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A Branch–Bound Cut Technique for Non-linear Fractional Multi-objective Optimization Problems

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Abstract

This article establishes a branch–bound technique to solve nonlinear convex–convex fractional multi-objective optimization problem in the non-convex feasible region. As far as the authors are concerned, this kind of problem is not solved by any other author in the literature. By transformation, multi-objective non-linear fractional problem is transformed into a multi-objective non-linear optimization problem. After giving preferences of weight to each objective, the original NLFMOOP is transformed into a nonlinear single-objective programming problem. Lagrange’s theorem of weak duality is used to find lower and upper bound for single objective nonlinear optimization problems in the feasible region. Some theoretical results for solving the multi-objective non-linear fractional problem have also been established. For showing the application of the proposed method, it has been applied to two numerical problems.

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Authors and Affiliations

  1. Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj, 211004, India

    Pitam Singh & Deepika Agarwal

  2. Department of Mathematics, Shyama Prasad Mukharji College, University of Delhi, New Delhi, India

    Deepak Bhati

  3. Department of Mathematics, University of Central Florida, Orlando, USA

    R. N. Mohapatra

Authors
  1. Pitam Singh
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  2. Deepika Agarwal
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  3. Deepak Bhati
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  4. R. N. Mohapatra
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Correspondence to Pitam Singh.

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Singh, P., Agarwal, D., Bhati, D. et al. A Branch–Bound Cut Technique for Non-linear Fractional Multi-objective Optimization Problems. Int. J. Appl. Comput. Math 6, 29 (2020). https://doi.org/10.1007/s40819-020-0771-3

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  • DOI: https://doi.org/10.1007/s40819-020-0771-3

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