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A Modified NSGA-II for Fuzzy Relational Multiobjective Optimization Problem

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Systems Thinking Approach for Social Problems

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 327))

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Abstract

This study presents a multiple objective optimization problem with the solution space designed by a system of fuzzy relational equations based on max-product algebraic composition. The solution set of the fuzzy relation equation is generally characterized by a unique maximal solution and finite number of minimal solutions and is non-convex by nature. Owing to the nature of feasible space, the traditional metaheuristics cannot be applied in their original form. To overcome this situation, a modified version of NSGA-II has been presented. The original NSGA-II has set standards in the area of multiobjective optimization in terms of efficiency. But in our case, the algorithm fails to give feasible solutions at the end. For this, the algorithm is modified to adapt the algorithm in our problem domain. The whole procedure is illustrated by some test problems.

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Acknowledgments

Authors are thankful to referees for their valuable suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Dayalbagh Educational Institute (Deemed University), Dayalbagh, Agra, India

    Garima Singh, Dhaneshwar Pandey & Antika Thapar

Authors
  1. Garima Singh
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  2. Dhaneshwar Pandey
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  3. Antika Thapar
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Corresponding author

Correspondence to Garima Singh .

Editor information

Editors and Affiliations

  1. Systems Science, Indian Institute of Technology Jodhpur, Jodhpur, Rajasthan, India

    Vivek Vijay

  2. Information and Communication Tech., Indian Institute of Technology Jodhpur, Jodhpur, Rajasthan, India

    Sandeep Kumar Yadav

  3. Systems Science, Indian Institute of Technology Jodhpur, Jodhpur, Rajasthan, India

    Bibhas Adhikari

  4. Systems Science, Indian Institute of Technology Jodhpur, Jodhpur, Rajasthan, India

    Harinipriya Seshadri

  5. Systems Science, Indian Institute of Technology Jodhpur, Jodhpur, Rajasthan, India

    Deepak Kumar Fulwani

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Singh, G., Pandey, D., Thapar, A. (2015). A Modified NSGA-II for Fuzzy Relational Multiobjective Optimization Problem. In: Vijay, V., Yadav, S., Adhikari, B., Seshadri, H., Fulwani, D. (eds) Systems Thinking Approach for Social Problems. Lecture Notes in Electrical Engineering, vol 327. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2141-8_4

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  • DOI: https://doi.org/10.1007/978-81-322-2141-8_4

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  • Publisher Name: Springer, New Delhi

  • Print ISBN: 978-81-322-2140-1

  • Online ISBN: 978-81-322-2141-8

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