Symmetry considerations for topology design in the elastic inverse homogenization problem

PurposeThe purpose of this study is to solve the inverse homogenization problem, or so-called material design problem, using the topological derivative concept.Design/methodology/approachThe optimal topology is obtained through a relaxed formulation of the problem by replacing the characteristic function with a continuous design variable, so-called density variable. The constitutive tensor is then parametrized with the density variable through an analytical interpolation scheme that is based on the topological derivative concept. The intermediate values that may appear in the optimal topologies are removed by penalizing the perimeter functional.FindingsThe optimization process benefits from the intermediate values that provide the proposed method reaching to solutions that the topological derivative had not been able to find before. In addition, the presented theory opens the path to propose a new framework of research where the topological derivative uses classical optimization algorithms.Originality/valueThe proposed methodology allows us to use the topological derivative concept for solving the inverse homogenization problem and to fulfil the optimality conditions of the problem with the use of classical optimization algorithms. The authors solved several material design examples through a projected gradient algorithm to show the advantages of the proposed method.

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Performance Modeling and Analysis of WDM Optical Networks under Wavelength Continuity Constraint using MILP

Recent Advances in Electrical & Electronic Engineering (Formerly Recent Patents on Electrical & Electronic Engineering) ◽

10.2174/2352096512666190214105927 ◽

2020 ◽

Vol 13 (2) ◽

pp. 203-211 ◽

Cited By ~ 1

Author(s):

Swati Bhalaik ◽

Ashutosh Sharma ◽

Rajiv Kumar ◽

Neeru Sharma

Keyword(s):

Network Design ◽

Optical Networks ◽

Wavelength Division Multiplexing ◽

Optical Network ◽

Optimal Path ◽

Topology Design ◽

Mixed Integer ◽

Wdm Optical Networks ◽

Virtual Topology ◽

Wdm Network

Objective: Optical networks exploit the Wavelength Division Multiplexing (WDM) to meet the ever-growing bandwidth demands of upcoming communication applications. This is achieved by dividing the enormous transmission bandwidth of fiber into smaller communication channels. The major problem with WDM network design is to find an optimal path between two end users and allocate an available wavelength to the chosen path for the successful data transmission. Methods: This communication over a WDM network is carried out through lightpaths. The merging of all these lightpaths in an optical network generates a virtual topology which is suitable for the optimal network design to meet the increasing traffic demands. But, this virtual topology design is an NP-hard problem. This paper aims to explore Mixed Integer Linear Programming (MILP) framework to solve this design issue. Results: The comparative results of the proposed and existing mathematical models show that the proposed algorithm outperforms with the various performance parameters. Conclusion: Finally, it is concluded that network congestion is reduced marginally in the overall performance of the network.

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