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  • Articles  (66)
  • Mathematics  (66)
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  • Articles  (66)
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  • 1
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    Supplier Selection and Production Planning by Using Guided Genetic Algorithm and Dynamic Nondominated Sorting Genetic Algorithm II Approaches (2015)
    Hindawi
    Details
    Publication Date: 2015-08-05
    Description: Through the global supply chain (SC), numerous firms participate in vertically integrated manufacturing, and industrial collaboration and cooperation is the norm. SC management activities, such as delivery time, quality, and defect rate, are characterized by uncertainty. Based on all of the aforementioned factors, this study established a multiobjective mathematical model, integrating the guided genetic algorithm (Guided-GA) and the nondominated sorting genetic algorithm II (NSGA-II), developed in previous studies, to improve the mechanisms of the algorithms, thereby increasing the efficiency of the model and quality of the solution. The mathematical model was used to address the problems of supplier selection, assembly sequence planning, assembly line balancing, and defect rate, to enable suppliers to respond rapidly to sales orders. The model was empirically tested using a case study, showing that it is suitable for assisting decision makers in planning production and conducting SS according to sales orders, enabling production activities to achieve maximum efficiency and the competitiveness of firms to improve.
    Print ISSN: 1024-123X
    Electronic ISSN: 1563-5147
    Topics: Mathematics , Technology
    Published by Hindawi
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  • 2
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    Minimization of the Total Traveling Distance and Maximum Distance by Using a Transformed-Based Encoding EDA to Solve the Multiple Traveling Salesmen Problem (2015)
    Hindawi
    Details
    Publication Date: 2015-09-18
    Description: Estimation of distribution algorithms (EDAs) have been used to solve numerous hard problems. However, their use with in-group optimization problems has not been discussed extensively in the literature. A well-known in-group optimization problem is the multiple traveling salesmen problem (mTSP), which involves simultaneous assignment and sequencing procedures and are shown in different forms. This paper presents a new algorithm, named , which is based on self-guided genetic algorithm with a minimum loading assignment (MLA) rule. This strategy uses the transformed-based encoding approach instead of direct encoding. The solution space of the proposed method is only . We compare the proposed algorithm against the optimal direct encoding technique, the two-part encoding genetic algorithm, and, in experiments on 34 TSP instances drawn from the TSPLIB, find that its solution space is . The scale of the experiments exceeded that presented in prior studies. The results show that the proposed algorithm was superior to the two-part encoding genetic algorithm in terms of minimizing the total traveling distance. Notably, the proposed algorithm did not cause a longer traveling distance when the number of salesmen was increased from 3 to 10. The results suggest that EDA researchers should employ the MLA rule instead of direct encoding in their proposed algorithms.
    Print ISSN: 1024-123X
    Electronic ISSN: 1563-5147
    Topics: Mathematics , Technology
    Published by Hindawi
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  • 3
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    Scheduling Problems with Due Date Assignment (2015)
    Hindawi
    Details
    Publication Date: 2015-04-13
    Print ISSN: 1026-0226
    Electronic ISSN: 1607-887X
    Topics: Mathematics
    Published by Hindawi
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  • 4
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    On exact forms of Taylor's theorem for vector-valued functions (2014)
    Oxford University Press
    Details
    Publication Date: 2014-11-25
    Description: Exact forms of Taylor expansion for vector-valued functions have been incorrectly used in many statistical publications. We offer two methods to correct this error.
