolutionary algorithms to solve multiobjective optimization problems (MOPs). It can reduce the difficulty of directly solving MOPs, increase the diversity of the obtained solutions, and facilitate parallel computing. However, with the increase of the number of decision variables, the performance of multiobjective evolutionary algorithms (MOEAs) often deteriorates sharply. The advantages of the decomposition strategy are not fully exploited when solving such large-scale MOPs (LSMOPs). To this end, this paper proposes a parallel MOEA based on two-space decomposition (TSD) to solve LSMOPs. The main idea of the algorithm is to decompose the objective space and decision space into multiple subspaces, each of which is expected to contain some complete Pareto-optimal solutions, and then use multiple populations to conduct parallel searches in these subspaces. Specifically, the objective space decomposition approach adopts the traditional reference vector-based method, whereas the decision space decomposition approach adopts the proposed method based on a diversity design subspace (DDS). The algorithm uses a message passing interface (MPI) to implement its parallel environment. The experimental results demonstrate the effectiveness of the proposed DDS-based method. Compared with the state-of-the-art MOEAs in solving various benchmark and real-world problems, the proposed algorithm exhibits advantages in terms of general performance and computational efficiency.

In 1970, Phillip Griffiths envisioned that points at infinity could be added to the classifying space D of polarized Hodge structures. In this book, Kazuya Kato and Sampei Usui realize this dream by creating a logarithmic Hodge theory. They use the logarithmic structures begun by Fontaine-Illusie to revive nilpotent orbits as a logarithmic Hodge structure. The book focuses on two principal topics. First, Kato and Usui construct the fine moduli space of polarized logarithmic Hodge structures with additional structures. Even for a Hermitian symmetric domain D, the present theory is a refinement of the toroidal compactifications by Mumford et al. For general D, fine moduli spaces may have slits caused by Griffiths transversality at the boundary and be no longer locally compact. Second, Kato and Usui construct eight enlargements of D and describe their relations by a fundamental diagram, where four of these enlargements live in the Hodge theoretic area and the other four live in the algebra-group theoretic area. These two areas are connected by a continuous map given by the SL(2)-orbit theorem of Cattani-Kaplan-Schmid. This diagram is used for the construction in the first topic.