Variable interaction in multi-objective optimization problems

14th International Conference on Parallel Problem Solving from Nature – PPSN XIV, 2016-09-17, 2016-09-21, Edinburgh, UK, pp. 399 - 409This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.The final publication is available at link.springer.comVariable interaction is an important aspect of a problem, which reflects its structure, and has implications on the design of efficient optimization algorithms. Although variable interaction has been widely studied in the global optimization community, it has rarely been explored in the multi-objective optimization literature. In this paper, we empirically and analytically study the variable interaction structures of some popular multi-objective benchmark problems. Our study uncovers nontrivial variable interaction structures for the ZDT and DTLZ benchmark problems which were thought to be either separable or non-separable

Unitarily invariant norm inequalities for operators

We present several operator and norm inequalities for Hilbert space operators. In particular, we prove that if $A_{1},A_{2},...,A_{n}\in {\mathbb B}({\mathscr H})$, then $$|||A_{1}A_{2}^{*}+A_{2}A_{3}^{*}+...+A_{n}A_{1}^{*}|||\leq|||\sum_{i=1}^{n}A_{i}A_{i}^{*}|||,$$ for all unitarily invariant norms. We also show that if $A_{1},A_{2},A_{3},A_{4}$ are projections in ${\mathbb B}({\mathscr H})$, then &&|||(\sum_{i=1}^{4}(-1)^{i+1}A_{i})\oplus0\oplus0\oplus0|||&\leq&|||(A_{1}+|A_{3}A_{1}|)\oplus (A_{2}+|A_{4}A_{2}|)\oplus(A_{3}+|A_{1}A_{3}|)\oplus(A_{4}+|A_{2}A_{4}|)||| for any unitarily invariant norm.Comment: 10 pages, Accepted pape

Radiance cache optimization for global illumination

Radiance caching methods have proven efficient for global illumination. Their goal is to compute precisely illumination values (incident radiance or irradiance) at a reasonable number of points lying on the scene surfaces. These points, called records, are stored in a cache used for estimating illumination of other points in the scene. Unfortunately, with records lying on glossy surfaces, the irradiance value alone is not sufficient to evaluate the reflected radiance; each record should also store the incident radiance for all incident directions. Memory storage can be reduced with projection techniques using spherical harmonics or other basis functions. These techniques provide good results with low shininess BRDFs. However, they get impractical for shininess of even moderate value since the number of projection coefficients increase drastically. In this paper, we propose a new radiance caching method, that handles highly glossy surfaces, while requiring a low memory storage. Each cache record stores a coarse representation of the incident illumination thanks to a new data structure called Equivalent Area light Sources (EAS), capable of handling fuzzy mirror surfaces. In addition, our method proposes a new simplification of the interpolation process since it avoids the need for expressing and evaluating complex gradients

Solving Incremental Optimization Problems via Cooperative Coevolution

Engineering designs can involve multiple stages, where at each stage, the design models are incrementally modified and optimized. In contrast to traditional dynamic optimization problems where the changes are caused by some objective factors, the changes in such incremental optimization problems are usually caused by the modifications made by the decision makers during the design process. While existing work in the literature is mainly focused on traditional dynamic optimization, little research has been dedicated to solving such incremental optimization problems. In this work, we study how to adopt cooperative coevolution to efficiently solve a specific type of incremental optimization problems, namely, those with increasing decision variables. First, we present a benchmark function generator on the basis of some basic formulations of incremental optimization problems with increasing decision variables and exploitable modular structure. Then, we propose a contribution based cooperative coevolutionary framework coupled with an incremental grouping method for dealing with them. On one hand, the benchmark function generator is capable of generating various benchmark functions with various characteristics. On the other hand, the proposed framework is promising in solving such problems in terms of both optimization accuracy and computational efficiency. In addition, the proposed method is further assessed using a real-world application, i.e., the design optimization of a stepped cantilever beam

An operator extension of čebyšev inequality

Abstract Some operator inequalities for synchronous functions that are related to the čebyšev inequality are given. Among other inequalities for synchronous functions it is shown that ∥ø(f(A)g(A)) - ø(f(A))ø(g(A))∥ ≤ max{║ø(f2(A)) - ø2(f(A))║, ║ø)G2(A)) - ø2(g(A))║} where A is a self-adjoint and compact operator on B(ℋ ), f, g ∈ C (sp (A)) continuous and non-negative functions and ø: B(ℋ ) → B(ℋ ) be a n-normalized bounded positive linear map. In addition, by using the concept of quadruple D-synchronous functions which is generalizes the concept of a pair of synchronous functions, we establish an inequality similar to čebyšev inequality.</jats:p

COVID-19 preventive behaviors and influencing factors in the Iranian population; a web-based survey

Background: COVID19 is a respiratory disease caused by a novel coronavirus. As there has been no definitive treatment for the disease so far, the only way to control the spread is to break the chain of infection. Our study aimed to analyze the preventive behaviors and influencing factors in the Iranian population. Methods: This cross-sectional study was a web-based survey in the Iranian population. We performed the study during the first peak of COVID-19 outbreak (from March 25th, 2020 to April 5th). We used demographic and Preventive behaviors questionnaires to collect the data. This web-based survey was publicized on the internet through the common platforms used by the Iranian population. This survey was released on the website “Porsline.com”. A total of 2097 acceptable questionnaires were filled. All data were analyzed, using Statistical Package for Social Sciences (SPSS) version 19. Results: 61.9% of the participants checked the hand-washing question as “Always”. 55.7 and 58.2% checked the wearing masks and gloves as “Always”, respectively. We found a significant relationship between gender and hand washing behavior (P = 0.006) and the use of masks and gloves (P < 0.001). Results showed that wearing gloves had a significant relation with the education status (P = 0.029) and economic status (P = 0.011). Wearing masks had a significant relation with economic status (P = 0.032). Overall women had better preventive behaviors. Conclusions: Preventive behaviors have a significant relation with some socio-demographic characteristics. According to the 3 main preventive behaviors of hand-washing, wearing masks and gloves 50% of the population has not taken these behaviors seriously

An experiment for the measurement of the bound-beta decay of the free neutron

The hyperfine-state population of hydrogen after the bound-beta decay of the neutron directly yields the neutrino left-handedness or a possible right-handed admixture and possible small scalar and tensor contributions to the weak force. Using the through-going beam tube of a high-flux reactor, a background free hydrogen rate of ca. 3 s$^{-1}$ can be obtained. The detection of the neutral hydrogen atoms and the analysis of the hyperfine states is accomplished by Lamb shift source type quenching and subsequent ionization. The constraints on the neutrino helicity and the scalar and tensor coupling constants of weak interaction can be improved by a factor of ten.Comment: 9 pages, 5 figures. Submitted to EPJ

ON SOME INEQUALITIES FOR -MEASURABLE OPERATORS

This paper deals with the Choi’s inequality for measurable operators affiliated with a given von Neumann algebra. Some Young and Cauchy-Schwarz type inequalities for -measurable operators are also given