    Print ISSN: 0006-3444
    Electronic ISSN: 1464-3510
    Topics: Biology , Mathematics , Medicine
    Published by Oxford University Press
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  • 5
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    Development and Analysis of Double-Faced Radial and Cluster-Arranged CMP Diamond Disk (2014)
    Hindawi
    Details
    Publication Date: 2014-09-01
    Description: In semiconductor manufacturing, diamond disks are indispensable for dressing chemical mechanical polishing (CMP) pads. Recently, 450 mm (18 inch) diameter wafers have been used to improve output and reduce wafer production cost. To polish 450 mm diameter wafers, the diameter of polishing pads must be increased to 1050 mm. In particular, because diamond disks are limited to 100 mm diameters, a much greater number of working crystals will be required for dressing a 1050 mm diameter pad. Consequently, new diamond disks must be developed. In this study, novel arrangements are made using a braze in diamond patterns, which are radial with a cluster arrangement of 3-4 grits per cluster. Furthermore, a double-faced combined diamond disk is developed. The polishing pad surface was characterized, and the effect of different diamond conditioners on wafer removal rate was studied. This research aims to develop a more suitable diamond disk for dressing 1050 mm diameter polishing pads.
    Print ISSN: 1024-123X
    Electronic ISSN: 1563-5147
    Topics: Mathematics , Technology
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  • 6
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    Stabilizing model predictive control of time-varying non-linear systems using linear matrix inequalities (2016)
    Oxford University Press
    Details
    Publication Date: 2016-03-17
    Description: The paper presents a stabilizing model predictive control (MPC) scheme for time-varying non-linear systems subject to input constraints. A state-feedback MPC law is computed by minimizing an upper bound of infinite horizon performance objective, which is formulated as a convex optimization involving linear matrix inequalities constraints. Time-varying linear dynamic approximation is used to derive the stability of the closed-loop system. In particular, a suboptimal algorithm of stabilizing MPC for time-varying non-linear systems is provided to decrease the online computation burden. The performance and effectiveness of the proposed approaches is illustrated by some comparisons with MPC algorithms based on linear polytopic descriptions.
    Print ISSN: 0265-0754
    Electronic ISSN: 1471-6887
    Topics: Mathematics
    Published by Oxford University Press
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  • 7
    Electronic Resource
    Electronic Resource
    A turbulence model with stochastic soliton motion (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 506-516 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A dissipative Benjamin–Ono equation is used to study fluid and plasma turbulence. The system is studied by an exact nonlinear mode truncation method in which a finite number of poles are used to present the solution. The justification of the pole expansion approach is discussed with the proof of a completeness theorem. The stability and spectrum analysis show that asymptotic behavior of the system is completely represented by a finite number of nonlinear modes. The behavior of those nonlinear modes resembles solitons, and exhibits a wide range of bifurcation phenomena and routes to turbulence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528884
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  • 8
    Electronic Resource
    Electronic Resource
    Symmetries and integrability of the cylindrical Korteweg–de Vries equation (1986)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 100-103 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The direct scheme to test integrability of a given nonlinear equation proposed by Chen, Lee, and Liu is tested on the cylindrical Korteweg–de Vries equation. The explicit dependence on t of this equation does not present any real difficulties. Constants of motion and symmetries are found readily and the Lax operators for the scattering problem constructed accordingly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527376
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  • 9
    Electronic Resource
    Electronic Resource
    On the integrability of multidimensional nonlinear evolution equations (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 347-350 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The integrability-test scheme of Chen, Lee, and Liu [H. H. Chen, Y. C. Lee, and C. S. Liu, Phys. Scr. 20, 490 (1979)] from one-space dimension to multispace dimensions is generalized. The temporal equation of the Lax pair is still the linearized perturbed equation that defines the symmetries. But the spectral operator in the Lax pair is no longer the linear recursion operator for symmetries. The absence of the linear recursion operator for symmetries in higher spatial dimensions therefore presents no direct obstacle to the Chen–Lee–Liu test scheme. The Kadomtsev–Petviashvili equation is shown as an example.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527665
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  • 10
    Electronic Resource
    Electronic Resource
    Basic adjoint relation for transient and stationary analysis of some Markovprocesses (1999)
    Springer
    Annals of operations research 87 (1999), S. 273-303 
    Details
    ISSN: 1572-9338
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The basic adjoint relation (BAR) was first introduced by Harrison and Williams [21,22] to characterize the stationary distribution of a diffusion process. Through simple examples, we show that this procedure can be used to characterize both the stationary and the transient distributions of a diffusion process, as well as other non‐diffusion Markov processes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018937103955
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