• Title/Summary/Keyword: Iterative Solution Technique

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A Study for Improving Computational Efficiency in Method of Moments with Loop-Star Basis Functions and Preconditioner (루프-스타(Loop-Star) 기저 함수와 전제 조건(Preconditioner)을 이용한 모멘트법의 계산 효율 향상에 대한 연구)

  • Yeom, Jae-Hyun;Park, Hyeon-Gyu;Lee, Hyun-Suck;Chin, Hui-Cheol;Kim, Hyo-Tae;Kim, Kyung-Tae
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.23 no.2
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    • pp.169-176
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    • 2012
  • This paper uses loop-star basis functions to overcome the low frequency breakdown problem in method of moments (MoM) based on electric field integral equation(EFIE). In addition, p-Type Multiplicative Schwarz preconditioner (p-MUS) technique is employed to reduce the number of iterations required for the conjugate gradient method(CGM). Low frequency instability with Rao Wilton Glisson(RWG) basis functions in EFIE can be resolved using loop-start basis functions and frequency normalized techniques. However, loop-star basis functions, consisting of irrotational and solenoidal components of RWG basis functions, require a large number of iterations to calculate a solution through iterative methods, such as conjugate gradient method(CGM), due to high condition number. To circumvent this problem, in this paper, the pMUS preconditioner technique is proposed to reduce the number of iterations in CGM. Simulation results show that pMUS preconditioner is much faster than block diagonal preconditioner(BDP) when the sparsity of pMUS is the same as that of BDP.

Evaluating Reverse Logistics Networks with Centralized Centers : Hybrid Genetic Algorithm Approach (집중형센터를 가진 역물류네트워크 평가 : 혼합형 유전알고리즘 접근법)

  • Yun, YoungSu
    • Journal of Intelligence and Information Systems
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    • v.19 no.4
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    • pp.55-79
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    • 2013
  • In this paper, we propose a hybrid genetic algorithm (HGA) approach to effectively solve the reverse logistics network with centralized centers (RLNCC). For the proposed HGA approach, genetic algorithm (GA) is used as a main algorithm. For implementing GA, a new bit-string representation scheme using 0 and 1 values is suggested, which can easily make initial population of GA. As genetic operators, the elitist strategy in enlarged sampling space developed by Gen and Chang (1997), a new two-point crossover operator, and a new random mutation operator are used for selection, crossover and mutation, respectively. For hybrid concept of GA, an iterative hill climbing method (IHCM) developed by Michalewicz (1994) is inserted into HGA search loop. The IHCM is one of local search techniques and precisely explores the space converged by GA search. The RLNCC is composed of collection centers, remanufacturing centers, redistribution centers, and secondary markets in reverse logistics networks. Of the centers and secondary markets, only one collection center, remanufacturing center, redistribution center, and secondary market should be opened in reverse logistics networks. Some assumptions are considered for effectively implementing the RLNCC The RLNCC is represented by a mixed integer programming (MIP) model using indexes, parameters and decision variables. The objective function of the MIP model is to minimize the total cost which is consisted of transportation cost, fixed cost, and handling cost. The transportation cost is obtained by transporting the returned products between each centers and secondary markets. The fixed cost is calculated by opening or closing decision at each center and secondary markets. That is, if there are three collection centers (the opening costs of collection center 1 2, and 3 are 10.5, 12.1, 8.9, respectively), and the collection center 1 is opened and the remainders are all closed, then the fixed cost is 10.5. The handling cost means the cost of treating the products returned from customers at each center and secondary markets which are opened at each RLNCC stage. The RLNCC is solved by the proposed HGA approach. In numerical experiment, the proposed HGA and a conventional competing approach is compared with each other using various measures of performance. For the conventional competing approach, the GA approach by Yun (2013) is used. The GA approach has not any local search technique such as the IHCM proposed the HGA approach. As measures of performance, CPU time, optimal solution, and optimal setting are used. Two types of the RLNCC with different numbers of customers, collection centers, remanufacturing centers, redistribution centers and secondary markets are presented for comparing the performances of the HGA and GA approaches. The MIP models using the two types of the RLNCC are programmed by Visual Basic Version 6.0, and the computer implementing environment is the IBM compatible PC with 3.06Ghz CPU speed and 1GB RAM on Windows XP. The parameters used in the HGA and GA approaches are that the total number of generations is 10,000, population size 20, crossover rate 0.5, mutation rate 0.1, and the search range for the IHCM is 2.0. Total 20 iterations are made for eliminating the randomness of the searches of the HGA and GA approaches. With performance comparisons, network representations by opening/closing decision, and convergence processes using two types of the RLNCCs, the experimental result shows that the HGA has significantly better performance in terms of the optimal solution than the GA, though the GA is slightly quicker than the HGA in terms of the CPU time. Finally, it has been proved that the proposed HGA approach is more efficient than conventional GA approach in two types of the RLNCC since the former has a GA search process as well as a local search process for additional search scheme, while the latter has a GA search process alone. For a future study, much more large-sized RLNCCs will be tested for robustness of our approach.

