Hironori Matsumoto

A branch-and-bound algorithm with fuzzy inference for a permutation flowshop scheduling problem

Abstract This paper considers an m-machine permutation flowshop scheduling problem of minimizing the makespan. This classical scheduling problem is still important in modern manufacturing systems, and is well known to be intractable (i.e., NP-hard). In fact branch-and-bound algorithms developed so far for this problem have not come to solve large scale problem instances with over a hundred jobs. In order to improve the performance of branch-and-bound algorithms this paper proposes a new dominance relation by which the search load could be reduced, and notices that it is based on a sufficient precondition. This suggests that the dominance relation holds with high possibility even if the precondition approximately holds, thus being more realistic. The branch-and-bound algorithm proposed here takes advantage of this possibility for obtaining an optimal solution as early as possible in the branch-and-bound search. For this purpose this paper utilizes membership functions in the context of the fuzzy inference. Extensive numerical experiments that were executed through Monte Carlo simulations and benchmark tests show that the developed branch-and-bound algorithm can solve 3-machine problem instances with up to 1000 jobs with probability of over 99%, and 4-machine ones with up to 900 jobs with over 97%.

Development of a lightweight x-ray mirror using thin carbon-fiber-reinforced plastic (CFRP)

We fabricated X-ray mirrors from carbon-fiber-reinforced-plastic (CFRP) with a tightly nested design for X-ray satellites. The mirror shape is Wolter type-I quadrant shell geometry with a diameter of 200 mm and a focal length of 12 m. The mirror substrates were successfully formed with a rms error of about 1 μm. Through a replication process, a smooth surface was obtained on the CFRP substrate. We are developing a positioning method of thin mirrors in a telescope housing. It is found that a piezo-linear motor is very useful to adjust the mirror position with accuracy of sub μm. The CFRP mirrors were evaluated by using 20 keV X-ray pencil beam at BL20B2 in SPring-8 synchrotron radiation facility. The HPD of the mirrors was estimated to be about 2.3 arc-minutes. The spread of X-ray image would be caused by small waviness on the mirror surface after replication.

The spectral response of X-ray CCDs in the energy band around Si-K edge: a solution to the Si-K edge problem for the XIS onboard Suzaku

X-ray Imaging Spectrometers (XIS) are the X-ray CCD cameras onboard Suzaku. They were operated in orbit from 2005 to 2015 and produced lots of findings with their good energy resolution and low non X-rat background. Precise calibration including the 10 eV accuracy in the energy scale reinforced them. Nevertheless, there has been a unresolved calibration issue in the spectral response around the Si-K edge (1.839 keV) appearing as systematic residuals up to 10%. The residual is negative peaking at 1.85 keV in the front illuminated (FI) sensors and positive peaking at 1.8 keV in the back illuminated (BI) sensor for X-ray sources dominated by continuum X-ray emission. Various attempts to eliminate these residuals by changing response parameters or quantum efficiency models have been insufficient. In this paper, we revisit this problem by focusing on the relation between incident X-ray energy and pulse height. We introduce a jump in that relation at the Si-K edge by modifying the , and optimize its value so as to minimize the residuals in the fit of the X-ray spectra for the black hole binary LMC X-3, a source dominated by continuum emission. We find the introduction of a jump significantly reduces the residuals. The optimized jump values are +4:2 channel, +4:0 channel, and -3:1 channel, corresponding to 15.3 eV, -11:3 eV, and 14.6 eV, for XIS0, XIS3 (FI), and XIS1 (BI), respectively. The direction of the jump is opposite for the FI and for the BI. We revise the response matrices generator so as to include the jump for each XIS sensor, and apply it to the X-ray spectra of the Perseus cluster of galaxies which has various emission lines in the spectra, and the blazar PKS2155-304 which was observed various epoch in the Suzakuoperation. We confirm the residuals are significantly reduced for these sources, too. We finally suggest the jump at Si-K edge in the energy and pulse height relation is qualitatively explained, if some of charges are lost in course of charger collection to the electrode of the CCD in the depletion later, and its amount is large for larger travel length in the depletion layer. If this explanation is correct, the Si-K edge problem and its solution presented in this paper is not specific only for the SuzakuXIS but also for other X-ray CCDs.