Informatics Publishing Limited

M. R. Hassan ¹

Affiliations
1 Computer Science Branch, Department of Mathematics, Faculty of Science, Aswan University, Aswan, EG

Abstract

Evaluation of system reliability in stochastic flow networks under time constraints depends on the transmission time of minimal paths. The lead-time of a minimal path plays an important role in calculating the transmission time. Component assignments not only affect on the lead-time of a path but also the reliability value. Components assignment problem subject to total lead-time is never discussed. Thus, this paper focuses on solving this problem under total-lead time constraint, in which each component has an assignment lead-time. Subsequently an optimization method based on genetic algorithm is proposed to search the optimal components for a minimum total lead-time that maximizes the system reliability. The mathematical programming formulation for the assignment problem with optimal network reliability subject to total lead-time is formulated and solved by the presented genetic algorithm. The presented algorithm is applied on two given examples with different number of available components to assert its efficiency in solving the given assignment problem.

Keywords

Component Assignment Problem, Genetic Algorithm, Stochastic-Flow Network (SFN), System Reliability, Total Lead-Time

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M. R. Hassan ¹

Affiliations
1 Department of Mathematics, Faculty of Science, Aswan University, Computer Science Branch, Aswan – 81528, EG

Abstract

In this study, a new method is presented to evaluate the system reliability of a flow network using spanning trees with flow. The proposed method includes two main tasks: 1. Identifying the spanning trees without flow by representing each network link as a binary string of length N (N is the number of nodes) and performing all possible combinations between N − 1 links, and 2. Using the generated spanning trees without flow to find the spanning trees with flow by calculating the total flow carried by the links. The proposed method is tested on different examples from the literature to illustrate its efficiency in generating the spanning trees with flow and calculating the system reliability.

Keywords

Stochastic - flow Network, Spanning Tees, System Reliability

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M. R. Hassan ¹, B. Kumari ², B. K. Sharma ³, Md. Aminul Hassan ⁴, N. Aneja ⁵

Affiliations
1 P.G. Department of Mathematics, S. M. College, Bhagalpur-812001, IN
2 T. M. Bhagalpur University, Bhagalpur-812007, IN
3 Department of Mathematics, SBS College, University of Delhi, IN
4 GTE, Yeshwanthpur, Bangalore-560022, Karnataka, IN
5 University of Delhi, New Delhi, IN

Abstract

In the paper, we have discussed the effect of resonance in the motion of two symmetrical rods in the light of Hassan et al. (2016), Bhatnagar (1978) and Sharma et al. (2009). Here we have calculated variation in the Eulerian angels due to resonance in terms of orbital elements a, e, ω, τ and unperturbed Eulerian angels θ_A0, φ_A0, ψ_A0 and θ_B0, φ_B0, ψ_B0. We have also determined the amplitude and time period for the resonance 2:1.

Keywords

Resonance, Rigid Bodies, Eulerian Angles, Inertia Ellipsoid.

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M. R. Hassan ¹, H. Abdou ¹

Affiliations
1 Computer Science Branch, Department of Mathematics, Aswan University, Aswan, EG

Abstract

Objectives: The study aims to present a multi objective genetic algorithm in order to solve multi-objective components assignment problem subject to lead-time constraints. Methods/Statistical Analysis: The study has used non-dominated sorting genetic algorithm II to solve component assignment problems under total lead-time constraints and determine the most optimal solution characterized by a maximum reliability and minimum total lead-time. The proposed method is tested on different examples from the literature to illustrate its efficiency in comparison with a single genetic algorithm. Findings: The proposed algorithm succeeded in identifying the optimal solution to the presented problem in comparison with the single genetic algorithm without guessing or determining the initial value for the total lead-time. Moreover, similar observation was identified for the six-node network example. However, no comparison for TANET example was present because there is no literature dealt it for the presented problem. The proposed approach succeeded by obtaining the most optimal solution to the presented problem. Application/Improvements: With the help of proposed approach, the system reliability is maximized and total lead-time is minimized. Future researches may focus on other algorithms to improve the reliability and lead-time.

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