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Xing, W. and Wu, B. (2012) Homotopy Continuous Method for Weak Efficient Solution of Multiobjective Optimization Problem with Feasible Set Unbounded Condition. Applied Mathematics, 3, 765-771.
https://doi.org/10.4236/am.2012.37114

has been cited by the following article:

• TITLE: Lagrangian Relaxation Method for Multiobjective Optimization Methods: Solution Approaches

  AUTHORS: H. S. Faruque Alam

  KEYWORDS: Multiobjective Optimization Problem, Lagrangian Relaxation, Lagrange Multipliers, Scalarization Method

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.5, May 25, 2022

  ABSTRACT: This paper introduces the Lagrangian relaxation method to solve multiobjective optimization problems. It is often required to use the appropriate technique to determine the Lagrangian multipliers in the relaxation method that leads to finding the optimal solution to the problem. Our analysis aims to find a suitable technique to generate Lagrangian multipliers, and later these multipliers are used in the relaxation method to solve Multiobjective optimization problems. We propose a search-based technique to generate Lagrange multipliers. In our paper, we choose a suitable and well-known scalarization method that transforms the original multiobjective into a scalar objective optimization problem. Later, we solve this scalar objective problem using Lagrangian relaxation techniques. We use Brute force techniques to sort optimum solutions. Finally, we analyze the results, and efficient methods are recommended.