Comparison of Effectiveness about Image Quality and Scan Time According to Reconstruction Method in Bone SPECT (영상 재구성 방법에 따른 Bone SPECT 영상의 질과 검사시간에 대한 실효성 비교)

  • Kim, Woo-Hyun;Jung, Woo-Young;Lee, Ju-Young;Ryu, Jae-Kwang
    • The Korean Journal of Nuclear Medicine Technology
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    • v.13 no.1
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    • pp.9-14
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    • 2009
  • Purpose: Nowadays in the nuclear medicine, many studies and efforts are being made to reduce the scan time, as well as the waiting time to be needed to execute exams after injection of radionuclide medicines. Several methods are being used in clinic, such as developing new radionuclide compounds that enable to be absorbed into target organs more quickly and reducing acquisition scan time by increase the number of Gamma Camera detectors to examine. Each medical equipment manufacturer has improved the imaging process techniques to reduce scan time. In this paper, we tried to analyze the difference of image quality between FBP, 3D OSEM reconstruction methods that commercialized and being clinically applied, and Astonish reconstruction method (A kind of Iterative fast reconstruction method of Philips), also difference of image quality on scan time. Material and Methods: We investigated in 32 patients that examined the Bone SPECT from June to July 2008 at department of nuclear medicine, ASAN Medical Center in Seoul. 40sec/frame and 20sec/frame images were acquired that using Philips‘ PRECEDENCE 16 Gamma Camera and then reconstructed those images by using the Astonish (Philips’ Reconstruction Method), 3D OSEM and FBP methods. The blinded test was performed to the clinical interpreting physicians with all images analyzed by each reconstruction method for qualitative analysis. And we analyzed target to non target ratio by draws lesions as the center of disease for quantitative analysis. At this time, each image was analyzed with same location and size of ROI. Results: In a qualitative analysis, there was no significant difference by acquisition time changes in image quality. In a quantitative analysis, the images reconstructed Astonish method showed good quality due to better sharpness and distinguish sharply between lesions and peripheral lesions. After measuring each mean value and standard deviation value of target to non target ratio with 40 sec/frame and 20sec/frame images, those values are Astonish (40 sec-$13.91{\pm}5.62$ : 20 sec-$13.88{\pm}5.92$), 3D OSEM (40 sec-$10.60{\pm}3.55$ : 20 sec-$10.55{\pm}3.64$), FBP (40 sec-$8.30{\pm}4.44$ : 20 sec-$8.19{\pm}4.20$). We analyzed target to non target ratio from 20 sec and 40 sec images. And we analyzed the result, In Astonish (t=0.16, p=0.872), 3D OSEM (t=0.51, p=0.610), FBP (t=0.73, p=0.469) methods, there was no significant difference statistically by acquisition time change in image quality. But FBP indicates no statistical differences while some images indicate difference between 40 sec/frame and 20 sec/frame images by various factors. Conclusions: In the circumstance, try to find a solution to reduce nuclear medicine scan time, the development of nuclear medicine equipment hardware has decreased while software has marched forward at a relentless. Due to development of computer hardware, the image reconstruction time was reduced and the expanded capacity to restore enables iterative methods that couldn't be performed before due to technical limits. As imaging process technique developed, it reduced scan time and we could observe that image quality keep similar level. While keeping exam quality and reducing scan time can induce the reduction of patient's pain and sensory waiting time, also accessibility of nuclear medicine exam will be improved and it provide better service to patients and clinical physician who order exams. Consequently, those things make the image of department of nuclear medicine be improved. Concurrent Imaging - A new function that setting up each image acquisition parameter and enables to acquire images simultaneously with various parameters to once examine.

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