A test problem for visual investigation of high-dimensional multi-objective search

An inherent problem in multiobjective optimization is that the visual observation of solution vectors with four or more objectives is infeasible, which brings major difficulties for algorithmic design, examination, and development. This paper presents a test problem, called the Rectangle problem, to aid the visual investigation of high-dimensional multiobjective search. Key features of the Rectangle problem are that the Pareto optimal solutions 1) lie in a rectangle in the two-variable decision space and 2) are similar (in the sense of Euclidean geometry) to their images in the four-dimensional objective space. In this case, it is easy to examine the behavior of objective vectors in terms of both convergence and diversity, by observing their proximity to the optimal rectangle and their distribution in the rectangle, respectively, in the decision space. Fifteen algorithms are investigated. Underperformance of Pareto-based algorithms as well as most state-of-the-art many-objective algorithms indicates that the proposed problem not only is a good tool to help visually understand the behavior of multiobjective search in a high-dimensional objective space but also can be used as a challenging benchmark function to test algorithms' ability in balancing the convergence and diversity of solutions

High precision predictions for exclusive VHVH production at the LHC

We present a resummation-improved prediction for $VH$ + 0 jets production at the Large Hadron Collider. We focus on highly-boosted final states in the presence of jet veto to suppress the $t{\bar t}$ background. In this case, conventional fixed-order calculations are plagued by the existence of large Sudakov logarithms $\alpha_s^n \log^m (p_T^{veto}/Q)$ for $Q\sim m_V + m_H$ which lead to unreliable predictions as well as large theoretical uncertainties, and thus limit the accuracy when comparing experimental measurements to the Standard Model. In this work, we show that the resummation of Sudakov logarithms beyond the next-to-next-to-leading-log accuracy, combined with the next-to-next-to-leading order calculation, reduces the scale uncertainty and stabilizes the perturbative expansion in the region where the vector bosons carry large transverse momentum. Our result improves the precision with which Higgs properties can be determined from LHC measurements using boosted Higgs techniques.Comment: 24 pages, 8 figure

顧客嗜好理解のための情報抽出とそのレコメンダーシステムへの応用

早大学位記番号:新6414早稲田大